International Journal of Nonlinear Analysis and Applications

Stability analysis of SIR and SIRS models with non monotone incidence function and various mortality rates

Articles in Press

Document Type : Research Paper

Authors

1 Quantitative Technics Department, Faculty of Legal and Economic Sciences, University of Nouakchott, Nouakchott, Mauritanie

2 Department of Applied Mathematics and Industrial Engineering, Professional University Institute, University of Nouakchott, Nouakchott, Mauritanie

Abstract

This study employs the Lyapunov method, the Poincar'e-Bendixson theorem, and the Dulac criterion to investigate the stability of SIR and SIRS models with non-monotone incidence and varying mortality rates. The analysis focuses on the stability properties of equilibrium points in the associated dynamical systems. For \( R_0 < 1 \), the eigenvalues of the Jacobian matrices at the equilibrium points have negative real parts, confirming their local asymptotic stability. When \( R_0 > 1 \), the global asymptotic stability of both the disease-free and endemic equilibrium points is demonstrated using a Lyapunov function and LaSalle's invariance principle. Additionally, an alternative approach leveraging the Poincar'e-Bendixson theorem and Dulac's criterion is introduced to establish global stability. Numerical simulations, performed with carefully chosen parameters, validate the analytical results and provide deeper insights into the system's behavior.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 15 June 2026
  • Receive Date: 13 August 2023
  • Revise Date: 01 February 2025
  • Accept Date: 15 March 2025