Analytical Properties and Numerical Preservation of an Age-Group Sir Model: Application to the Diffusion of Information

Abstract

This paper analyzes an age-group SIR (Susceptible-Infected-Recovered) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations, a numerical approximation is considered, based on Standard and non Standard Finite Difference methods, and on the Modified Patankar Euler method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks. The effectiveness of the different numerical approaches is shown through several numerical tests on real data.