Optimal non-pharmaceutical interventions considering limited healthcare system capacity and economic costs in the Republic of Korea

¹ Department of Mathematics, Konkuk University, Seoul 05029, Korea
² Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines

^* Corresponding author: junge@konkuk.ac.kr

Received: 24 May 2023
Accepted: 7 March 2024

Abstract

Due to the relatively low severity and fatality rates of the omicron variant of COVID-19, strict non-pharmaceutical interventions (NPIs) with high economic costs may not be necessary. We develop a mathematical model of the COVID-19 outbreak in Korea that considers NPIs, variants, medical capacity, and economic costs. Using optimal control theory, we propose an optimal strategy for the omicron period. To suggest a realistic strategy, we consider limited hospital beds for severe cases and incorporate it as a penalty term in the objective functional using a logistic function. This transforms the constrained problem into an unconstrained one. Given that the solution to the optimal control problem is continuous, we propose the adoption of a sub-optimal control as a more practically implementable alternative. Our study demonstrates how to strategically balance the trade-off between minimizing the economic cost for NPIs and ensuring that the number of severe cases in hospitals is manageable.