Single and Multiobjective Optimal Control of the COVID Pandemic Model Involving Hospitalizations and Non-Pharmaceutical Control Actions

Abstract

Objectives: In this paper, single and multiobjective optimal control is performed on a Corona Virus disease model involving hospitalizations and non-pharmaceutical intervention tasks to minimize the damage done by the virus. This model considers the effects of hospitalization and non-pharmaceutical interventions like quarantining and social distancing. Methods: This method does not use weighted functions but minimizes the distance from the utopia point. The utopia point is obtained by the single objective optimal control procedure and the multiobjective optimal control is performed by minimizing the distance from the Utopia point. The optimization program, Pyomo where the differential equations are automatically converted to a Nonlinear Program is used in conjunction with the state-of-the-art global optimization solver BARON. Results: Four single objective optimal control and one multiobjective optimal control problem were solved. The single optimal control involves minimizing the infections, death rate, and the cost of performing the control tasks and maximizing the recovered subjects. The multiobjective optimization involves minimizing the infections, death rate, and the cost of performing the control tasks and maximizing the recovered subjects at the same time. It is observed that the multiobjective optimal control is as effective as the single objective optimization in addition to having the advantage of controlling many variables. Conclusions: The multiobjective optimization involving the minimization of the distance from the Utopia point is very effective to obtain the best control profiles and enables one to maximize the number of recovered subjects while keeping the cost of performing the control tasks as low as possible. In fact, it is as effective as the single objective optimal control that involves maximizing the recovered subjects without dealing with the cost of performing the control tasks.