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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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[1] P. Adda and D. Bichara, Global stability for SIR and SIRS models with differential mortality, Int. J. Pure Appl. Math. 80 (2012), no. 3, 425-433.
[2] R.M. Anderson and R.M. May, Infectious Diseases of humans: Dynamics and Control, Oxford University Press, 1991.
[3] F. Brauer and C.C. Chavez, Mathematical Models in Population Biology and Epidemiology, Springer New York, 2012.
[4] S. Busenberg and K. Cooke, Vertically Transmitted Diseases: Models and Dynamics, Springer‑Verlag Berlin Heidelberg, Biomathematics, vol. 23, 1993.
[5] V. Capasso and G. Serio, A Generalization of the Kermack‑McKendrick deterministic epidemic model, Math. Biosci. 42 (1978), no. 1-2, 43-61.
[6] W.R. Derrick and P. van den Driessche, A disease transmission model in a nonconstant population, J. Math. Biol. 31 (1993), 495-512.
[7] O. Diekmann, J.A.P. Heesterbeek, and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), 365-382.
[8] F. Habott, A. Ahmedou, Y. Mohamed, and M.A. Sambe, Analysis of COVID‑19's dynamic behavior using a modified SIR model characterized by a nonlinear function, Symmetry 16 (2024), 1448.
[9] J.K. Hale, Ordinary Differential Equations, John Wiley & Sons, New York, 1969.
[10] H.W. Hethcote and P. van Den Driessche, Some epidemiological models with nonlinear incidence, J. Math. Bio. 29 (1991), 271-287.
[11] W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics‑I, Bull. Math. Bio. 53 (1991), 33-55.
[12] W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics‑II. The problem of endemicity, Bull. Math. Bio. 53 (1991), 57-87.
[13] W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics‑III. Further studies of the problem of endemicity, Bull. Math. Bio. 53 (1991), 89-118.
[14] A. Korobeinikov and G.C. Wake, Lyapunov Functions and Global stability for SIR, SIRS and SIS Epidemiological Models, Appl. Math. Lett. 15 (2002), 955-960.
[15] A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol. 69 (2007), 1871-1886.
[16] P.R. Kumar, S. Basu, D. Ghosh, P.K. Santra, and G.S. Mahapatra, Dynamical analysis of novel COVID‑19 epidemic model with non‑monotonic incidence function, J. Public Affairs 22 (2022), e2754.
[17] M.A. Kudus and A. Rahman, Analysis of COVID‑19 using a modified SLIR model with nonlinear incidence, Results Phys. 27 (2021), 104478.
[18] J.P. La Salle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.
[19] J.P. La Salle and S. Lefschetz, Stability by Liapunov's Direct Method with Applications, Research Institute for Advanced Studies, New York, Academic Press, London, 1961.
[20] W. Liu, S.A. Levin, and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol. 23 (1986), 187-204.
[21] Y. Mohamed, A. Ahmedou, and M.S.B. Elemine Vall, Global analysis for a modified SEIR model with general non‑linear incidence function, Nonlinear Dyn. 112 (2024), no. 13, 11661-11678.
[22] P. Van Den Driessche and J. Watmough, Reproduction numbers and sub‑threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), no. 1-2, 29-48.
[23] C. Vargas‑De‑León, On the global stability of SIS, SIR and SIRS epidemic models with standard incidence, Chaos Solitons Fractals (2011).
[24] C. Vargas‑De‑León, Stability Analysis of a SIS Epidemic Model with Standard Incidence, ForoRed‑Mat: Revista Electr. Contenido Matem. 28 (2011), no. 4, 1-11.
[25] D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci. 208 (2007), no. 2, 419-429. | ||
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