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Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 اسفند 1403 اصل مقاله (12.9 M) | ||
| 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 interac- tion among susceptible, asymptomatic, symptomatic, and recovered individuals. Two general incidence functions describing the infection caused by the asymptomatic and symptomatic indi- viduals 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 de- pends 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 asymptotically stable when R 0 > 1. The numerical simu- lation 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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