Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment

For decades, mathematical models have been used to predict the behavior of physical and biological systems, as well as to define strategies aiming at the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of the novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the objective is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. Two optimal control problems (mono- and multi-objective) to determine a strategy for vaccine administration in COVID-19 pandemic treatment are proposed. The first consists of minimizing the quantity of infected individuals during the treatment. The second considers minimizing together the quantity of infected individuals and the prescribed vaccine concentration during the treatment.

An inverse problem is formulated and solved in order to determine the parameters of the compartmental Susceptible-Infectious-Removed model. The solutions for both optimal control problems proposed are obtained by using Differential Evolution and Multi-objective Optimization Differential Evolution algorithms.

A comparative analysis on the influence related to the inclusion of a control strategy in the population subject to the epidemic is carried out, in terms of the compartmental model and its control parameters. The results regarding the proposed optimal control problems provide information from which an optimal strategy for vaccine administration can be defined.

The solution of the optimal control problem can provide information about the effect of vaccination of a population in the face of an epidemic, as well as essential elements for decision making in the economic and governmental spheres.