18-02-network-diffusion.ipynb

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    "\n",
    "\n",
    "# Simulating Network Diffusion With NDlib\n",
    "\n",
    " <span><img src=images/network11.png   align='center'/></span>\n",
    "\n",
    "\n",
    "\n",
    "[**NDlib**](https://ndlib.readthedocs.io/en/latest/overview.html) is a Python language software package for the describing, simulate, and study diffusion processes on complex networks."
   ]
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    "NDlib is built upon the `NetworkX ` python library and is intended to provide:\n",
    "\n",
    "- tools for the study diffusion dynamics on social, biological, and infrastructure networks,\n",
    "- a standard programming interface and diffusion models \n",
    "- implementation that is suitable for many applications,\n",
    "a rapid development environment for collaborative, multidisciplinary, projects."
   ]
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   "source": [
    "## The SI Model \n",
    "![image.png](images/network12.png)"
   ]
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    "$$\\frac{dS}{dt} = -\\beta S I$$\n",
    "\n",
    "$$\\frac{dI}{dt} = \\beta S I$$\n",
    "\n",
    "Given every individual in the system must be either susceptible or infected, $I + S = 1$. Thus, the equations above can be transformed to:\n",
    "\n",
    "$$\\frac{dI}{dt} = \\beta I (1-I)$$\n",
    "\n"
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   "source": [
    "To solve this differential equation, we can get the cumulative growth curve as a function of time:\n",
    "\n",
    "$$I_{t} = \\frac{x_0 e^{\\beta t}}{1-x_0 + x_0 e^{\\beta t}}$$\n",
    "\n",
    "Interestingly, this is a logistic growth featured by its S-shaped curve. The curve grows exponentially shortly after the system is infected, and then saturates as the number of susceptible shrinks which makes it harder to find the next victims. "
   ]
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      "text/latex": [
       "$\\displaystyle I{\\left(t \\right)} = \\frac{1}{C_{1} e^{- b t} + 1}$"
      ],
      "text/plain": [
       "Eq(I(t), 1/(C1*exp(-b*t) + 1))"
      ]
     },
     "execution_count": 65,
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   ],
   "source": [
    "from sympy import dsolve, Eq, symbols, Function\n",
    "\n",
    "t = symbols('t')\n",
    "b = symbols('b')\n",
    "I = symbols('I', cls=Function)\n",
    "deqn1 = Eq(I(t).diff(t), b*I(t)*(1 - I(t)))\n",
    "dsolve(deqn1, I(t))"
   ]
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   "source": [
    "import scipy.integrate as spi\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
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    "# Integrate a system of ordinary differential equations.\n",
    "# Solves the initial value problem for stiff or non-stiff systems\n",
    "# of first order ode-s::\n",
    "# dy/dt = func(y, t, ...)  [or func(t, y, ...)]\n",
    "spi.odeint?\n"
   ]
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    "# N为人群总数\n",
    "N = 10000\n",
    "# β为传染率系数\n",
    "beta = 0.25\n",
    "# I_0为感染者的初始人数\n",
    "I_0 = 1\n",
    "# S_0为易感者的初始人数\n",
    "S_0 = N - I_0\n",
    "# T为传播时间\n",
    "T = 150"
   ]
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   "source": [
    "def funcSI(inivalue,_):\n",
    "    # inivalue = (S_0,I_0)\n",
    "    Y = np.zeros(2)\n",
    "    X = inivalue\n",
    "    # 易感个体变化\n",
    "    Y[0] = - (beta * X[0] * X[1]) / N \n",
    "    # 感染个体变化\n",
    "    Y[1] = (beta * X[0] * X[1]) / N \n",
    "    return Y\n",
    "\n",
    "# INI为初始状态下的数组\n",
    "INI = (S_0,I_0)\n",
    "T_range = np.arange(0,T + 1)\n",
    "RES = spi.odeint(funcSI,INI,T_range)\n"
   ]
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     "text": [
      "Help on function odeint in module scipy.integrate.odepack:\n",
      "\n",
      "odeint(func, y0, t, args=(), Dfun=None, col_deriv=0, full_output=0, ml=None, mu=None, rtol=None, atol=None, tcrit=None, h0=0.0, hmax=0.0, hmin=0.0, ixpr=0, mxstep=0, mxhnil=0, mxordn=12, mxords=5, printmessg=0, tfirst=False)\n",
      "    Integrate a system of ordinary differential equations.\n",
      "    \n",
      "    .. note:: For new code, use `scipy.integrate.solve_ivp` to solve a\n",
      "              differential equation.\n",
      "    \n",
      "    Solve a system of ordinary differential equations using lsoda from the\n",
      "    FORTRAN library odepack.\n",
      "    \n",
      "    Solves the initial value problem for stiff or non-stiff systems\n",
      "    of first order ode-s::\n",
      "    \n",
      "        dy/dt = func(y, t, ...)  [or func(t, y, ...)]\n",
      "    \n",
      "    where y can be a vector.\n",
      "    \n",
      "    .. note:: By default, the required order of the first two arguments of\n",
      "              `func` are in the opposite order of the arguments in the system\n",
      "              definition function used by the `scipy.integrate.ode` class and\n",
      "              the function `scipy.integrate.solve_ivp`.  To use a function with\n",
      "              the signature ``func(t, y, ...)``, the argument `tfirst` must be\n",
      "              set to ``True``.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    func : callable(y, t, ...) or callable(t, y, ...)\n",
      "        Computes the derivative of y at t.\n",
      "        If the signature is ``callable(t, y, ...)``, then the argument\n",
      "        `tfirst` must be set ``True``.\n",
      "    y0 : array\n",
      "        Initial condition on y (can be a vector).\n",
      "    t : array\n",
      "        A sequence of time points for which to solve for y.  The initial\n",
      "        value point should be the first element of this sequence.\n",
      "        This sequence must be monotonically increasing or monotonically\n",
      "        decreasing; repeated values are allowed.\n",
      "    args : tuple, optional\n",
      "        Extra arguments to pass to function.\n",
      "    Dfun : callable(y, t, ...) or callable(t, y, ...)\n",
      "        Gradient (Jacobian) of `func`.\n",
      "        If the signature is ``callable(t, y, ...)``, then the argument\n",
      "        `tfirst` must be set ``True``.\n",
      "    col_deriv : bool, optional\n",
      "        True if `Dfun` defines derivatives down columns (faster),\n",
      "        otherwise `Dfun` should define derivatives across rows.\n",
      "    full_output : bool, optional\n",
      "        True if to return a dictionary of optional outputs as the second output\n",
      "    printmessg : bool, optional\n",
      "        Whether to print the convergence message\n",
      "    tfirst: bool, optional\n",
      "        If True, the first two arguments of `func` (and `Dfun`, if given)\n",
      "        must ``t, y`` instead of the default ``y, t``.\n",
      "    \n",
      "        .. versionadded:: 1.1.0\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    y : array, shape (len(t), len(y0))\n",
      "        Array containing the value of y for each desired time in t,\n",
      "        with the initial value `y0` in the first row.\n",
      "    infodict : dict, only returned if full_output == True\n",
      "        Dictionary containing additional output information\n",
      "    \n",
      "        =======  ============================================================\n",
      "        key      meaning\n",
      "        =======  ============================================================\n",
      "        'hu'     vector of step sizes successfully used for each time step.\n",
      "        'tcur'   vector with the value of t reached for each time step.\n",
      "                 (will always be at least as large as the input times).\n",
      "        'tolsf'  vector of tolerance scale factors, greater than 1.0,\n",
      "                 computed when a request for too much accuracy was detected.\n",
      "        'tsw'    value of t at the time of the last method switch\n",
      "                 (given for each time step)\n",
      "        'nst'    cumulative number of time steps\n",
      "        'nfe'    cumulative number of function evaluations for each time step\n",
      "        'nje'    cumulative number of jacobian evaluations for each time step\n",
      "        'nqu'    a vector of method orders for each successful step.\n",
      "        'imxer'  index of the component of largest magnitude in the\n",
