An epidemic model in inhomogeneous environment

TL;DR

This paper develops an epidemic model on inhomogeneous complete graphs, analyzing its behavior through limit theorems and showing that inhomogeneity in susceptibility can reduce epidemic impact.

Contribution

It generalizes existing models by incorporating vertex heterogeneity and provides rigorous limit theorems for epidemic dynamics in large populations.

Findings

Law of large numbers for epidemic duration

Central limit theorem for infected count

Inhomogeneous susceptibility reduces epidemic impact

Abstract

The current work deals with an epidemic model on the complete graph K_n on n vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types differ in the probability of getting infected, and/or in the capacity of infecting other vertices. This generalizes previous models where vertices are all of the same type and have equal probabilities of being infected. We prove laws of large numbers and central limit theorems for the the total duration of the process and for the number of infected vertices, respectively, when n goes to infinity. By coupling the epidemic model with a Poisson process, we also obtain continuous-time counterparts of the above-mentioned limit results. Moreover, we also prove that when all individuals have the same spread capacity, then a population with inhomogeneous susceptibility is less affected by the epidemics than a homogeneous population.