Résumé
The paper presents some non-standard finite difference methods for the MSEIR model. Following a short description of the methods, they are compared with the standard methods usually implemented in scientific software. It is shown that the non-standard schemes are superior to the standard ones with respect to their qualitative properties and the CPU running time. We show that non-local approximations of non linear terms in the equations can be of utmost importance to capture the dynamic of the system.