Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.

2 Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco.

3 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

This paper studies the dynamics of a SAIR mathematical model that describes the interaction among susceptible, asymptomatic, symptomatic, and recovered individuals. Two general incidence functions describing the infection caused by the asymptomatic and symptomatic individuals are introduced. We also take into account a temporary immunity, that is, a proportion of the recovered individuals becomes susceptible again. The basic reproduction number $R_0$ depends on the general incidence functions. The local and global asymptotical stability for each equilibrium will depend on the basic reproduction number $R_0$. In precise terms, the disease-free equilibrium is locally and globally asymptotically stable when $R_0<1$, while   the endemic equilibrium is locally and globally asymptotic stable when $R_0>1$. The numerical simulation is performed for different incidence rate cases, such as bilinear, Beddington-DeAngelis, Crowley Martin, and non-monotonic incidence rate functions. The simulation results are found to agree with the theoretical endings.

Keywords

Main Subjects

References

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Computational Methods for Differential Equations
Volume 14, Issue 2
April 2026
Pages 908-918

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History

  • Receive Date: 30 October 2024
  • Revise Date: 26 January 2025
  • Accept Date: 17 February 2025

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