      "                 weighted local error vector (e / ewt) on an error return, -1\n",
      "                 otherwise.\n",
      "        'lenrw'  the length of the double work array required.\n",
      "        'leniw'  the length of integer work array required.\n",
      "        'mused'  a vector of method indicators for each successful time step:\n",
      "                 1: adams (nonstiff), 2: bdf (stiff)\n",
      "        =======  ============================================================\n",
      "    \n",
      "    Other Parameters\n",
      "    ----------------\n",
      "    ml, mu : int, optional\n",
      "        If either of these are not None or non-negative, then the\n",
      "        Jacobian is assumed to be banded.  These give the number of\n",
      "        lower and upper non-zero diagonals in this banded matrix.\n",
      "        For the banded case, `Dfun` should return a matrix whose\n",
      "        rows contain the non-zero bands (starting with the lowest diagonal).\n",
      "        Thus, the return matrix `jac` from `Dfun` should have shape\n",
      "        ``(ml + mu + 1, len(y0))`` when ``ml >=0`` or ``mu >=0``.\n",
      "        The data in `jac` must be stored such that ``jac[i - j + mu, j]``\n",
      "        holds the derivative of the `i`th equation with respect to the `j`th\n",
      "        state variable.  If `col_deriv` is True, the transpose of this\n",
      "        `jac` must be returned.\n",
      "    rtol, atol : float, optional\n",
      "        The input parameters `rtol` and `atol` determine the error\n",
      "        control performed by the solver.  The solver will control the\n",
      "        vector, e, of estimated local errors in y, according to an\n",
      "        inequality of the form ``max-norm of (e / ewt) <= 1``,\n",
      "        where ewt is a vector of positive error weights computed as\n",
      "        ``ewt = rtol * abs(y) + atol``.\n",
      "        rtol and atol can be either vectors the same length as y or scalars.\n",
      "        Defaults to 1.49012e-8.\n",
      "    tcrit : ndarray, optional\n",
      "        Vector of critical points (e.g. singularities) where integration\n",
      "        care should be taken.\n",
      "    h0 : float, (0: solver-determined), optional\n",
      "        The step size to be attempted on the first step.\n",
      "    hmax : float, (0: solver-determined), optional\n",
      "        The maximum absolute step size allowed.\n",
      "    hmin : float, (0: solver-determined), optional\n",
      "        The minimum absolute step size allowed.\n",
      "    ixpr : bool, optional\n",
      "        Whether to generate extra printing at method switches.\n",
      "    mxstep : int, (0: solver-determined), optional\n",
      "        Maximum number of (internally defined) steps allowed for each\n",
      "        integration point in t.\n",
      "    mxhnil : int, (0: solver-determined), optional\n",
      "        Maximum number of messages printed.\n",
      "    mxordn : int, (0: solver-determined), optional\n",
      "        Maximum order to be allowed for the non-stiff (Adams) method.\n",
      "    mxords : int, (0: solver-determined), optional\n",
      "        Maximum order to be allowed for the stiff (BDF) method.\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    solve_ivp : Solve an initial value problem for a system of ODEs.\n",
      "    ode : a more object-oriented integrator based on VODE.\n",
      "    quad : for finding the area under a curve.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    The second order differential equation for the angle `theta` of a\n",
      "    pendulum acted on by gravity with friction can be written::\n",
      "    \n",
      "        theta''(t) + b*theta'(t) + c*sin(theta(t)) = 0\n",
      "    \n",
      "    where `b` and `c` are positive constants, and a prime (') denotes a\n",
      "    derivative.  To solve this equation with `odeint`, we must first convert\n",
      "    it to a system of first order equations.  By defining the angular\n",
      "    velocity ``omega(t) = theta'(t)``, we obtain the system::\n",
      "    \n",
      "        theta'(t) = omega(t)\n",
      "        omega'(t) = -b*omega(t) - c*sin(theta(t))\n",
      "    \n",
      "    Let `y` be the vector [`theta`, `omega`].  We implement this system\n",
      "    in python as:\n",
      "    \n",
      "    >>> def pend(y, t, b, c):\n",
      "    ...     theta, omega = y\n",
      "    ...     dydt = [omega, -b*omega - c*np.sin(theta)]\n",
      "    ...     return dydt\n",
      "    ...\n",
      "    \n",
      "    We assume the constants are `b` = 0.25 and `c` = 5.0:\n",
      "    \n",
      "    >>> b = 0.25\n",
      "    >>> c = 5.0\n",
      "    \n",
      "    For initial conditions, we assume the pendulum is nearly vertical\n",
      "    with `theta(0)` = `pi` - 0.1, and is initially at rest, so\n",
      "    `omega(0)` = 0.  Then the vector of initial conditions is\n",
      "    \n",
      "    >>> y0 = [np.pi - 0.1, 0.0]\n",
      "    \n",
      "    We will generate a solution at 101 evenly spaced samples in the interval\n",
      "    0 <= `t` <= 10.  So our array of times is:\n",
      "    \n",
      "    >>> t = np.linspace(0, 10, 101)\n",
      "    \n",
      "    Call `odeint` to generate the solution.  To pass the parameters\n",
      "    `b` and `c` to `pend`, we give them to `odeint` using the `args`\n",
      "    argument.\n",
      "    \n",
      "    >>> from scipy.integrate import odeint\n",
      "    >>> sol = odeint(pend, y0, t, args=(b, c))\n",
      "    \n",
      "    The solution is an array with shape (101, 2).  The first column\n",
      "    is `theta(t)`, and the second is `omega(t)`.  The following code\n",
      "    plots both components.\n",
      "    \n",
      "    >>> import matplotlib.pyplot as plt\n",
      "    >>> plt.plot(t, sol[:, 0], 'b', label='theta(t)')\n",
      "    >>> plt.plot(t, sol[:, 1], 'g', label='omega(t)')\n",
      "    >>> plt.legend(loc='best')\n",
      "    >>> plt.xlabel('t')\n",
      "    >>> plt.grid()\n",
      "    >>> plt.show()\n",
      "\n"
     ]
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   "source": [
    "help(spi.odeint)"
   ]
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       "(9999, 1)"
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    "INI"
   ]
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       "array([[9.99900000e+03, 1.00000000e+00],\n",
       "       [9.99871601e+03, 1.28398894e+00],\n",
       "       [9.99835139e+03, 1.64861432e+00]])"
      ]
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    "RES[:3]"
   ]
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(RES[:,0],color = 'darkblue',label = 'Susceptible',marker = '.')\n",
    "plt.plot(RES[:,1],color = 'red',label = 'Infection',marker = '.')\n",
    "plt.title('SI Model')\n",
    "plt.legend()\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The SIS Model\n",
    "\n",
    "Another extension of the SI model is the one that allows for reinfection. \n",
    "\n",
    "$$\\frac{dS}{dt} =\\gamma I -\\beta S I$$\n",
    "\n",
    "$$\\frac{dI}{dt} = \\beta S I - \\gamma I$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Given S + I = 1, the differential equations have the solution:\n",
    "\n",
    "$$I_t = (1- \\frac{\\gamma}{\\beta})\\frac{C e^{(\\beta-\\gamma)t}}{1+C e^{(\\beta-\\gamma)t}})$$\n",
    "\n",
    "The constant $C = \\frac{\\beta x_0}{\\beta - \\gamma - \\beta x_0}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:16:04.499760Z",
     "start_time": "2020-08-09T14:16:04.496209Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# N为人群总数\n",
    "N = 10000\n",
    "# β为传染率系数\n",
    "beta = 0.25\n",
    "# gamma为恢复率系数\n",
    "gamma = 0.05\n",
    "# I_0为感染者的初始人数\n",
    "I_0 = 1\n",
    "# S_0为易感者的初始人数\n",
    "S_0 = N - I_0\n",
    "# T为传播时间\n",
    "T = 150\n",
    "\n",
    "# INI为初始状态下的数组\n",
    "INI = (S_0,I_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:16:15.107356Z",
     "start_time": "2020-08-09T14:16:15.101237Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def funcSIS(inivalue,_):\n",
    "    Y = np.zeros(2)\n",
    "    X = inivalue\n",
    "    # 易感个体变化\n",
    "    Y[0] = - (beta * X[0]) / N * X[1] + gamma * X[1]\n",
    "    # 感染个体变化\n",
    "    Y[1] = (beta * X[0] * X[1]) / N - gamma * X[1]\n",
    "    return Y\n",
    "\n",
    "T_range = np.arange(0,T + 1)\n",
