Analytical and numerical preservation properties of a modified SIR model with contact matrix: application to the diffusion of information

In this talk, we aim to analyze a modified SIR (Susceptible-Infected-Recovered) model with contact matrix. Theoretical results concerning the positivity of the analytical solution, the conservation of the total population, and the stability of the equilibrium points are given. Moreover, the numerical preservation of these properties through by step by schemes based on Standard and non Standard Finite Difference methods, and on the Modified Patankar Euler method, is studied. The above results are applied to the diffusion of information in social networks. Several numerical experiments on real data on social platforms, like Twitter, Instagram and Facebook, are shown in order to prove the effectiveness of the different numerical approaches.