The most common epidemiological models (those on which the R0 calculation is based) are designed on compartmentalization of the population. Usually, it is decomposed into three compartments of individuals: Susceptible to be infected (S), Infected (I), Removed (no longer participating in the propagation of the virus). In these compartmental models, the only particularity of an individual is therefore the epidemiological class to which he belongs. In this project, the environmental underpinnings of the model will be questioned in order to reintroduce the spatial patterns of the disease.

To simplify we consider that the individual spatial mobility is a Brownian motion. Therefore, population mobility is described by a diffusion process. During the workshop, we will provide mathematical and numerical tools to solve partial differential equations of the form

Prerequisites
1. Basic knowledge about ordinary differential equation

2. Variational formulation of PDE

3. Programming basics

Materials:

1. Install Freefem++ http://www3.freefem.org

2. J.D. Murray, Mathematical Biology: I. An Introduction, Springer, 2002.