    "RES = spi.odeint(funcSIS,INI,T_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:16:19.031230Z",
     "start_time": "2020-08-09T14:16:18.885711Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(RES[:,0],color = 'darkblue',label = 'Susceptible',marker = '.')\n",
    "plt.plot(RES[:,1],color = 'red',label = 'Infection',marker = '.')\n",
    "plt.title('SIS Model')\n",
    "plt.legend()\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The SIR Model \n",
    "\n",
    "For many diseases, there is usually a status of recovery denoted by $R$. Let $\\gamma$ denote the removal or recovery rate.\n",
    "\n",
    "![image.png](images/network13.png)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\frac{dS}{dt} = -\\beta S I$$\n",
    "\n",
    "$$\\frac{dI}{dt} = \\beta S I - \\gamma I$$\n",
    "\n",
    "$$\\frac{dR}{dt} =  \\gamma I$$\n",
    "\n",
    "However, the differential equations above could not be analytically solved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:19:30.553939Z",
     "start_time": "2020-08-09T14:19:30.550630Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# N为人群总数\n",
    "N = 10000\n",
    "# β为传染率系数\n",
    "beta = 0.25\n",
    "# gamma为恢复率系数\n",
    "gamma = 0.05\n",
    "# I_0为感染者的初始人数\n",
    "I_0 = 1\n",
    "# R_0为治愈者的初始人数\n",
    "R_0 = 0\n",
    "# S_0为易感者的初始人数\n",
    "S_0 = N - I_0 - R_0\n",
    "# T为传播时间\n",
    "T = 150\n",
    "\n",
    "# INI为初始状态下的数组\n",
    "INI = (S_0,I_0,R_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:20:08.030424Z",
     "start_time": "2020-08-09T14:20:08.023773Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def funcSIR(inivalue,_):\n",
    "    Y = np.zeros(3)\n",
    "    X = inivalue\n",
    "    # 易感个体变化\n",
    "    Y[0] = - (beta * X[0] * X[1]) / N\n",
    "    # 感染个体变化\n",
    "    Y[1] = (beta * X[0] * X[1]) / N - gamma * X[1]\n",
    "    # 治愈个体变化\n",
    "    Y[2] = gamma * X[1]\n",
    "    return Y\n",
    "\n",
    "T_range = np.arange(0,T + 1)\n",
    "RES = spi.odeint(funcSIR,INI,T_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:20:09.287480Z",
     "start_time": "2020-08-09T14:20:09.071396Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(RES[:,0],color = 'darkblue',label = 'Susceptible',marker = '.')\n",
    "plt.plot(RES[:,1],color = 'red',label = 'Infection',marker = '.')\n",
    "plt.plot(RES[:,2],color = 'green',label = 'Recovery',marker = '.')\n",
    "plt.title('SIR Model')\n",
    "plt.legend()\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The SEIR Model\n",
    "\n",
    "![image.png](images/network14.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:22:27.630910Z",
     "start_time": "2020-08-09T14:22:27.627428Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# N为人群总数\n",
    "N = 10000\n",
    "# β为传染率系数\n",
    "beta = 0.6\n",
    "# gamma为恢复率系数\n",
    "gamma = 0.1\n",
    "# Te为疾病潜伏期\n",
    "Te = 14\n",
    "# I_0为感染者的初始人数\n",
    "I_0 = 1\n",
    "# E_0为潜伏者的初始人数\n",
    "E_0 = 0\n",
    "# R_0为治愈者的初始人数\n",
    "R_0 = 0\n",
    "# S_0为易感者的初始人数\n",
    "S_0 = N - I_0 - E_0 - R_0\n",
    "# T为传播时间\n",
    "T = 150"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:24:35.358335Z",
     "start_time": "2020-08-09T14:24:35.350771Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# INI为初始状态下的数组\n",
    "INI = (S_0,E_0,I_0,R_0)\n",
    "def funcSEIR(inivalue,_):\n",
    "    Y = np.zeros(4)\n",
    "    X = inivalue\n",
    "    # 易感个体变化\n",
    "    Y[0] = - (beta * X[0] * X[2]) / N\n",
    "    # 潜伏个体变化\n",
    "    Y[1] = (beta * X[0] * X[2]) / N - X[1] / Te\n",
    "    # 感染个体变化\n",
    "    Y[2] = X[1] / Te - gamma * X[2]\n",
    "    # 治愈个体变化\n",
    "    Y[3] = gamma * X[2]\n",
    "    return Y\n",
    "\n",
    "T_range = np.arange(0,T + 1)\n",
    "RES = spi.odeint(funcSEIR,INI,T_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:24:49.180925Z",
     "start_time": "2020-08-09T14:24:49.013897Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(RES[:,0],color = 'darkblue',label = 'Susceptible',marker = '.')\n",
    "plt.plot(RES[:,1],color = 'orange',label = 'Exposed',marker = '.')\n",
    "plt.plot(RES[:,2],color = 'red',label = 'Infection',marker = '.')\n",
    "plt.plot(RES[:,3],color = 'green',label = 'Recovery',marker = '.')\n",
    "\n",
    "plt.title('SEIR Model')\n",
    "plt.legend()\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## The SEIRS Model\n",
    "\n",
    "![image.png](images/network15.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:31:48.957681Z",
     "start_time": "2020-08-09T14:31:48.953611Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# N为人群总数\n",
    "N = 10000\n",
    "# β为传染率系数\n",
    "beta = 0.6\n",
    "# gamma为恢复率系数\n",
    "gamma = 0.1\n",
    "# Ts为抗体持续时间\n",
    "Ts = 7\n",
    "# Te为疾病潜伏期\n",
    "Te = 14\n",
    "# I_0为感染者的初始人数\n",
    "I_0 = 1\n",
    "# E_0为潜伏者的初始人数\n",
    "E_0 = 0\n",
    "# R_0为治愈者的初始人数\n",
    "R_0 = 0\n",
    "# S_0为易感者的初始人数\n",
    "S_0 = N - I_0 - E_0 - R_0\n",
    "# T为传播时间\n",
    "T = 150"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:31:58.488415Z",
     "start_time": "2020-08-09T14:31:58.480604Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# INI为初始状态下的数组\n",
    "INI = (S_0,E_0,I_0,R_0)\n",
    "\n",
    "\n",
    "def funcSEIRS(inivalue,_):\n",
    "    Y = np.zeros(4)\n",
    "    X = inivalue\n",
    "    # 易感个体变化\n",
    "    Y[0] = - (beta * X[0] * X[2]) / N + X[3] / Ts\n",
    "    # 潜伏个体变化\n",
    "    Y[1] = (beta * X[0] * X[2]) / N - X[1] / Te\n",
    "    # 感染个体变化\n",
    "    Y[2] = X[1] / Te - gamma * X[2]\n",
    "    # 治愈个体变化\n",
    "    Y[3] = gamma * X[2] - X[3] / Ts\n",
    "    return Y\n",
    "\n",
    "T_range = np.arange(0,T + 1)\n",
    "\n",
    "RES = spi.odeint(funcSEIRS,INI,T_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T14:32:07.766740Z",
     "start_time": "2020-08-09T14:32:07.600407Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(RES[:,0],color = 'darkblue',label = 'Susceptible',marker = '.')\n",
    "plt.plot(RES[:,1],color = 'orange',label = 'Exposed',marker = '.')\n",
    "plt.plot(RES[:,2],color = 'red',label = 'Infection',marker = '.')\n",
    "plt.plot(RES[:,3],color = 'green',label = 'Recovery',marker = '.')\n",
    "\n",
    "plt.title('SEIRS Model')\n",
    "plt.legend()\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T16:23:31.758533Z",
     "start_time": "2020-08-09T16:23:30.852257Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://zhuanlan.zhihu.com/p/115869172\n",
    "import scipy.integrate as spi\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# N为人群总数\n",
    "N =11000000\n",
    "# β为传染率系数\n",
    "beta = 0.01\n",
    "# gamma为恢复率系数\n",
    "gamma = 0.1\n",
    "#δ为受到治疗系数\n",
    "δ = 0.3\n",
    "# Te为疾病潜伏期\n",
    "Te = 5\n",
    "# I_0为感染未住院的初始人数\n",
    "I_0 = 4058\n",
    "# E_0为潜伏者的初始人数\n",
    "E_0 = 3178\n",
    "# R_0为治愈者的初始人数\n",
    "R_0 = 91750\n",
    "#T_0为治疗中的初始人数\n",
    "T_0 = 53941\n",
    "# S_0为易感者的初始人数\n",
    "S_0 = N - I_0 - E_0 - R_0 - T_0\n",
    "# T为传播时间\n",
    "T = 100\n",
    "\n",
    "# INI为初始状态下的数组\n",
    "INI = (S_0,E_0,I_0,R_0,T_0)\n",
    "\n",
    "def funcSEIR(inivalue,_):\n",
    "    Y = np.zeros(5)\n",
    "    X = inivalue\n",
    "    # 易感个体变化\n",
    "    Y[0] = - (beta * X[0] *( X[2]+X[1])) / N\n",
    "    # 潜伏个体变化\n",
    "    Y[1] = (beta * X[0] *( X[2]+X[1])) / N - X[1] / Te\n",
    "    # 感染未住院\n",
    "    Y[2] = X[1] / Te - δ * X[2]\n",
    "    # 治愈个体变化\n",
    "    Y[3] = gamma * X[4]\n",
    "    #治疗中个体变化\n",
    "    Y[4] = δ* X[2] - gamma* X[4]\n",
    "    return Y\n",
    "\n",
    "T_range = np.arange(0,T + 1)\n",
    "\n",
    "RES = spi.odeint(funcSEIR,INI,T_range)\n",
    "\n",
    "\n",
    "plt.figure(figsize = [8, 8])\n",
    "\n",
    "plt.subplot(221)\n",
    "plt.plot(RES[:,0],color = 'darkblue',label = 'Susceptible',marker = '.')\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.legend()\n",
    "plt.title('“SEITR” Model')\n",
    "\n",
    "plt.subplot(222)\n",
    "plt.plot(RES[:,1],color = 'orange',label = 'Exposed',marker = '.')\n",
    "plt.legend()\n",
    "plt.subplot(223)\n",
    "plt.plot(RES[:,2],color = 'red',label = 'Infection',marker = '.')\n",
    "plt.legend()\n",
    "plt.subplot(224)\n",
    "plt.plot(RES[:,3],color = 'green',label = 'Recovery',marker = '.')\n",
    "plt.plot(RES[:,4],color = 'purple',label = 'Under Treatment',marker = '.')\n",
    "plt.legend()\n",
    "\n",
    "\n",
    "plt.xlabel('Day')\n",
    "plt.ylabel('Number')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Install"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:08:23.554793Z",
