| تعداد نشریات | 32 |
| تعداد شمارهها | 868 |
| تعداد مقالات | 8,458 |
| تعداد مشاهده مقاله | 53,537,690 |
| تعداد دریافت فایل اصل مقاله | 9,676,132 |
Full and partial controllability of the Kermack-Mckendrick system with time- varying incidence rates | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 2، مرداد 2026، صفحه 673-697 اصل مقاله (2.16 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.31390.2818 | ||
| نویسندگان | ||
| Hamza El Mahjour* 1؛ Aadil Lahrouz2؛ Omar Zakary3؛ Mariam Redouane2 | ||
| 1MASI research Team Department of Information Systems and Communication ENSAT, Abdelmalek Esaadi University, Morocco | ||
| 2LAM research laboratory Department of Mathematics FSTT, Abdelmalek Essaadi University | ||
| 3Statistics and Modelling research team Department of Mathematics FSBM, University of Hassan II | ||
| چکیده | ||
| This study contributes to epidemic control literature by introducing a time-varying incidence rate and establishing global controllability of the nonlinear SIR system, offering a practical framework for adaptive control strategies. We derive explicit solutions for partial controllability, demonstrating the feasibility of controlling the infected population, providing guidance for outbreak management. Numerical methods exploiting an algorithmic approach achieve full control, targeting a desired state (Sd, Id). A novel hybrid method integrates analytical solutions with algorithmic optimization, leveraging explicit expressions for I(t) and S(t) to enhance precision and efficiency of epidemic control strategies, advancing adaptive management approaches | ||
| کلیدواژهها | ||
| Epidemic model؛ varying infection rate؛ full control؛ partial control؛ hybrid method | ||
| مراجع | ||
|
[1] V. Andreasen, The final size of an epidemic and its relation to the basic reproduction number, Bull. Math. Biol. 73 (2011) 2305–2321. [2] N. Baca¨er, A Short History of Mathematical Population Dynamics, Springer-Verlag London Lim ited, 2011. [3] R. Balderrama, J. Peressutti, J. Pinasco, F. Vazquez, C. Vega, Optimal control for a SIR epidemic model with limited quarantine, Sci. Rep. 12, (2022) 12583. [4] L. Boujallal, M. Elhia, O. Balatif, A novel control set-valued approach with application to epidemic models, J. Appl. Math. Comp. 65 (2021) 295–319. [5] F. Brauer, The Kermack–McKendrick epidemic model revisited, Math. Biosci. 198 (2005) 119–131. [6] V. Capasso, Mathematical Structures of Epidemic Systems. Springer Berlin Heidelberg, 1993. [7] A. Carvalho, S. Gonc¸alves, An analytical solution for the Kermack–McKendrick model, Phys. A 566 (2021) 125659. [8] D. Clancy, A. Piunovskiy, An explicit optimal isolation policy for a deterministic epidemic model, Appl. Math. Comput. 163 (2005) 1109–1121. [9] I. Dehaj, A. Dehaj, M. Aziz-Alaoui, M. Rachik, A new concept of controllability for a class of nonlinear continuous SIR systems, Chaos Solitons Fract. 192 (2025) 116013. [10] O. Diekmann, J. Heesterbeek, J. Metz, On the definition and the computation of the basic repro duction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990) 365–382. [11] P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002) 29–48 . [12] S. Effati, A. Mansoori, M. Eshaghnezhad, Linear quadratic optimal control problem with fuzzy variables via neural network, J. Exp. Theor. AI. 33(2) (2021) 283–296. [13] A. Haluszczynski, C. R¨ath, Controlling nonlinear dynamical systems into arbitrary states using machine learning, Sci. Rep. 11 (2021) 12991. [14] N. Hansen, The CMA evolution strategy: a comparing review, Towards a New Evolutionary Com putation: Studies in Fuzziness and Soft Computing, vol 192, Springer, Berlin, Heidelberg (2006) 75–102. [15] N. Hansen, The CMA evolution strategy: A tutorial, arXiv preprint arXiv:1604.00772 (2016) [16] P. Hartman, Ordinary Differential Equations, SIAM (2002). 697 [17] J. Heffernan, R. Smith, L. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface 2 (2005) 281–293. [18] R. Heydari Dastjerdi, G. Ahmadi, M. Dadkhah, A. Yari, Optimal control of infectious diseases using artificial neural networks, Control. Optim. Appl. Math. 8(2) (2023) 17–32. [19] R. Hirschorn, Controllability in nonlinear systems, J. Differ. Equ. 19 (1975) 46–61. [20] W. Kermack, A. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. Lond. Ser. A. 115 (1927) 700–721. [21] C. Michaud, Global burden of infectious diseases, Encyclopedia Microbio. 444 (2009). [22] R. Morton, K. Wickwire, On the optimal control of a deterministic epidemic, Adv. in Appl. Probab. 6 (1974) 622–635. [23] Y. Ozaki, S. Takenaga, M. Onishi, Global search versus local search in hyperparameter optimiza tion, Proc. IEEE Congr. Evol. Comput. (CEC) (2022) 1–9. [24] H. Sussmann, Nonlinear Controllability and Optimal Control, Routledge (2017). [25] M. Turkyilmazoglu, Explicit formulae for the peak time of an epidemic from the SIR model, Phys. D. 422 (2021) 132902. [26] K. Wickwire, Optimal control policies for reducing the maximum size of a closed epidemic—I. Deterministic dynamics, Math. Biosci. 30 (1976) 129–137. [27] O. Zakary, S. Bidah, M. Rachik, Optimizing infection trajectories: innovation in controllability of nonlinear SIR model, Rev. Mex. Ing. Biom´ed. 45 (2024) 151–171 | ||
|
آمار تعداد مشاهده مقاله: 281 تعداد دریافت فایل اصل مقاله: 239 |
||