Global stability of multi-group SAIRS epidemic models

TL;DR

This paper analyzes the global stability of a multi-group SAIRS epidemic model with vaccination, determining conditions for disease eradication or persistence, and compares epidemic spread across different network structures.

Contribution

It extends the homogeneous SAIRS model to a multi-group network, providing comprehensive stability analysis and numerical comparisons for various network topologies.

Findings

Disease-free equilibrium is globally stable if R0<1

Endemic equilibrium exists and is stable if R0>1

Numerical simulations compare epidemic spread across network types

Abstract

We study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population is divided. This is a natural extension of the homogeneous mixing SAIRS model with vaccination studied in Ottaviano et. al (2021) to a network of communities. We provide a global stability analysis for the model. We determine the value of the basic reproduction number $\mathcal{R}_0$ and prove that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0 < 1$. In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when $\mathcal{R}_0=1$. Moreover, if $\mathcal{R}_0 > 1$, the disease-free equilibrium is unstable and a unique endemic equilibrium exists. First, we investigate the local asymptotic stability of the endemic equilibrium and subsequently its global stability, for two variations of the original model. Last, we provide numerical simulations to compare the epidemic spreading on different networks topologies.