Rajaei Arman, Raeiszadeh Mahsa, Azimi Vahid, Sharifi Mojtaba
Department of Mechanical Engineering, School of Engineering, Shiraz University, Shiraz, Iran.
Department of Computer Science & Engineering and IT, School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran.
J Process Control. 2021 Jun;102:1-14. doi: 10.1016/j.jprocont.2021.03.008. Epub 2021 Apr 12.
In this study, a nonlinear robust control policy is designed together with a state observer in order to manage the novel coronavirus disease (COVID-19) outbreak having an uncertain epidemiological model with unmeasurable variables. This nonlinear model for the COVID-19 epidemic includes eight state variables (susceptible, exposed, infected, quarantined, hospitalized, recovered, deceased, and insusceptible populations). Two plausible scenarios are put forward in this article to control this epidemic before and after its vaccine invention. In the first scenario, the social distancing and hospitalization rates are employed as two applicable control inputs to diminish the exposed and infected groups. However, in the second scenario after the vaccine development, the vaccination rate is taken into account as the third control input to reduce the susceptible populations, in addition to the two objectives of the first scenario. The proposed feedback control measures are defined in terms of the hospitalized and deceased populations due to the available statistical data, while other unmeasurable compartmental variables are estimated by an extended Kalman filter (EKF). In other words, the susceptible, exposed, infected, quarantined, recovered, and insusceptible individuals cannot be identified precisely because of the asymptomatic infection of COVID-19 in some cases, its incubation period, and the lack of an adequate community screening. Utilizing the Lyapunov theorem, the stability and bounded tracking convergence of the closed-loop epidemiological system are investigated in the presence of modeling uncertainties. Finally, a comprehensive simulation study is conducted based on Canada's reported cases for two defined timing plans (with different treatment rates). Obtained results demonstrate that the developed EKF-based control scheme can achieve desired epidemic goals (exponential decrease of infected, exposed, and susceptible people).
在本研究中，设计了一种非线性鲁棒控制策略并结合一个状态观测器，以应对新型冠状病毒肺炎（COVID - 19）疫情，该疫情具有一个流行病学模型不确定且存在不可测变量的情况。这个COVID - 19疫情的非线性模型包括八个状态变量（易感人群、暴露人群、感染人群、隔离人群、住院人群、康复人群、死亡人群和不易感人群）。本文提出了两种合理的情景，用于在疫苗发明前后控制疫情。在第一种情景中，采用社交距离措施和住院率作为两个适用的控制输入，以减少暴露人群和感染人群。然而，在疫苗研发后的第二种情景中，除了第一种情景的两个目标外，还将疫苗接种率作为第三个控制输入，以减少易感人群。由于可获得统计数据，所提出的反馈控制措施是根据住院人群和死亡人群来定义的，而其他不可测的 compartments 变量则通过扩展卡尔曼滤波器（EKF）进行估计。换句话说，由于COVID - 19在某些情况下的无症状感染、其潜伏期以及缺乏足够的社区筛查，易感、暴露、感染、隔离、康复和不易感个体无法被精确识别。利用李雅普诺夫定理，研究了在存在建模不确定性的情况下闭环流行病学系统的稳定性和有界跟踪收敛性。最后，基于加拿大报告的病例，针对两个定义的时间计划（具有不同的治疗率）进行了全面的模拟研究。获得的结果表明，所开发的基于EKF的控制方案能够实现期望的疫情目标（感染、暴露和易感人群的指数下降）。