     "start_time": "2020-08-02T06:08:21.633737Z"
    },
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: ndlib in /opt/anaconda3/lib/python3.7/site-packages (5.0.2)\n",
      "Requirement already satisfied: python-igraph in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (0.8.2)\n",
      "Requirement already satisfied: bokeh in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (1.4.0)\n",
      "Requirement already satisfied: netdispatch in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (0.0.5)\n",
      "Requirement already satisfied: numpy in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (1.18.1)\n",
      "Requirement already satisfied: dynetx in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (0.2.3)\n",
      "Requirement already satisfied: scipy in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (1.4.1)\n",
      "Requirement already satisfied: networkx in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (2.4)\n",
      "Requirement already satisfied: future in /opt/anaconda3/lib/python3.7/site-packages (from ndlib) (0.18.2)\n",
      "Requirement already satisfied: texttable>=1.6.2 in /opt/anaconda3/lib/python3.7/site-packages (from python-igraph->ndlib) (1.6.2)\n",
      "Requirement already satisfied: Jinja2>=2.7 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (2.11.1)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (2.8.1)\n",
      "Requirement already satisfied: tornado>=4.3 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (6.0.3)\n",
      "Requirement already satisfied: pillow>=4.0 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (7.0.0)\n",
      "Requirement already satisfied: packaging>=16.8 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (20.1)\n",
      "Requirement already satisfied: six>=1.5.2 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (1.14.0)\n",
      "Requirement already satisfied: PyYAML>=3.10 in /opt/anaconda3/lib/python3.7/site-packages (from bokeh->ndlib) (5.3)\n",
      "Requirement already satisfied: decorator>=4.3.0 in /opt/anaconda3/lib/python3.7/site-packages (from networkx->ndlib) (4.4.1)\n",
      "Requirement already satisfied: MarkupSafe>=0.23 in /opt/anaconda3/lib/python3.7/site-packages (from Jinja2>=2.7->bokeh->ndlib) (1.1.1)\n",
      "Requirement already satisfied: pyparsing>=2.0.2 in /opt/anaconda3/lib/python3.7/site-packages (from packaging>=16.8->bokeh->ndlib) (2.4.6)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install ndlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Tutorial\n",
    "https://ndlib.readthedocs.io/en/latest/tutorial.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:46:43.874822Z",
     "start_time": "2020-08-09T13:46:41.520212Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import ndlib.models.epidemics as ep\n",
    "import ndlib.models.ModelConfig as mc\n",
    "from bokeh.io import output_notebook, show\n",
    "from ndlib.viz.bokeh.DiffusionTrend import DiffusionTrend\n",
    "from ndlib.viz.bokeh.DiffusionPrevalence import DiffusionPrevalence\n",
    "from ndlib.viz.bokeh.MultiPlot import MultiPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<span><img src=images/network16.png   width = '400px' align='center'/></span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:26:41.325317Z",
     "start_time": "2020-08-02T06:26:41.193007Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Network Definition\n",
    "g = nx.erdos_renyi_graph(1000, 0.1)\n",
    "\n",
    "# Model Selection\n",
    "model = ep.SIRModel(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:26:41.828440Z",
     "start_time": "2020-08-02T06:26:41.823839Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Model Configuration\n",
    "config = mc.Configuration()\n",
    "config.add_model_parameter('beta', 0.001)\n",
    "config.add_model_parameter('gamma', 0.01)\n",
    "config.add_model_parameter(\"fraction_infected\", 0.05)\n",
    "model.set_initial_status(config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:26:43.626868Z",
     "start_time": "2020-08-02T06:26:42.529407Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 183.84it/s]\n"
     ]
    }
   ],
   "source": [
    "# Simulation\n",
    "iterations = model.iteration_bunch(200)\n",
    "trends = model.build_trends(iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:28:14.860343Z",
     "start_time": "2020-08-02T06:28:14.785328Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
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       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
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       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
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       "    if (js_urls == null || js_urls.length === 0) {\n",
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       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
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       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
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       "\n",
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       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
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       "\n",
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       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1238\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1238\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1238' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1238\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"d6149ac4-a504-48e8-8ade-1ea33558fcae\" data-root-id=\"1239\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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- Diffusion Trend\"},\"id\":\"1277\",\"type\":\"Title\"},{\"attributes\":{\"items\":[{\"id\":\"1284\",\"type\":\"LegendItem\"},{\"id\":\"1299\",\"type\":\"LegendItem\"},{\"id\":\"1316\",\"type\":\"LegendItem\"}],\"orientation\":\"horizontal\"},\"id\":\"1283\",\"type\":\"Legend\"}],\"root_ids\":[\"1239\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
       "  var render_items = [{\"docid\":\"727eaad6-6f39-46a6-a367-58febb95a457\",\"roots\":{\"1239\":\"d6149ac4-a504-48e8-8ade-1ea33558fcae\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
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       "id": "1239"
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook() # show bokeh in notebook\n",
    "viz = DiffusionTrend(model, trends)\n",
    "p = viz.plot(width=400, height=400)\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    "ExecuteTime": {
     "end_time": "2020-08-02T06:28:18.713916Z",
     "start_time": "2020-08-02T06:28:18.656586Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
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       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
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      "application/vnd.bokehjs_exec.v0+json": ""
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     "output_type": "display_data"
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   ],
   "source": [
    "viz2 = DiffusionPrevalence(model, trends)\n",
    "p2 = viz2.plot(width=400, height=400)\n",
    "show(p2)"
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  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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       "  <div class=\"bk-root\" id=\"82dc4cc9-b767-4782-a768-de742e57619e\" data-root-id=\"1625\"></div>\n"
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    "vm = MultiPlot()\n",
    "vm.add_plot(p)\n",
    "vm.add_plot(p2)\n",
    "m = vm.plot()\n",
    "show(m)"
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   "source": [
    "### Kertesz Threshold model\n",
    "\n",
    "The Kertesz Threshold model was introduced in 2015 by `Ruan` et al. [1] and it is an extension of the Watts threshold model [2].\n",
    "\n",
    "We set the initial infected as well blocked node sets equals to the 10% of the overall population, assign a threshold of 0.25 to all the nodes and impose an probability of spontaneous adoptions of 40%.\n",
    "\n",
    "- [1]\tZ. Ruan, G. In ̃iguez, M. Karsai, and J. Kertész, “Kinetics of social contagion,” Phys. Rev. Lett., vol. 115, p. 218702, Nov 2015.\n",
    "- [2]\tD.J. Watts, “A simple model of global cascades on random networks,” Proceedings of the National Academy of Sciences, vol. 99, no. 9, pp. 5766–5771, 2002."
