Spatial SIR epidemic model with varying infectivity without movement of individuals: Law of Large Numbers

TL;DR

This paper introduces a spatial SIR epidemic model with variable infectivity and no individual movement, establishing a law of large numbers for the empirical measures as population size grows.

Contribution

It presents a novel approach to spatial epidemic modeling with variable infectivity, proving a law of large numbers for the model's empirical measures.

Findings

Law of large numbers established for the model

Empirical measures describe disease spread spatially

Model accounts for variable infectivity without movement

Abstract

In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define empirical measures which describe the evolution of the state (susceptible, infectious, recovered) of the individuals in the various locations, and the total force of infection in the population. In our model, the individuals do not move. We establish a law of large numbers for these measures, as the population size tends to infinity.