Mathematical modeling and optimal control strategies for COVID-19: insights from initial public interventions in Thailand

Volume 41, Issue 2, pp 150--182 https://dx.doi.org/10.22436/jmcs.041.02.02

Publication Date: October 03, 2025 Submission Date: July 01, 2025 Revision Date: July 30, 2025 Accteptance Date: August 14, 2025

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Authors

C. Modnak - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand. A. Thongtha - Energy Policy and Planning Office, Ministry of Energy, Bangkok, 10400, Thailand. P. Kumpai - Ministry of Digital Economy and Society (MDES), the Government Complex, Bldg. C, Chaeng Watthana Rd., Laksi, Bangkok, 10210, Thailand.

Abstract

Since 2020, Thailand has been actively combating the COVID-19 pandemic. Initially, the country faced a significant surge in infections but has since adapted its strategies to manage the virus more effectively. During the fourth wave in 2021, Thailand categorized its population into eight groups: susceptible individuals, exposed, and infectious individuals, those treated in field hospitals, individuals receiving ICU care without oxygen support, those in ICU with oxygen support, individuals in critical condition, recovered individuals, and the deceased. Treatment in field hospitals is considered equivalent to care in standard hospitals.We aim to gain insight into the dynamics of the disease to better prepare for similar diseases in the future. To achieve this, we developed a mathematical framework consisting of eight differential equations, grounded in fundamental mathematical principles. We calculated the reproduction number and analyzed the initial intervention strategies implemented by the Thailand Public Health Administration. Numerical simulations of the optimal control problem highlight the critical role of preventing exposed and infectious individuals from infecting the susceptible population in curbing COVID-19 transmission. Additionally, our optimal control simulation indicates that vaccination policies should aim to inoculate approximately 46 percent (rather that 70 percent) of the population (at a daily rate of 0.2 percent) within the first 230 days of an outbreak to effectively halt disease transmission. However, this result is based on certain assumptions in the model simulations, and the outbreak was not the first wave. Therefore, the public health intervention program should be implemented as broadly as possible to cover the population effectively.

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Keywords

• Mathematical modeling
• Covid-19
• infectious disease modeling
• optimal control study
• COVID-19 Thailand modeling

MSC

•  92B05
•  37N25
•  34D20

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