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

Document Type : Research Article

Authors

• G.P. Sahu
• A.S. Thakur

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

10.22067/ijnao.2025.92605.1612

Abstract

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 nonpharmaceutical interventions. These strategies, extensively covered by the media, were vital in promoting preventive behaviors to limit viral transmission. This research introduces a new mathematical model, SAEIaIRU M , to analyze COVID-19’s transmission dynamics. It includes a saturation functional response to depict the media’s role in influencing public behavior. The control reproduction number (Rc) is determined, and both local and global stability of the disease-free equilibrium are analyzed. Using the least-squares 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 Rc. The study advances by for mulating 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. 

Keywords

• COVID-19
• Environmental transmission
• Saturated awareness
• Optimal control

Main Subjects

• Computational Mathematics

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