The so-called SEIR model is commonly used to model the outbreak of pandemics. The plain SEIR model consists of four differential equations, modeling the dynamics of susceptible, exposed, infected, and recovered people. Undeniably, a portion of infected people needs intensive care. To account for this fact variants of the model exist, see for instance here for the current Covid-19 pandemic (German), or here (German), or here (English). As with every mathematical model there are parameters that need to be chosen. Usually, not precise figures exist. Hence, uncertainty quantification can play a vital role.
| Resource | Explanation |
|---|---|
| corona.rki.de | Dashboard by Robert Koch Institut; goes down to communal level |
| corona.rki.de -- API | API for resource from above |
| RKI - Meldedaten | Meldedaten nach Infektionsschutzgesetz, Robert Koch Institut |
| Epidemiologisches Bulletin | by Robert Koch Institut |
| Epidemic calculator | Epidemilogical simulation tool |
| CovidSim | Epidemilogical simulation tool (for Europe) |
| Risklayer Explorer | This company grew out ouf KIT; they still work together closely. Provides more than just information about Germany. |
| The Mathematics of Infectious Diseases | Great SIAM paper by Herbert W. Hethcote |
| Data against Covid | Initiative to share and provide expertise |
| Estimating $R_0$ | Estimation of basic reproduction number for Germany |
| SIAM Resources for Covid-19 | Excellent collection of online resources |
The code introduces uncertainty with respect to the basic reproduction number and the percentage of infected persons that require intensive care (see the code for precise numbers). Unfortunately, the numbers sketch a rather glim future (here for the German scenario). For instance, here is the number of infected patients over the course of one year.
And here the number of patients required intensive care
The basic equations for the SEIR model are (see for example this excellent reference)
and we augment them by equations for patients requiring intensive care units (ICUs) motivated by this press release
The code is written in Julia. To run it, install all required packages. The main dependencies are DifferenialEquations.jl and PolyChaos.jl.
This repository contains Julia code and a documentation to show how polynomial chaos expansion can help quantify uncertainties for the SEIR model.