Optimal Non-Pharmaceutical Interventions Considering Limited Healthcare System Capacity and Economic Costs in the Republic of Korea

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 tradeoff between minimizing the economic cost for NPIs and ensuring that the number of severe cases in hospitals is manageable.