Global stability of SAIRS epidemic models. (June 2022)

• Record Type: Journal Article
• Authors: Ottaviano, Stefania; Sensi, Mattia; Sottile, Sara
• Is Part Of: Nonlinear analysis. Volume 65(2022)
• Publication Date: 2022-06
• Subjects: Susceptible–asymptomatic infected–symptomatic infected–recovered–susceptible -- Vaccination -- Basic reproduction number -- Lyapunov functions -- Global asymptotic stability -- Geometric approach; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103501
• Languages: English
• ISSNs: 1468-1218

Abstract

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 R 0 and prove that the disease-free equilibrium is globally asymptotically stable if R 0 < 1 . If R 0 > 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 R 0 = 1 . We provide a thorough numerical exploration of our model to illustrate our analytical results.