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

Abstract

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 an optimization problem that minimizes the stringency of NPIs during the prevaccination and vaccination phases and guarantees 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 µ 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 the penalty method, the constrained minimization is transformed into a non-convex, multi-modal unconstrained optimization problem, which is solved using a metaheuristic algorithm called the improved multi-operator differential evolution. 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 µ 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 severe bed capacity is low. In Korea, a gradual easing of NPIs without exceeding the severe bed capacity is possible if there are at least seven million antiviral drugs and the effectiveness of the drug in reducing disease severity is at least 86%. Model parameters can be adapted to a specific region or country, or other infectious disease. The framework can also be used as a decision support tool in planning practical and economic policies, especially in countries with limited healthcare resources.Mathematics Subject Classification34A55, 34H05, 90C26, 92-10