Kinetic SIR equations and particle limits

Abstract

We present and analyze two simple $N$-particle systems for the spread of an infection, respectively with binary and with multi-body interactions. We establish a convergence result, as $N\to \infty$, to a set of kinetic equations, providing a mathematical justification of related numerical schemes. We analyze rigorously the time asymptotics of these equations, and compare the models numerically.