Nepomuceno Erivelton G, Peixoto Márcia L C, Lacerda Márcio J, Campanharo Andriana S L O, Takahashi Ricardo H C, Aguirre Luis A
Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei, Brazil.
Graduate Program in Electrical Engineering (PPGEE), Federal University of Minas Gerais, Belo Horizonte, Brazil.
SN Comput Sci. 2021;2(5):405. doi: 10.1007/s42979-021-00794-3. Epub 2021 Aug 7.
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.
在过去几十年里，传染病的最优控制受到了越来越多的关注。一般来说，成本状态变量和控制努力的组合已被用作成本指标。已经报道了许多重要成果。然而，似乎对流行病系统最优控制律的解释受到的关注较少。在本文中，我们应用庞特里亚金极大值原理来制定一种最优控制律，以尽量减少感染个体的数量和疫苗接种率。我们采用了SIR compartmental模型来测试我们的技术。我们已经表明，所提出的控制律可以为在无模型情况下制定控制策略提供一些见解。数值例子表明，与恒定疫苗接种相比，感染个体的数量减少了50%。在制定和解决最优控制问题时，并不总是需要关于易感、感染和康复个体数量的先验知识。在无模型情况下，提出了一种基于解析函数的策略，其中不需要对该情况有先验知识。这种见解在新冠疫苗研发出来之后也可能有用，因为它表明在全球范围内快速、广泛地接种疫苗可以尽量减少感染个体的数量，从而减少死亡人数。所考虑的方法能够比恒定疫苗接种控制方法更快地根除疾病。
