Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function
Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function
In this paper the global dynamics of susceptible-infected-recovered-susceptible (SIRS) epidemic model with saturated incidence rate and saturated treatment function is studied. Firstly, the basic reproduction number $R_0$ is calculated and the existence of the disease-free and positive equilibria is showed. In addition, local stability of the equilibria is investigated. Then, sufficient conditions are achieved for global stability of disease-free and endemic equilibria. Finally, the numerical examples are presented to validate the theoretical results.
Keywords:
Global stability, Lyapunov function SIRS epidemic model,
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- [1] F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Berlin, Springer, 2011.
- [2] V. Capasso, G. Serio, A generalization of the Kermack–Mckendrick deterministic epidemic model, Math. Biosci. 42 (1978), 43-61.
- [3] X. Zhang, X. N. Liu, Backward bifurcation of an epidemic model with saturated treatment function, J. Math. Anal. Appl. 348(1) (2008), 433–443.
- [4] E. J. Avila-Vales, A. G. Cervantes-P´erez, Global Stability for SIRS Epidemic Models with General Incidence Rate and Transfer from Infectious to Susceptible, SeMA J. Bolet´ın de la Sociedad Matem´atica Mexicana. 25 (2019), 637–658.
- [5] JP. LaSalle, The Stability of Dynamical Systems, Philadelphia, PA, USA: Soc. Ind. Appl. Math. 1976.
- [6] M. Lu, J. Huang, S. Ruan, P. Yu, Bifurcation Analysis of a SIRS Epidemic Model with a Generalized Nonmonotone and Saturated Incidence Rate, . J. Differ. Equ. 267 (2019), 1859-1898.
- [7] S. Liao, J. Wang, Global Stability Analysis of Epidemiological Models Based on Volterra Lyapunov Stable Matrices, Chaos Solitons Fractals. 45 (2012), 966-977.
- ISSN: 2636-8692
- Yayın Aralığı: Yılda 3 Sayı
- Başlangıç: 2018
- Yayıncı: Mahmut AKYİĞİT
Sayıdaki Diğer Makaleler
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Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function
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