Optimal Control of the Coronavirus Pandemic with Impacts of Implemented Control Measures

Abstract

This paper considers the current global issue of containing the coronavirus pandemic as an optimal control problem. The goal is to determine the most advantageous levels of effectiveness of the various control and preventive measures that should be attained in order to effectively reduce the burden of the disease within a relatively short time. Thus, the problem’s objective functional is constructed such that it minimizes the prevalence as well as the cost of implementing four control measures (namely personal protection, contact tracing and testing control for asymptotically infected individuals, detection control for symptomatic infected individuals and management control for hospitalized individuals) subject to a model for the disease transmission dynamics which incorporates four time-dependent control variables. The optimality system of the model is derived based on Pontryagin’s maximum principle. Thereafter, the resulting optimality system is solved numerically using the Runge-Kutta fourth order scheme with forward-backward sweep approach to evaluate the effect of combining at least any three of the control functions with personal protection always in use on the disease dynamics. Findings from our results show that the new cases and the prevalence of the disease can be remarkably reduced in a cost effective way by implementing any of the control strategies analysed in this work. However, the results of efficiency analysis suggest that a strategy which combines all the four preventive and control measures is most effective in reducing the disease burden in the population.