   ]
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    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 207.32it/s]\n"
     ]
    }
   ],
   "source": [
    "# Network topology\n",
    "g = nx.erdos_renyi_graph(1000, 0.1)\n",
    "\n",
    "# Model selection\n",
    "th_model = ep.KerteszThresholdModel(g)\n",
    "\n",
    "# Model Configuration\n",
    "config = mc.Configuration()\n",
    "config.add_model_parameter('adopter_rate', 0.4)\n",
    "config.add_model_parameter('percentage_blocked', 0.1)\n",
    "config.add_model_parameter('fraction_infected', 0.1)\n",
    "\n",
    "# Setting node parameters\n",
    "threshold = 0.25\n",
    "for i in g.nodes():\n",
    "    config.add_node_configuration(\"threshold\", i, threshold)\n",
    "\n",
    "th_model.set_initial_status(config)\n",
    "\n",
    "# Simulation execution\n",
    "iterations = th_model.iteration_bunch(200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:43:42.346680Z",
     "start_time": "2020-08-02T06:43:42.248361Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"2455\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"2455\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"2455\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2455' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"2455\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"2455\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"2455\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '2455' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"2455\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"0c599d0f-d482-4756-86d4-7fd57c14674a\" data-root-id=\"2456\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Application\",\"version\":\"1.4.0\"}};\n",
       "  var render_items = [{\"docid\":\"d0e616ad-7803-47b8-8f80-60c240c64391\",\"roots\":{\"2456\":\"0c599d0f-d482-4756-86d4-7fd57c14674a\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2456"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook() # show bokeh in notebook\n",
    "\n",
    "trends = th_model.build_trends(iterations)\n",
    "\n",
    "viz = DiffusionTrend(th_model, trends)\n",
    "p = viz.plot(width=400, height=400)\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-02T06:44:51.346018Z",
     "start_time": "2020-08-02T06:44:51.263002Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"8f6f8a05-7834-4101-952c-92cb4ab0e166\" data-root-id=\"2725\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
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       "  function embed_document(root) {\n",
       "    \n",
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   "source": [
    "viz2 = DiffusionPrevalence(th_model, trends)\n",
    "p2 = viz2.plot(width=400, height=400)\n",
    "show(p2)"
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   "source": [
    "### Model Comparisions"
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  },
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   "outputs": [
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 149.48it/s]\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "100%|██████████| 200/200 [00:01<00:00, 198.91it/s]\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "100%|██████████| 60/60 [00:00<00:00, 94.43it/s] \n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
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       "id": "2076"
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   "source": [
    "# model comparisions\n",
    "vm = MultiPlot()\n",
    "vm.add_plot(p)\n",
    "\n",
    "# SIS\n",
    "sis_model = ep.SISModel(g)\n",
    "config = mc.Configuration()\n",
    "config.add_model_parameter('beta', 0.001)\n",
    "config.add_model_parameter('lambda', 0.01)\n",
    "config.add_model_parameter(\"fraction_infected\", 0.05)\n",
    "sis_model.set_initial_status(config)\n",
    "iterations = sis_model.iteration_bunch(200)\n",
    "trends = sis_model.build_trends(iterations)\n",
    "\n",
    "viz = DiffusionTrend(sis_model, trends)\n",
    "p3 = viz.plot(width=400, height=400)\n",
    "vm.add_plot(p3)\n",
    "\n",
    "# SI\n",
    "si_model = ep.SIModel(g)\n",
    "config = mc.Configuration()\n",
    "config.add_model_parameter('beta', 0.001)\n",
    "config.add_model_parameter(\"fraction_infected\", 0.05)\n",
    "si_model.set_initial_status(config)\n",
    "iterations = si_model.iteration_bunch(200)\n",
    "trends = si_model.build_trends(iterations)\n",
    "\n",
    "viz = DiffusionTrend(si_model, trends)\n",
    "p4 = viz.plot(width=400, height=400)\n",
    "vm.add_plot(p4)\n",
    "\n",
    "# Threshold\n",
    "th_model = ep.ThresholdModel(g)\n",
    "config = mc.Configuration()\n",
    "\n",
    "# Set individual node threshold\n",
    "threshold = 0.40\n",
    "for n in g.nodes():\n",
    "    config.add_node_configuration(\"threshold\", n, threshold)\n",
    "\n",
    "config.add_model_parameter(\"fraction_infected\", 0.30)\n",
    "th_model.set_initial_status(config)\n",
    "iterations = th_model.iteration_bunch(60)\n",
    "trends = th_model.build_trends(iterations)\n",
    "\n",
    "viz = DiffusionTrend(th_model, trends)\n",
    "p5 = viz.plot(width=400, height=400)\n",
    "vm.add_plot(p5)\n",
    "\n",
    "m = vm.plot()\n",
    "show(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Threshold model\n",
    "The threshold model was introduced in 1978 by Granovetter [1]. A node has two distinct and mutually exclusive behavioral alternatives, e.g., the decision to do or not do something. Individual decision depends on the percentage of `its neighbors` have made the same choice, thus imposing a threshold.\n",
    "- each node has its own threshold; \n",
    "- during a generic iteration every node is observed: \n",
    "    - if the percentage of its infected neighbors is grater than its threshold it becomes infected as well.\n",
    "    \n",
    "Granovetter, “Threshold models of collective behavior,” The American Journal of Sociology, vol. 83, no. 6, pp. 1420–1443, 1978."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![image.png](images/network17.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![image.png](images/network18.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![image.png](images/network19.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![image.png](images/network20.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:57:14.012917Z",
     "start_time": "2020-08-09T13:57:14.007801Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import ndlib.models.ModelConfig as mc\n",
    "import ndlib.models.epidemics as ep\n",
    "\n",
    "def watts_model_ba_network(m, threshold, fraction_infected, iteration_num):\n",
    "    # change these two parameters\n",
    "    # num_neighbors = 1\n",
    "    # threshold = 0.5\n",
    "    # fraction_infected = 0.1\n",
    "    # iteration_num = 30\n",
    "\n",
    "    # Network topology\n",
    "    #g = nx.erdos_renyi_graph(1000, 0.1)\n",
    "    g = nx.barabasi_albert_graph(1000, m)\n",
    "    # Model selection\n",
    "    model = ep.ThresholdModel(g)\n",
    "    # Model Configuration\n",
    "    config = mc.Configuration()\n",
    "    config.add_model_parameter('fraction_infected', fraction_infected)\n",
    "    # Setting node parameters\n",
    "    for i in g.nodes():\n",
    "        config.add_node_configuration(\"threshold\", i, threshold)\n",
    "\n",
    "    model.set_initial_status(config)\n",
    "    # Simulation execution\n",
    "    iterations = model.iteration_bunch(iteration_num)\n",
    "    return model, iterations\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:55:31.615421Z",
     "start_time": "2020-08-09T13:55:31.611095Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_diffusion(model, iterations):\n",
    "    output_notebook() # show bokeh in notebook\n",
    "    trends = model.build_trends(iterations)\n",
    "    viz = DiffusionTrend(model, trends)\n",
    "    p = viz.plot(width=400, height=400)\n",
    "\n",
    "    viz2 = DiffusionPrevalence(model, trends)\n",
    "    p2 = viz2.plot(width=400, height=400)\n",
    "\n",
    "    vm = MultiPlot()\n",
    "    vm.add_plot(p)\n",
    "    vm.add_plot(p2)\n",
    "    m = vm.plot()\n",
    "    show(m)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:57:20.240542Z",
     "start_time": "2020-08-09T13:57:20.024662Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 30/30 [00:00<00:00, 465.02it/s]\n"
