We present and analyze two simple -particle systems for the spread of an infection, respectively with binary and with multi-body interactions. We establish a convergence result, as , 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.
Cite this article
Alessandro Ciallella, Mario Pulvirenti, Sergio Simonella, Kinetic SIR equations and particle limits. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 2, pp. 295–315DOI 10.4171/RLM/937