Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19
Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19
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DOI：
10.1016/j.chaos.2020.110054
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发表时间：
2020-10-01
影响因子：
7.8
通讯作者：
Ibeas, Asier
中科院分区：
文献类型：
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作者：
Abbasi, Zohreh;Zamani, Iman;Ibeas, Asier
本文提出了一种考虑隔离个体(Q)的SEIAR模型，称为SQEIAR模型。SQEIAR模型的动力学由描述易感、隔离、暴露、感染、无症状和康复的人数的六个常微分方程式定义。本文的目的是通过对感染者的隔离和治疗两个行动来减少易感人群、感染人群、暴露人群和无症状人群的规模，从而消除感染。为了达到这一目的，提出了最优控制理论，在自由端最优时间控制的基础上，以最优代价控制传染病模型。利用庞特里亚金最大值原理对最优控制和最优终止时间进行了刻画。此外，我们还考虑了SQEIAR的脉冲流行病模型，以处理由于移民或旅行而可能导致的人口突然增加的问题。由于该模型适合于描述新冠肺炎大流行，因此特别关注了这种情况。在此基础上，给出了数值模拟结果，验证了理论结果的正确性，并应用于该传染病的具体数据。此外，新冠肺炎的数值计算还与埃博拉和流感等疾病进行了比较。此外，利用中国的实际数据，用辨识出的系统参数对控制器进行评估。最后，将经过中国数据估计参数调整的控制器应用于西班牙的实际数据，对两国的检疫和待遇政策进行了比较。(C)2020爱思唯尔有限公司。保留所有权利。
This paper presents a SEIAR-type model considering quarantined individuals (Q), called SQEIAR model. The dynamic of SQEIAR model is defined by six ordinary differential equations that describe the numbers of Susceptible, Quarantined, Exposed, Infected, Asymptomatic, and Recovered individuals. The goal of this paper is to reduce the size of susceptible, infected, exposed and asymptomatic groups to consequently eradicate the infection by using two actions: the quarantine and the treatment of infected people. To reach this purpose, optimal control theory is presented to control the epidemic model over free terminal optimal time control with an optimal cost. Pontryagin's maximum principle is used to characterize the optimal controls and the optimal final time. Also, an impulsive epidemic model of SQEIAR is considered to deal with the potential suddenly increased in population caused by immigration or travel. Since this model is suitable to describe the COVID-19 pandemic, especial attention is devoted to this case. Thus, numerical simulations are given to prove the accuracy of the theoretical claims and applied to the particular data of this infection. Moreover, numerical computations of the COVID-19 are compared with diseases like Ebola and Influenza. In addition, the controller is evaluated with system parameters identified by using actual data of China. Finally, the controller tuned with the estimated parameters of the Chinese data is applied to the actual data of Spain to compare the quarantine and treatment policies in both countries. (C) 2020 Elsevier Ltd. All rights reserved.