Nepomuceno, Erivelton and Peixoto, Márcia L. C. and Lacerda, Márcio J. and Campanharo, Andriana S. L. O. and Takahashi, Ricardo H. C. and Aguirre, Luis A. (2021) Application of Optimal Control of Infectious Diseases in a Model-Free Scenario. SN Computer Science, 2 (5). ISSN 2662-995X

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Abstract

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin’s maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method.

Item Type:	Article
Keywords:	Optimal control; SIR model; Vaccination; Epidemiology; Complex systems; COVID-19;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16821
Identification Number:	https://doi.org/10.1007/s42979-021-00794-3
Depositing User:	Erivelton Nepomuceno
Date Deposited:	09 Jan 2023 14:51
Journal or Publication Title:	SN Computer Science
Publisher:	Springer
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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