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       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"3185\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"3185\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '3185' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"3185\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"3185\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"3185\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '3185' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"3185\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"274e15de-82fe-4266-84ed-57cd31cb1507\" data-root-id=\"3339\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = {\"e784d739-8e4b-4904-aa67-67cce5637a1f\":{\"roots\":{\"references\":[{\"attributes\":{\"children\":[{\"id\":\"3338\",\"type\":\"ToolbarBox\"},{\"id\":\"3336\",\"type\":\"GridBox\"}]},\"id\":\"3339\",\"type\":\"Column\"},{\"attributes\":{\"align\":\"center\",\"text\":\"fraction infected: 0.1\"},\"id\":\"3248\",\"type\":\"Title\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3297\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"3254\",\"type\":\"LinearScale\"},{\"attributes\":{\"data_source\":{\"id\":\"3295\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3296\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3297\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3299\",\"type\":\"CDSView\"}},\"id\":\"3298\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"callback\":null},\"id\":\"3252\",\"type\":\"DataRange1d\"},{\"attributes\":{\"source\":{\"id\":\"3295\",\"type\":\"ColumnDataSource\"}},\"id\":\"3299\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3307\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"3256\",\"type\":\"LinearScale\"},{\"attributes\":{\"label\":{\"value\":\"Infected\"},\"renderers\":[{\"id\":\"3298\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3309\",\"type\":\"LegendItem\"},{\"attributes\":{\"data_source\":{\"id\":\"3218\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3219\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3220\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3222\",\"type\":\"CDSView\"}},\"id\":\"3221\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"axis_label\":\"Iterations\",\"formatter\":{\"id\":\"3289\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3259\",\"type\":\"BasicTicker\"}},\"id\":\"3258\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"3205\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"3264\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"3320\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"tools\":[{\"id\":\"3205\",\"type\":\"PanTool\"},{\"id\":\"3206\",\"type\":\"WheelZoomTool\"},{\"id\":\"3207\",\"type\":\"BoxZoomTool\"},{\"id\":\"3208\",\"type\":\"SaveTool\"},{\"id\":\"3209\",\"type\":\"ResetTool\"},{\"id\":\"3210\",\"type\":\"HelpTool\"},{\"id\":\"3268\",\"type\":\"PanTool\"},{\"id\":\"3269\",\"type\":\"WheelZoomTool\"},{\"id\":\"3270\",\"type\":\"BoxZoomTool\"},{\"id\":\"3271\",\"type\":\"SaveTool\"},{\"id\":\"3272\",\"type\":\"ResetTool\"},{\"id\":\"3273\",\"type\":\"HelpTool\"}]},\"id\":\"3337\",\"type\":\"ProxyToolbar\"},{\"attributes\":{},\"id\":\"3206\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"3259\",\"type\":\"BasicTicker\"},{\"attributes\":{\"children\":[[{\"id\":\"3186\",\"subtype\":\"Figure\",\"type\":\"Plot\"},0,0],[{\"id\":\"3249\",\"subtype\":\"Figure\",\"type\":\"Plot\"},0,1]]},\"id\":\"3336\",\"type\":\"GridBox\"},{\"attributes\":{\"align\":\"center\",\"text\":\"fraction infected: 0.1\"},\"id\":\"3311\",\"type\":\"Title\"},{\"attributes\":{\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3259\",\"type\":\"BasicTicker\"}},\"id\":\"3262\",\"type\":\"Grid\"},{\"attributes\":{\"toolbar\":{\"id\":\"3337\",\"type\":\"ProxyToolbar\"},\"toolbar_location\":\"above\"},\"id\":\"3338\",\"type\":\"ToolbarBox\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"3205\",\"type\":\"PanTool\"},{\"id\":\"3206\",\"type\":\"WheelZoomTool\"},{\"id\":\"3207\",\"type\":\"BoxZoomTool\"},{\"id\":\"3208\",\"type\":\"SaveTool\"},{\"id\":\"3209\",\"type\":\"ResetTool\"},{\"id\":\"3210\",\"type\":\"HelpTool\"}]},\"id\":\"3211\",\"type\":\"Toolbar\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3283\",\"type\":\"Line\"},{\"attributes\":{\"overlay\":{\"id\":\"3229\",\"type\":\"BoxAnnotation\"}},\"id\":\"3207\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"dimension\":1,\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3264\",\"type\":\"BasicTicker\"}},\"id\":\"3267\",\"type\":\"Grid\"},{\"attributes\":{\"axis_label\":\"#Delta 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- Prevalence\"},\"id\":\"3287\",\"type\":\"Title\"},{\"attributes\":{\"items\":[{\"id\":\"3294\",\"type\":\"LegendItem\"},{\"id\":\"3309\",\"type\":\"LegendItem\"}],\"orientation\":\"horizontal\"},\"id\":\"3293\",\"type\":\"Legend\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#aec7e8\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3233\",\"type\":\"Line\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"mpmZmZmZuT9SuB6F61HIP4XrUbgehcs/KVyPwvUozD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/0SLb+X5qzD/RItv5fmrMP9Ei2/l+asw/\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3321\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3320\",\"type\":\"UnionRenderers\"}},\"id\":\"3232\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3282\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3234\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"3281\",\"type\":\"ColumnDataSource\"}},\"id\":\"3285\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3289\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"below\":[{\"id\":\"3258\",\"type\":\"LinearAxis\"},{\"id\":\"3311\",\"type\":\"Title\"}],\"center\":[{\"id\":\"3262\",\"type\":\"Grid\"},{\"id\":\"3267\",\"type\":\"Grid\"},{\"id\":\"3293\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"3263\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"plot_width\":400,\"renderers\":[{\"id\":\"3284\",\"type\":\"GlyphRenderer\"},{\"id\":\"3298\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"3287\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"3274\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"3250\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"3254\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"3252\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"3256\",\"type\":\"LinearScale\"}},\"id\":\"3249\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"3292\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"data_source\":{\"id\":\"3232\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3233\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3234\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3236\",\"type\":\"CDSView\"}},\"id\":\"3235\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"3291\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"source\":{\"id\":\"3232\",\"type\":\"ColumnDataSource\"}},\"id\":\"3236\",\"type\":\"CDSView\"},{\"attributes\":{\"label\":{\"value\":\"Susceptible\"},\"renderers\":[{\"id\":\"3284\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3294\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"3243\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"callback\":null},\"id\":\"3189\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"3332\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"label\":{\"value\":\"Infected\"},\"renderers\":[{\"id\":\"3235\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3246\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"3306\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#aec7e8\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3296\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"3244\",\"type\":\"Selection\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAIBWQAAAAAAAADlAAAAAAAAAFEAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3333\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3332\",\"type\":\"UnionRenderers\"}},\"id\":\"3295\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"axis_label\":\"Iterations\",\"formatter\":{\"id\":\"3226\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3196\",\"type\":\"BasicTicker\"}},\"id\":\"3195\",\"type\":\"LinearAxis\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3220\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"3193\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3219\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"3201\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis_label\":\"#Nodes\",\"formatter\":{\"id\":\"3228\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3201\",\"type\":\"BasicTicker\"}},\"id\":\"3200\",\"type\":\"LinearAxis\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"zczMzMzM7D/sUbgehevpPx+F61G4Huk/9ihcj8L16D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/TDeJQWDl6D9MN4lBYOXoP0w3iUFg5eg/\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3244\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3243\",\"type\":\"UnionRenderers\"}},\"id\":\"3218\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3196\",\"type\":\"BasicTicker\"}},\"id\":\"3199\",\"type\":\"Grid\"},{\"attributes\":{\"below\":[{\"id\":\"3195\",\"type\":\"LinearAxis\"},{\"id\":\"3248\",\"type\":\"Title\"}],\"center\":[{\"id\":\"3199\",\"type\":\"Grid\"},{\"id\":\"3204\",\"type\":\"Grid\"},{\"id\":\"3230\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"3200\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"plot_width\":400,\"renderers\":[{\"id\":\"3221\",\"type\":\"GlyphRenderer\"},{\"id\":\"3235\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"3224\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"3211\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"3187\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"3191\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"3189\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"3193\",\"type\":\"LinearScale\"}},\"id\":\"3186\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"3196\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"3191\",\"type\":\"LinearScale\"},{\"attributes\":{\"text\":\"Threshold - Diffusion Trend\"},\"id\":\"3224\",\"type\":\"Title\"},{\"attributes\":{\"dimension\":1,\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3201\",\"type\":\"BasicTicker\"}},\"id\":\"3204\",\"type\":\"Grid\"}],\"root_ids\":[\"3339\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
       "  var render_items = [{\"docid\":\"e784d739-8e4b-4904-aa67-67cce5637a1f\",\"roots\":{\"3339\":\"274e15de-82fe-4266-84ed-57cd31cb1507\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "3339"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model, iterations = watts_model_ba_network(1, 0.5, 0.1, 30)\n",
    "plot_diffusion(model, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:57:31.361301Z",
