Stability Analysis of a Delayed Epidemic Model with General Incidence and Treatment Functions

Authors

  • Amine Bernoussi Laboratory: E´quations aux de´rive´es partielles, Alge`bre et Ge´ome´trie spectrales, Faculty of Science, Ibn Tofail University, BP 133, 14000 Kenitra, Morocco
  • Khalid Hattaf Equipe de Recherche en Mod´elisation et Enseignement des Math´ematiques (ERMEM), Centre R´egional des M´etiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco; Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco
  • Brahim El Boukari Laboratory of Applied Mathematics and Scientific Calculus (LMACS), Higher school of technology, Sultan Moulay Slimane University, 23000 B´eni Mellal, Morocco

DOI:

https://doi.org/10.25728/assa.2025.2025.1.1417

Keywords:

Treatment, nonlinear incidence, time delay, global stability, Hopf bifurcation.

Abstract

In this paper, we study an SIR epidemic model with general nonlinear incidence function, general function of treatment and two discrete time delays, the first described the time delay due to the latent period of the disease and the second is the time delay due to the period that the infected individuals use to move into the recovered class. Lyapunov’s method is used to show the global stability of the disease-free equilibrium if the basic reproduction number R0 ≤ 1, while if R0 > 1 and under some conditions of delays, the existence of Hopf bifurcation appears for the endemic equilibrium.

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Published

2025-08-24

Issue

Vol. 2025 No. 1 (2025): Advances in Systems Science and Applications

Section

Articles

How to Cite

Stability Analysis of a Delayed Epidemic Model with General Incidence and Treatment Functions. (2025). Advances in Systems Science and Applications, 2025(1), 55-85. https://doi.org/10.25728/assa.2025.2025.1.1417