Spatial SIR epidemic model with varying infectivity in an unbounded domain: Law of Large Numbers

TL;DR

This paper extends a spatial SIR epidemic model to unbounded domains, incorporating age-dependent infectivity and non-local infections, and proves a law of large numbers as population size grows.

Contribution

It generalizes previous bounded domain results to unbounded domains, providing a rigorous law of large numbers for the model with age-dependent infectivity.

Findings

Law of large numbers established for unbounded domains

Model incorporates non-local infections and age-dependent infectivity

Extends previous bounded domain results

Abstract

We consider a spatial SIR epidemic model where the infectivity of infected individuals depends upon their age of infection, and infections are non local. The domain is an unbounded subset of $\R^d$,and the individuals do not move. We extend our earlier result in \cite{AK-EP}, where the domain was bounded, and prove a law of large numbers as the size of the population tends to $\infty$.