     "start_time": "2020-08-09T13:57:31.104213Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 30/30 [00:00<00:00, 308.63it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"3626\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"3626\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"3626\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '3626' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"3626\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"3626\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"3626\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '3626' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"3626\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"00d6429b-564d-4508-a820-8047cfe0c073\" data-root-id=\"3780\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = {\"8e447537-5c2b-4a65-922b-e5d4727cc4ad\":{\"roots\":{\"references\":[{\"attributes\":{\"children\":[{\"id\":\"3779\",\"type\":\"ToolbarBox\"},{\"id\":\"3777\",\"type\":\"GridBox\"}]},\"id\":\"3780\",\"type\":\"Column\"},{\"attributes\":{\"callback\":null},\"id\":\"3693\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"3748\",\"type\":\"Selection\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3661\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"3695\",\"type\":\"LinearScale\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAAAQQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3774\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3773\",\"type\":\"UnionRenderers\"}},\"id\":\"3736\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"toolbar\":{\"id\":\"3778\",\"type\":\"ProxyToolbar\"},\"toolbar_location\":\"above\"},\"id\":\"3779\",\"type\":\"ToolbarBox\"},{\"attributes\":{\"tools\":[{\"id\":\"3646\",\"type\":\"PanTool\"},{\"id\":\"3647\",\"type\":\"WheelZoomTool\"},{\"id\":\"3648\",\"type\":\"BoxZoomTool\"},{\"id\":\"3649\",\"type\":\"SaveTool\"},{\"id\":\"3650\",\"type\":\"ResetTool\"},{\"id\":\"3651\",\"type\":\"HelpTool\"},{\"id\":\"3709\",\"type\":\"PanTool\"},{\"id\":\"3710\",\"type\":\"WheelZoomTool\"},{\"id\":\"3711\",\"type\":\"BoxZoomTool\"},{\"id\":\"3712\",\"type\":\"SaveTool\"},{\"id\":\"3713\",\"type\":\"ResetTool\"},{\"id\":\"3714\",\"type\":\"HelpTool\"}]},\"id\":\"3778\",\"type\":\"ProxyToolbar\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"3646\",\"type\":\"PanTool\"},{\"id\":\"3647\",\"type\":\"WheelZoomTool\"},{\"id\":\"3648\",\"type\":\"BoxZoomTool\"},{\"id\":\"3649\",\"type\":\"SaveTool\"},{\"id\":\"3650\",\"type\":\"ResetTool\"},{\"id\":\"3651\",\"type\":\"HelpTool\"}]},\"id\":\"3652\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"3761\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"data_source\":{\"id\":\"3659\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3660\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3661\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3663\",\"type\":\"CDSView\"}},\"id\":\"3662\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"3646\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"3697\",\"type\":\"LinearScale\"},{\"attributes\":{\"items\":[{\"id\":\"3735\",\"type\":\"LegendItem\"},{\"id\":\"3750\",\"type\":\"LegendItem\"}],\"orientation\":\"horizontal\"},\"id\":\"3734\",\"type\":\"Legend\"},{\"attributes\":{},\"id\":\"3774\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"3647\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"axis_label\":\"Iterations\",\"formatter\":{\"id\":\"3730\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3700\",\"type\":\"BasicTicker\"}},\"id\":\"3699\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"3762\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"3705\",\"type\":\"BasicTicker\"},{\"attributes\":{\"overlay\":{\"id\":\"3670\",\"type\":\"BoxAnnotation\"}},\"id\":\"3648\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"3700\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"3773\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"3649\",\"type\":\"SaveTool\"},{\"attributes\":{\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3700\",\"type\":\"BasicTicker\"}},\"id\":\"3703\",\"type\":\"Grid\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3724\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"3650\",\"type\":\"ResetTool\"},{\"attributes\":{\"dimension\":1,\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3705\",\"type\":\"BasicTicker\"}},\"id\":\"3708\",\"type\":\"Grid\"},{\"attributes\":{\"axis_label\":\"#Delta Nodes\",\"formatter\":{\"id\":\"3732\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3705\",\"type\":\"BasicTicker\"}},\"id\":\"3704\",\"type\":\"LinearAxis\"},{\"attributes\":{\"label\":{\"value\":\"Susceptible\"},\"renderers\":[{\"id\":\"3725\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3735\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"3651\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"3632\",\"type\":\"LinearScale\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"3709\",\"type\":\"PanTool\"},{\"id\":\"3710\",\"type\":\"WheelZoomTool\"},{\"id\":\"3711\",\"type\":\"BoxZoomTool\"},{\"id\":\"3712\",\"type\":\"SaveTool\"},{\"id\":\"3713\",\"type\":\"ResetTool\"},{\"id\":\"3714\",\"type\":\"HelpTool\"}]},\"id\":\"3715\",\"type\":\"Toolbar\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#aec7e8\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3737\",\"type\":\"Line\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAAAQwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3748\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3747\",\"type\":\"UnionRenderers\"}},\"id\":\"3722\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data_source\":{\"id\":\"3722\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3723\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3724\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3726\",\"type\":\"CDSView\"}},\"id\":\"3725\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"3667\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"3709\",\"type\":\"PanTool\"},{\"attributes\":{\"source\":{\"id\":\"3659\",\"type\":\"ColumnDataSource\"}},\"id\":\"3663\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3710\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"3670\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"overlay\":{\"id\":\"3733\",\"type\":\"BoxAnnotation\"}},\"id\":\"3711\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"3712\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"3669\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"3713\",\"type\":\"ResetTool\"},{\"attributes\":{\"label\":{\"value\":\"Susceptible\"},\"renderers\":[{\"id\":\"3662\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3672\",\"type\":\"LegendItem\"},{\"attributes\":{\"dimension\":1,\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3642\",\"type\":\"BasicTicker\"}},\"id\":\"3645\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"3714\",\"type\":\"HelpTool\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#aec7e8\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3674\",\"type\":\"Line\"},{\"attributes\":{\"children\":[[{\"id\":\"3627\",\"subtype\":\"Figure\",\"type\":\"Plot\"},0,0],[{\"id\":\"3690\",\"subtype\":\"Figure\",\"type\":\"Plot\"},0,1]]},\"id\":\"3777\",\"type\":\"GridBox\"},{\"attributes\":{\"axis_label\":\"#Nodes\",\"formatter\":{\"id\":\"3669\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3642\",\"type\":\"BasicTicker\"}},\"id\":\"3641\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"3642\",\"type\":\"BasicTicker\"},{\"attributes\":{\"text\":\"Threshold - Prevalence\"},\"id\":\"3728\",\"type\":\"Title\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"mpmZmZmZuT85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/ObTIdr6fuj85tMh2vp+6Pzm0yHa+n7o/\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3762\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3761\",\"type\":\"UnionRenderers\"}},\"id\":\"3673\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"grid_line_alpha\":0.5,\"ticker\":{\"id\":\"3637\",\"type\":\"BasicTicker\"}},\"id\":\"3640\",\"type\":\"Grid\"},{\"attributes\":{\"align\":\"center\",\"text\":\"fraction infected: 0.1\"},\"id\":\"3752\",\"type\":\"Title\"},{\"attributes\":{\"text\":\"Threshold - Diffusion Trend\"},\"id\":\"3665\",\"type\":\"Title\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3675\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3660\",\"type\":\"Line\"},{\"attributes\":{\"data_source\":{\"id\":\"3673\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3674\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3675\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3677\",\"type\":\"CDSView\"}},\"id\":\"3676\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"3722\",\"type\":\"ColumnDataSource\"}},\"id\":\"3726\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3730\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"3733\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"source\":{\"id\":\"3673\",\"type\":\"ColumnDataSource\"}},\"id\":\"3677\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3684\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"3637\",\"type\":\"BasicTicker\"},{\"attributes\":{\"label\":{\"value\":\"Infected\"},\"renderers\":[{\"id\":\"3676\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3687\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"3732\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"3685\",\"type\":\"Selection\"},{\"attributes\":{\"align\":\"center\",\"text\":\"fraction infected: 