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Journal of Applied Nonlinear Dynamics 13(3) (2024) 557--569 | DOI:10.5890/JAND.2024.09.011

Khaled Boudjema Djeffal$^1$, Abdelheq Mezouaghi$^{1,2}$, Salih Djilali$^{1,3}$, Anwar Zeb$^4$

$^1$ Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef 02000, Algeria

$^2$ Laboratory of Pure and Applied Mathematics, University of Mostaganem, Mostaganem, Algeria

$^3$ Laboratoire d'Analyse Non Lin'{e}aire et Math'{e}matiques Appliqu'{e}es, Universit'{e} de Tlemcen, Tlemcen 13000, Algeria

$^4$ Department of Mathematics, COMSATS University Islamabad, Abbottabad, 22060, Pakistan

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Abstract

This research investigates an SVIR epidemic model with a time delay that represents the latency period and immigration into all classes. The presence of Immigration will eliminate the disease-free equilibrium, and then there is no extinction scenario of the epidemic, and we deduce that immigration will eliminate the notion of threshold dynamics, and hence there is no basic reproduction number.~We obtained that the epidemic is always persistent and the unique endemic equilibrium is globally stable, which has been proved using the Lyapunov approach.

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