Corona and Mathematics
Currently (March 2020) the COVID-19 or Corona epidemic affects many and is a topic widely discussed. Information on the number of infected individuals make headlines every day. Almost every evening special issues are broadcast in TV, where experts explain the latest findings.
On this page we want to explain the mathematics behind such facts. Why can we know that the infections are so dangerous? Why do politicians and epicemiologists suggest such drastic measures restricting our lifes, where each winter seemingly more people die from the flu?
Such assumptions and prognostics are backed mathematical models, that have proved to be useful in the past. They allow accurate projections on the development of such an epicemic or pandemic. We want to explain such modeling by a simple example, the so called SIR model. Prof. Jörn Behrens, together with his daughters Laila and Janka, produced two short videos explaining in everyday (German) lanuage, understandable by interested lay persons, how the SIR model is derived, and how to solve it numerically (see videos at the end of this page, English subtitles available).
- Video 1: How to derive the SIR model
- Video 2: How to solve and interpret results of the SIR model
If you are interested in knowing a little more about the model, and want to solve it by yourself on a computer, you may be interested in using the attached Python Notebook. It allows to play with parameters, such as infection rate and initial values. The notebook requires an installation of Python 3.7, with packages Jupyter, SciPy and NumPy. These software packages are most easily installed by using the Anaconda-Distribution (for Windows, MacOS and Linux).
- Jupyter Notebook implementing the SIR model (ZIP-File, 61KB)
Update: Konrad Simon has implemented a nice Python program with a graphical user interface for solving the SIR model. This tool is available via GitHub. It is based on pyqt and pyqtgraph packages (additional to the ones above).
The information provided here is by no means comprehensive or authoritative, the data are not realistic and conclusions to the true development of the Corona pandemic are not applicable, nor admissible. The material is meant exclusively to educate about the mathematical methods behind epidemiologic projections. They are largely simplified and therefore need to be taken with caution. We accept no liability or responsibility whatsoever for correctnes or usefulness of the data. In particular, we warn users to take premature conclusions.
Please follow the official health suggestions and rules!