School of Computer Science, China University of Geosciences, Wuhan 430074, PR China.
Department of Mechanical Engineering (MESA-Lab), University of California, Merced, CA 95343, USA.
ISA Trans. 2021 Sep;115:143-152. doi: 10.1016/j.isatra.2021.01.023. Epub 2021 Jan 15.
This paper addresses the optimal vaccination and treatment control problems for regional approximate controllability of a new spatiotemporal epidemic model that is developed by afterwards adding at the basic susceptible-infected-recovered (SIR) epidemic system with the Caputo time-fractional derivative of order α∈(0,1] and the diffusion term in each compartment. The obtained results can be used by policy-makers in any nation to optimally plan the limited vaccination and treatment resources ahead of ongoing outbreaks. Toward this aim the Sakawa-type controller is introduced, which is a finite-dimensional controller that prevents and controls the spreading of infection. Using the semigroup theory, we provide a framework to analyze the sufficient conditions under which the considered time-fractional reaction-diffusion SIR epidemic system is regionally approximately controllable with the proposed control actuation architecture. An approach on finding the optimal solution that minimizes the cost of corresponding vaccination and treatment control programs for the studied regional controllability problem is then presented. Finally, we finish with numerical results to illustrate our theoretical results.
本文针对一个新的时空传染病模型的区域近似可控性问题，提出了最优的疫苗接种和治疗控制方案。该模型是在基本的易感-感染-恢复（SIR）传染病系统的基础上，通过在后添加具有 Caputo 时间分数阶导数的α∈(0,1]和每个区域的扩散项而得到的。所得到的结果可以供任何国家的决策者在疫情爆发前优化有限的疫苗接种和治疗资源的规划。为此，引入了 Sakawa 型控制器，这是一种有限维控制器，可以预防和控制感染的传播。利用半群理论，我们提供了一个框架来分析在所考虑的时分数阶反应扩散 SIR 传染病系统中，在所提出的控制激励架构下具有区域近似可控性的充分条件。然后，提出了一种寻找最小化研究区域可控性问题的相应疫苗接种和治疗控制方案成本的最优解的方法。最后，通过数值结果来说明我们的理论结果。
