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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

Stability Analysis of an Seirs Epidemic Model with Relapse, Immune and General Incidence Rates

Journal of Applied Nonlinear Dynamics 11(1) (2022) 217--231 | DOI:10.5890/JAND.2022.03.013

Amine Bernoussi$^1$ , Soufiane Elkhaiar$^2$, Chakib Jerry$^3$

$^1$ 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

$^2$ Department of Mathematics, Faculty of Applied Sciences, PO Box 6146, Ait Melloul, Morocco

$^3$ 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

This paper has the goal to broaden the incidence rate of an SEIRS epidemic model to a wide range of monotonic, concave incidence rates and some non-monotonic or concave cases. These incidence functions could reflect media education or psychological effect or mass action. The model takes into account relapse, recovery and immunity rates but without disease-induced death one. Applying the novel geometric approach we establish the global stability of the SEIRS model. Our analytical results reveal that the basic reproduction number completely determines the global stability of equilibria. Our conclusions are applied to two special incidence functions reflecting media and mass action.

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