Mathematical modeling of COVID-19 spread with media coverage and optimal control analysis

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 خرداد 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92605.1612

نویسندگان

Govind Prasad Sahu؛ Amit Singh Thakur^*

Center for Basic Sciences, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh, India.

چکیده

The COVID-19 pandemic, initiated by the SARS-CoV-2 virus, first emerged in Wuhan, China, and quickly propagated worldwide. In India, lacking immediate access to effective vaccines and antiviral drugs, the response primarily relied on non-pharmaceutical interventions (NPIs). These strategies, extensively covered by the media, were vital in promoting preventive behaviours to limit viral transmission. This research introduces a new mathematical model, $SAEI_aIRUM$, to analyze COVID-19's transmission dynamics. It includes a saturation functional response to depict the media's role in influencing public behaviour. The control reproduction number ($R_c$) is determined, and both local and global stability of the disease-free equilibrium are analyzed. Using the least-square method, the model fits daily case data from India from March 30, 2020, to January 24, 2021. We evaluate the impact of various control parameters on disease progression through numerical simulations and employ normalized forward sensitivity analysis to identify critical parameters affecting $R_c$. The study advances by formulating an optimal control problem, incorporating the cost of preventive actions as control variables. Findings indicate that an early optimal control strategy could lessen the severity of epidemic peaks by distributing their effects over a longer duration. Simulations demonstrate that combining four control measures outperforms a single or no control.

کلیدواژه‌ها

COVID-19؛ Environmental Transmission؛ Saturated Awareness؛ Optimal Control