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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Effect of Disease-Induced Death Rate and Latent Period on Global Stability for SIRS Epidemic Models with General Incidence Rate

Journal of Applied Nonlinear Dynamics 12(3) (2023) 497--521 | DOI:10.5890/JAND.2023.09.006

Amine Bernoussi$^1$, Chakib Jerry$^2$

$^1$ Laboratory: '{E}quations aux d'{e}riv'{e}es partielles, Alg`{e}bre et G'{e}om'{e}trie spectrales, Faculty of Science, Ibn Tofail University, BP 133, 14000 Kenitra, Morocco,

$^2$ Moulay Ismail University of Meknes, Team O.M.E.G.A, Faculty of Law, Economics and Socials Sciences, B.P. 3102 Toulal, Meknes, Morocco

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Abstract

In this paper, We study a class of delayed SIRS epidemic dynamical models with a general nonlinear incidence rate representing the transfer from susceptible class to infected class. Besides we incorporate a surviving probability from susceptibles to infectious. Throughout the paper, Lyapunov and Euler's stability tools are used to establish the global and local stability for both disease-free and endemic equilibriums depending on reproduction number value $R_0$ and disease-induced death rate. Finally, a sensitivity analysis over basic reproduction number with respect to controllable model's parameters and numerical simulations are presented to illustrate and explain our theoretical results.

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