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Nyamoradi, Nemat, Allali, Karam, Ahmad, Bashir. (1405). Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity. سامانه مدیریت نشریات علمی, 14(2), 908-918. doi: 10.22034/cmde.2025.64267.2901
Nemat Nyamoradi; Karam Allali; Bashir Ahmad. "Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity". سامانه مدیریت نشریات علمی, 14, 2, 1405, 908-918. doi: 10.22034/cmde.2025.64267.2901
Nyamoradi, Nemat, Allali, Karam, Ahmad, Bashir. (1405). 'Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity', سامانه مدیریت نشریات علمی, 14(2), pp. 908-918. doi: 10.22034/cmde.2025.64267.2901
Nyamoradi, Nemat, Allali, Karam, Ahmad, Bashir. Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity. سامانه مدیریت نشریات علمی, 1405; 14(2): 908-918. doi: 10.22034/cmde.2025.64267.2901

Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity

Computational Methods for Differential Equations
مقاله 25، دوره 14، شماره 2، تیر 2026، صفحه 908-918    اصل مقاله (534.79 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64267.2901
نویسندگان
Nemat Nyamoradi* 1؛ Karam Allali2؛ Bashir Ahmad3
1Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.
2Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco.
3Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
چکیده
This paper studies the dynamics of a SAIR mathematical model that describes the interaction among susceptible, asymptomatic, symptomatic, and recovered individuals. Two general incidence functions describing the infection caused by the asymptomatic and symptomatic individuals are introduced. We also take into account a temporary immunity, that is, a proportion of the recovered individuals becomes susceptible again. The basic reproduction number $R_0$ depends on the general incidence functions. The local and global asymptotical stability for each equilibrium will depend on the basic reproduction number $R_0$. In precise terms, the disease-free equilibrium is locally and globally asymptotically stable when $R_0<1$, while   the endemic equilibrium is locally and globally asymptotic stable when $R_0>1$. The numerical simulation is performed for different incidence rate cases, such as bilinear, Beddington-DeAngelis, Crowley Martin, and non-monotonic incidence rate functions. The simulation results are found to agree with the theoretical endings.
کلیدواژه‌ها
SAIR mathematical model؛ Stability؛ Basic reproduction number؛ Periodic orbit
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