model_output.tex

\newcommand{\Rotherfit}{0.0398 (0.00898 -- 0.0716}
\newcommand{\probtransmissionfit}{43.4\% (24.9 -- 77.7\%}
\newcommand{\posteriortable}{\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}clll@{\extracolsep{\fill}}}
\hline
Parameter & \multicolumn{1}{c}{\begin{tabular}[c]{@{}c@{}}Posterior mean\\ (95\% CI)\end{tabular}} & \multicolumn{1}{c}{Prior distribution} & \multicolumn{1}{c}{Description} \\ 
\hline
\multicolumn{4}{c}{Population structure and initial condition parameters} \\ \hline
$\alpha_m$ & 2.36 (0.284, 5.73)& $Exp(1)$ & \begin{tabular}[c]{@{}l@{}}Dispersion parameter for\\ metapopulation sizes.\end{tabular}  \\ 
\hline
$\iota_0$  & 6.11 (0.861, 14.9)& $LogNormal(\ln(5), 1)$  & \begin{tabular}[c]{@{}l@{}}Scale parameter for\\ the number of initial\\ infected people.\end{tabular}\\ 
\hline
\multicolumn{4}{c}{Detection probability parameters} \\ \hline
$p_d$  & 0.454 (0.167, 0.869)& $Beta(5,5)$ & \begin{tabular}[c]{@{}l@{}}Mean weekly probability\\ of case detection.\\ Weekly probability of\\ detection was random\\ with $P_w \sim Beta(\alpha,\beta)$\\ with $\mathbb{E}[P_w]=p_d$.\end{tabular}  \\ \hline
$\Phi_d=\frac{1}{M+1}$ & 0.00156 (0.000317, 0.00592)& $M \sim Gamma(3,1000/3)$  & \begin{tabular}[c]{@{}l@{}}Dispersion of weekly\\ probability of case\\ detection (M is the\\ effective sample size\\ $\alpha + \beta$ for the weekly\\ $P_w \sim Beta(\alpha,\beta)$\\ distributed probability\\ of case detection).\end{tabular} \\ \hline
\multicolumn{4}{c}{Baseline transmission parameters}  \\ \hline
$p_{gbmsm}(0)$ & 0.434 (0.249, 0.777)& $Uniform(0,1)$  & \begin{tabular}[c]{@{}l@{}}Baseline probability\\ of transmission per\\ sexual contact.\end{tabular}\\ \hline
$R_{other}(0)$  & 0.0398 (0.00898, 0.0716)& $LogNormal(\ln(0.25),1)$ & \begin{tabular}[c]{@{}l@{}}Baseline reproductive\\ number non-GBMSM\\ sexual contacts.\end{tabular} \\ \hline
\multicolumn{4}{c}{Behaviour and risk change point parameters}  \\ \hline
$T_1$ & \begin{tabular}[c]{@{}l@{}}11-June\\(18-May, 13-July)\end{tabular}  & $U$(15 May, 18 July) & \begin{tabular}[c]{@{}l@{}}Change point time for\\ reduction in transmission\\ due to awareness of MPX.\end{tabular} \\ \hline
$\rho_{gbmsm,1}$  & 0.381 (0.0753, 0.655)& $Beta(1.5,1.5)$ & \begin{tabular}[c]{@{}l@{}}Reduction in GBMSM\\ reproduction number after\\ change point at $T_1$.\end{tabular} \\ \hline
$\rho_{gbmsm,2}$ & 0.338 (0.0466, 0.633) & \begin{tabular}[c]{@{}l@{}}$\rho_{gbmsm,2} \sim Beta(1.5,1.5)$\end{tabular} & \begin{tabular}[c]{@{}l@{}}Further reduction in GBMSM\\ reproduction number after\\ WHO announcement of\\ PHEIC.\end{tabular}  \\ \hline
\end{tabular*}}
\newcommand{\gbmsmR}{5.16 (2.96 -- 9.24}
\newcommand{\efftransmissionperiod}{6.01}
\newcommand{\gbmsmRredbv}{3.02 (1.94 -- 4.31}
\newcommand{\gbmsmRredwho}{1.98 (1.06 -- 3.42}
\newcommand{\reductionone}{38.1\%}\n\newcommand{\totalR}{5.16 (2.96 -- 9.24}