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Stability analysis of SIR and SIRS models with non monotone incidence function and various mortality rates | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 25 خرداد 1405 اصل مقاله (461.22 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.31493.4645 | ||
| نویسندگان | ||
| Yahya Mohamed1؛ Aziza Ahmedou2؛ Mohamed Saad Bouh Elemine Vall* 2 | ||
| 1Quantitative Technics Department, Faculty of Legal and Economic Sciences, University of Nouakchott, Nouakchott, Mauritanie | ||
| 2Department of Applied Mathematics and Industrial Engineering, Professional University Institute, University of Nouakchott, Nouakchott, Mauritanie | ||
| تاریخ دریافت: 22 مرداد 1402، تاریخ بازنگری: 13 بهمن 1403، تاریخ پذیرش: 25 اسفند 1403 | ||
| چکیده | ||
| This study employs the Lyapunov method, the Poincar'e-Bendixson theorem, and the Dulac criterion to investigate the stability of SIR and SIRS models with non-monotone incidence and varying mortality rates. The analysis focuses on the stability properties of equilibrium points in the associated dynamical systems. For \( R_0 < 1 \), the eigenvalues of the Jacobian matrices at the equilibrium points have negative real parts, confirming their local asymptotic stability. When \( R_0 > 1 \), the global asymptotic stability of both the disease-free and endemic equilibrium points is demonstrated using a Lyapunov function and LaSalle's invariance principle. Additionally, an alternative approach leveraging the Poincar'e-Bendixson theorem and Dulac's criterion is introduced to establish global stability. Numerical simulations, performed with carefully chosen parameters, validate the analytical results and provide deeper insights into the system's behavior. | ||
| کلیدواژهها | ||
| SIR epidemic model؛ Non monotone incidence rate؛ Global stability؛ Direct Lyapunov method؛ Dulac's criterion؛ Poincar\'e Bendixson theorem | ||
| مراجع | ||
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