Adjusting non-pharmaceutical interventions based on hospital bed capacity using a multi-operator differential evolution

Without vaccines and medicine, non-pharmaceutical interventions (NPIs) such as social distancing, have been the main strategy in controlling the spread of COVID-19. Strict social distancing policies may lead to heavy economic losses, while relaxed social distancing policies can threaten public health systems. We formulate optimization problems that minimize the stringency of NPIs during the prevaccination and vaccination phases and guarantee that cases requiring hospitalization will not exceed the number of available hospital beds. The approach utilizes an SEIQR model that separates mild from severe cases and includes a parameter $\mu$ that quantifies NPIs. Payoff constraints ensure that daily cases are decreasing at the end of the prevaccination phase and cases are minimal at the end of the vaccination phase. Using a penalty method, the constrained minimization is transformed into a non-convex, multi-modal unconstrained optimization problem. We solve this problem using the improved multi-operator differential evolution, which fared well when compared with other optimization algorithms. We apply the framework to determine optimal social distancing strategies in the Republic of Korea given different amounts and types of antiviral drugs. The model considers variants, booster shots, and waning of immunity. The optimal $\mu$ values show that fast administration of vaccines is as important as using highly effective vaccines. The initial number of infections and daily imported cases should be kept minimum especially if the bed capacity is low. In Korea, a gradual easing of NPIs without exceeding the bed capacity is possible if there are at least seven million antiviral drugs and the effectiveness of the drug in reducing severity is at least 86%. Model parameters can be adapted to a specific region or country, or other infectious diseases. The framework can be used as a decision support tool in planning economic policies, especially in countries with limited healthcare resources.