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

Articles in Press

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 interac-
tion among susceptible, asymptomatic, symptomatic, and recovered individuals. Two general
incidence functions describing the infection caused by the asymptomatic and symptomatic indi-
viduals 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 de-
pends 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 asymptotically stable when R 0 > 1. The numerical simu-
lation 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

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 26 February 2025

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History

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

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