0.1\"},\"id\":\"3689\",\"type\":\"Title\"},{\"attributes\":{\"below\":[{\"id\":\"3699\",\"type\":\"LinearAxis\"},{\"id\":\"3752\",\"type\":\"Title\"}],\"center\":[{\"id\":\"3703\",\"type\":\"Grid\"},{\"id\":\"3708\",\"type\":\"Grid\"},{\"id\":\"3734\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"3704\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"plot_width\":400,\"renderers\":[{\"id\":\"3725\",\"type\":\"GlyphRenderer\"},{\"id\":\"3739\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"3728\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"3715\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"3691\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"3695\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"3693\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"3697\",\"type\":\"LinearScale\"}},\"id\":\"3690\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3738\",\"type\":\"Line\"},{\"attributes\":{\"callback\":null},\"id\":\"3628\",\"type\":\"DataRange1d\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"zczMzMzM7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/eekmMQis7D956SYxCKzsP3npJjEIrOw/\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"3685\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"3684\",\"type\":\"UnionRenderers\"}},\"id\":\"3659\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"callback\":null},\"id\":\"3691\",\"type\":\"DataRange1d\"},{\"attributes\":{\"data_source\":{\"id\":\"3736\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"3737\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"3738\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"3740\",\"type\":\"CDSView\"}},\"id\":\"3739\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"source\":{\"id\":\"3736\",\"type\":\"ColumnDataSource\"}},\"id\":\"3740\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3723\",\"type\":\"Line\"},{\"attributes\":{\"label\":{\"value\":\"Infected\"},\"renderers\":[{\"id\":\"3739\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3750\",\"type\":\"LegendItem\"},{\"attributes\":{\"axis_label\":\"Iterations\",\"formatter\":{\"id\":\"3667\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3637\",\"type\":\"BasicTicker\"}},\"id\":\"3636\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"3747\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"items\":[{\"id\":\"3672\",\"type\":\"LegendItem\"},{\"id\":\"3687\",\"type\":\"LegendItem\"}],\"orientation\":\"horizontal\"},\"id\":\"3671\",\"type\":\"Legend\"},{\"attributes\":{\"callback\":null},\"id\":\"3630\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"3634\",\"type\":\"LinearScale\"},{\"attributes\":{\"below\":[{\"id\":\"3636\",\"type\":\"LinearAxis\"},{\"id\":\"3689\",\"type\":\"Title\"}],\"center\":[{\"id\":\"3640\",\"type\":\"Grid\"},{\"id\":\"3645\",\"type\":\"Grid\"},{\"id\":\"3671\",\"type\":\"Legend\"}],\"left\":[{\"id\":\"3641\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"plot_width\":400,\"renderers\":[{\"id\":\"3662\",\"type\":\"GlyphRenderer\"},{\"id\":\"3676\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"3665\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"3652\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"3628\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"3632\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"3630\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"3634\",\"type\":\"LinearScale\"}},\"id\":\"3627\",\"subtype\":\"Figure\",\"type\":\"Plot\"}],\"root_ids\":[\"3780\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
       "  var render_items = [{\"docid\":\"8e447537-5c2b-4a65-922b-e5d4727cc4ad\",\"roots\":{\"3780\":\"00d6429b-564d-4508-a820-8047cfe0c073\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "3780"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model, iterations = watts_model_ba_network(5, 0.5, 0.1, 30)\n",
    "plot_diffusion(model, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:58:23.188076Z",
     "start_time": "2020-08-09T13:58:22.977876Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 30/30 [00:00<00:00, 1237.37it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"6161\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"6161\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };var element = document.getElementById(\"6161\");\n",
       "  if (element == null) {\n",
       "    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '6161' but no matching script tag was found. \")\n",
       "    return false;\n",
       "  }\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"6161\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"6161\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"6161\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '6161' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.4.0.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.4.0.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"6161\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n",
      "BokehDeprecationWarning: 'legend' keyword is deprecated, use explicit 'legend_label', 'legend_field', or 'legend_group' keywords instead\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"9661559e-d3cc-4453-abcf-d2b148331648\" data-root-id=\"6315\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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- Prevalence\"},\"id\":\"6263\",\"type\":\"Title\"},{\"attributes\":{\"text\":\"Threshold - Diffusion Trend\"},\"id\":\"6200\",\"type\":\"Title\"},{\"attributes\":{\"items\":[{\"id\":\"6270\",\"type\":\"LegendItem\"},{\"id\":\"6285\",\"type\":\"LegendItem\"}],\"orientation\":\"horizontal\"},\"id\":\"6269\",\"type\":\"Legend\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"6210\",\"type\":\"Line\"},{\"attributes\":{\"data_source\":{\"id\":\"6208\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"6209\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"6210\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"6212\",\"type\":\"CDSView\"}},\"id\":\"6211\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"6177\",\"type\":\"BasicTicker\"},{\"attributes\":{\"source\":{\"id\":\"6257\",\"type\":\"ColumnDataSource\"}},\"id\":\"6261\",\"type\":\"CDSView\"},{\"attributes\":{\"source\":{\"id\":\"6208\",\"type\":\"ColumnDataSource\"}},\"id\":\"6212\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"6265\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"6268\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"6219\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"axis_label\":\"#Nodes\",\"formatter\":{\"id\":\"6204\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"6177\",\"type\":\"BasicTicker\"}},\"id\":\"6176\",\"type\":\"LinearAxis\"},{\"attributes\":{\"label\":{\"value\":\"Infected\"},\"renderers\":[{\"id\":\"6211\",\"type\":\"GlyphRenderer\"}]},\"id\":\"6222\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"6220\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"6267\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#aec7e8\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"6272\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"6169\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#1f77b4\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"6195\",\"type\":\"Line\"},{\"attributes\":{\"label\":{\"value\":\"Susceptible\"},\"renderers\":[{\"id\":\"6260\",\"type\":\"GlyphRenderer\"}]},\"id\":\"6270\",\"type\":\"LegendItem\"},{\"attributes\":{\"align\":\"center\",\"text\":\"fraction infected: 0.1\"},\"id\":\"6224\",\"type\":\"Title\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],\"y\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAABrQAAAAAAAYG5AAAAAAAAQdUAAAAAAAIBZQAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",\"dtype\":\"float64\",\"shape\":[30]}},\"selected\":{\"id\":\"6309\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"6308\",\"type\":\"UnionRenderers\"}},\"id\":\"6271\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"6315\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
       "  var render_items = [{\"docid\":\"04606982-d725-4adf-95d8-617fbf55dc15\",\"roots\":{\"6315\":\"9661559e-d3cc-4453-abcf-d2b148331648\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "6315"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model, iterations = watts_model_ba_network(2, 0.2, 0.1, 30)\n",
    "plot_diffusion(model, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-09T13:47:11.981708Z",
     "start_time": "2020-08-09T13:47:05.410231Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(g, node_size = 10)\n"
   ]
  },
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   "source": [
    "## General Threshold\n",
    "The General Threshold model was introduced in 2003 by Kempe [1].\n",
    "\n",
    "In this model, during an epidemics, a node is allowed to change its status from Susceptible to Infected.\n",
    "\n",
    "At time t nodes become Infected if the sum of the weight of the infected neighbors is greater than the threshold\n",
    "\n",
    "- David Kempe , Jon Kleinberg, and Éva Tardos. “Maximizing the spread of influence through a social network.” Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 2003.\n",
    "\n",
    "https://ndlib.readthedocs.io/en/latest/reference/models/epidemics/GeneralThreshold.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "## Generalised Threshold\n",
    "It was introduced in 2017 by Török and Kertesz [1]. In this model, a node is allowed to change its status from Susceptible to Infected. The model is instantiated on a graph having a non-empty set of infected nodes. \n",
    "\n",
    "- At time `t` nodes become Infected with rate `mu t/tau`\n",
    "- Nodes for which the ratio of the active friends dropped below the threshold are moved to the Infected queue\n",
    "- Nodes in the Infected queue become infected with rate tau. If this happens check all its friends for threshold\n",
    "\n",
    "\n",
    "> János Török and János Kertész “Cascading collapse of online social networks” Scientific reports, vol. 7 no. 1, 2017 \n",
    "\n",
    "\n",
    "https://ndlib.readthedocs.io/en/latest/reference/models/epidemics/GeneralisedThreshold.html"
   ]
  },
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   "source": [
    "![image.png](images/end.png)"
   ]
  }
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