Epidemic Models as Scaling Limits of Individual Dynamics

TL;DR

This paper demonstrates how epidemic models like SIR and its variants can be derived as large-scale limits of individual-based models governed by spatially dependent Markov processes, under different scaling regimes.

Contribution

It introduces a framework connecting individual spatial interactions with classical epidemic models through scaling limits, providing a rigorous derivation of well-known models from microscopic dynamics.

Findings

SIR and non-local epidemic models emerge as limits of individual-based Markov processes.

Different scaling regimes lead to different epidemic models.

The approach bridges microscopic interactions and macroscopic epidemic dynamics.

Abstract

Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large scale limits of the individual based model in two different scaling regimes of the interaction.