Global stability of multi-group SAIRS epidemic models - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2023

Global stability of multi-group SAIRS epidemic models

Résumé

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). 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.

Dates et versions

hal-03874780 , version 1 (28-11-2022)

Identifiants

Citer

Stefania Ottaviano, Mattia Sensi, Sara Sottile. Global stability of multi-group SAIRS epidemic models. Mathematical Methods in the Applied Sciences, 2023, ⟨10.1002/mma.9303⟩. ⟨hal-03874780⟩
27 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More