Global stability of SAIRS epidemic models

Journal article (2022)

Authors

Stefania Ottaviano Università di Trento
M. Sensi Network Architectures and Services - EEMCS
Sara Sottile Università di Trento
Research Group
Network Architectures and Services (EEMCS) (TU Delft)
Copyright: © 2022 Stefania Ottaviano, M. Sensi, Sara Sottile
DOI
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https://doi.org/10.1016/j.nonrwa.2021.103501
Vaccination Basic reproduction number Geometric approach Global asymptotic stability Lyapunov functions Susceptible–asymptomatic infected–symptomatic infected–recovered–susceptible
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

Abstract

We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for the model. We determine the value of the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0<1. If R0>1, the disease free equilibrium is unstable and a unique endemic equilibrium exists. We investigate the global stability of the endemic equilibrium for some variations of the original model under study and answer an open problem proposed in Ansumali et al. (2020). In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R0=1. We provide a thorough numerical exploration of our model to illustrate our analytical results.