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Modelling the Dynamics and Optimal Control of COVID-19 Transmission in Mashhad, Iran | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 مرداد 1405 | ||
| نوع مقاله: Review Article | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.31929.1856 | ||
| نویسندگان | ||
| Atena Ghasemabadi* 1؛ Somayeh Ghiasi Hafazi2؛ Habib Allah Esmaeili3؛ Maryam Salari3 | ||
| 1Esfarayen University of Technology, Esfarayen, North Khorasan, Iran. | ||
| 2Department of Biostatistics, School of Health, Mashhad University of Medical Sciences, Mashhad, Iran. | ||
| 3Department of Statistics, Faculty of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran. | ||
| تاریخ دریافت: 06 خرداد 1405، تاریخ بازنگری: 25 خرداد 1405، تاریخ پذیرش: 25 خرداد 1405 | ||
| چکیده | ||
| This paper develops and analyzes a deterministic compartmental model for COVID-19 transmission in Mashhad, Iran, incorporating two time-dependent control functions: social distancing \(u(t)\) and home quarantine \(u_q(t)\). The model extends the classical SIR framework by including asymptomatic infections and a quarantined susceptible compartment. Using linearization, we derive the basic reproduction numbers \(R_0\) and \(R_1\) and prove that the disease-free equilibrium is locally asymptotically stable when \(R_0 < 1\) and \(R_1 < 1\). A Hopf bifurcation analysis shows that no Hopf bifurcation occurs under the proposed controls. The optimal control problem is formulated with a quadratic cost functional, and Pontryagin's maximum principle is applied to characterize the optimal controls. The resulting optimality system is solved numerically using MATLAB. Numerical simulations reveal that the optimal strategy consists of an intense but short-term home quarantine (\(u_q = 0.39\) applied only in the first month) combined with a gradually decreasing social distancing intervention, starting at \(0.35\) and decaying to negligible levels after approximately six months. This combined strategy sufficiently suppresses disease transmission that no further interventions are required after six months. The model provides a rigorous mathematical framework for assessing non-pharmaceutical interventions and offers quantitative insights for epidemic management in urban populations. | ||
| کلیدواژهها | ||
| COVID-19 modelling؛ Optimal control؛ Hopf bifurcation؛ Social distancing؛ Home quarantine | ||
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آمار تعداد مشاهده مقاله: 5 |
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