Global stability of SAIRS epidemic models

Stefania Ottaviano, Mattia Sensi*, Sara Sottile

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

17 Citations (Scopus)
62 Downloads (Pure)


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.

Original languageEnglish
Article number103501
Pages (from-to)1-25
Number of pages25
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - 2022


  • Basic reproduction number
  • Geometric approach
  • Global asymptotic stability
  • Lyapunov functions
  • Susceptible–asymptomatic infected–symptomatic infected–recovered–susceptible
  • Vaccination


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