Stochastic and deterministic SIS patch model

TL;DR

This paper develops a stochastic SIS epidemic model with multiple patches, proves its convergence to a deterministic model, and analyzes the stability and equilibrium states, comparing them across different population structures.

Contribution

It introduces a stochastic patch model for SIS epidemics, proves convergence to a deterministic limit, and analyzes equilibrium stability under specific migration conditions.

Findings

Convergence of stochastic to deterministic model as population grows

Existence and global stability of a unique endemic equilibrium

Comparison of equilibria with homogeneous and isolated patch models

Abstract

Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to infinity. Furthermore, we show the existence and the global stability of a unique endemic equilibrium provided that the migration rates of susceptible and infectious individuals are equal. Finally, we compare the equilibra with those of the homogeneous model, and with those of isolated patches.