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)

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

Global Dynamics of an SIRSI Epidemic Model with Discrete Delay and General Incidence Rate

Journal of Applied Nonlinear Dynamics 10(3) (2021) 547--562 | DOI:10.5890/JAND.2021.09.013

Amine Bernoussi$^1$ , Khalid Hattaf$^2$

$^1$ 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

$^2$ Centre R$mbox{'e}$gional des M$mbox{'e}$tiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco

Abstract

In this paper, we propose the global dynamics of an SIRSI epidemic model with discrete latent period and general nonlinear incidence function. By analyzing the corresponding characteristic equations, the local stability of the endemic equilibrium is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, the global stability of the disease-free equilibrium and the endemic equilibrium are established for the SIRSI epidemic model with discrete latent period.

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