پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 620 |
| تعداد مقالات | 9,100 |
| تعداد مشاهده مقاله | 67,311,857 |
| تعداد دریافت فایل اصل مقاله | 7,797,265 |
Global asymptotic stability of a networked fractional SIR model | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 16، شماره 4، تیر 2025، صفحه 15-26 اصل مقاله (2.16 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.31829.4722 | ||
| نویسندگان | ||
| Jiaming Li؛ Yajing Li* ؛ Ao Huang؛ Hongtao Fan؛ Jiawei Hao؛ Huiyuan Wang؛ Jiaping Cui | ||
| College of Science, Northwest A&F University, Yangling 712100, Shaanxi, P.R. China | ||
| تاریخ دریافت: 27 آذر 1402، تاریخ پذیرش: 14 فروردین 1403 | ||
| چکیده | ||
| In this paper, we consider a networked fractional SIR model. After proving the existence and uniqueness of the solution, we obtain the basic reproduction number, the disease-free equilibrium point and the endemic equilibrium point. By constructing the Lyapunov function, we show that the endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than 1, and the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1. Finally, numerical simulations are carried out to verify these theoretical results. Thus, the stability theory of Laplacian diffusion is extended to the graph Laplacian model. | ||
| کلیدواژه‌ها | ||
| Fractional SIR model؛ Network؛ Graph Laplacian operator؛ Global asymptotic stability؛ Lyapunov function | ||
| مراجع | ||
|
[1] R. Almeida, Analysis of a fractional SEIR model with treatment, Appl. Math. Lett. 84 (2018), 56–62. [2] R. Almeida, A.M.C. Brito da Cruz, N. Martins, M. Teresa, and T. Monteiro, An epidemiological MSEIR model described by the Caputo fractional derivative, Int. J. Dyn. Control 7 (2019), 776–784. [3] Y.L. Chen, F.W. Liu, Q. Yu, and T.Z. Li, Review of fractional epidemic models, Appl. Math. Model. 97 (2021), 281–307. [4] K. Diethelm, A fractional calculus based model for the simulation of an outbreak of dengue fever, Nonlinear Dyn. 71 (2013) 613–619. [5] J.R. Graef, L.G. Kong, A. Ledoan, and M. Wang, Stability analysis of a fractional online social network model, Math. Comput. Simul. 178 (2020), 625–645. [6] P.T. Karaji and N. Nyamoradi, Analysis of a fractional SIR model with general incidence function, Appl. Math. Lett. 108 (2020), 106499. [7] W.O. Kermack and A.G. McKendrick, A contribution to mathematical theory of epidemics, Proc. Royal Soc. A 115 (1927), 700–721. [8] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Boston, Elsevier, 2006. [9] T. Khan, Z. Ullah, N. Ali, and G. Zaman, Modeling and control of the hepatitis B virus spreading using an epidemic model, Chaos Solitons Fractals 124 (2019), 1–9. [10] Z.H. Liu and C.R. Tian, A weighted networked SIRS epidemic model, J. Differ. Equ. 269 (2020), 10995–11019. [11] W. Lin, Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appl. 332 (2007), 709–726. [12] R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, Epidemic processes in complex networks, Rev. Modern Phys. 87 (2015), 925–986. [13] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives, Translated from the 1987 Russian original, Gordon and Breach, Yverdon, 1993. [14] A. Slavik, Lotka-Volterra competition model on graphs, SIAM J. Appl. Dyn. Syst. 192 (2020), 725–762. [15] A.A. Stanislavsky, Memory effects and macroscopic manifestation of randomness, Phys. Rev. E 61 (2008), no. 5, 4752–4759. [16] C.R. Tian, Z.H. Liu, and S.G. Ruan, Asymptotic and transient dynamics of SEIR epidemic models on weighted networks, Eur. J. Appl. Math. 34 (2023), 238–261. [17] C.R. Tian, Q.Y. Zhang, and L. Zhang, Global stability in a networked SIR epidemic model, Appl. Math. Lett. 107 (2020), 106444. [18] P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endmic equlibria for compartmental models of diesease transmission, Math. Biosci. 180 (2002), 29–48. | ||
|
آمار تعداد مشاهده مقاله: 174 تعداد دریافت فایل اصل مقاله: 185 |
||