Highlights An optimal strategy for vaccine administration in COVID-19 pandemic treatment is determined considering both mono and multi-objective optimization context. The present work proposes a methodology to solve an inverse problem aiming to determine the SIR model parameters to simulate the COVID-19 pandemic. The results indicate that optimal control approaches based on epidemiological models can provide information to assist in mitigating the spread of disease.

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Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables, and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead, and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multiobjective optimization problem is formulated, considering the minimization of uncertainties associated with the estimation process and the maximization of the robustness parameter. To solve this problem, the Multiobjective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.

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