AI 中文总结
研究有界区域上含分数阶扩散的非线性时空流行病学模型的区域最优控制问题，考虑疾病传播及两种控制方式，建立解的性质，证明最优控制存在并推导条件，发现集中接种疫苗可减轻疾病传播，给出数值模拟。
AI 中文摘要
本文研究了一个有界区域上涉及分数阶扩散的非线性时空流行病学模型的区域最优控制问题。考虑了一般形式的疾病传播以及疫苗接种和治疗两种控制方式。建立了所提系统全局时间解的存在唯一性，证明了存在使感染个体以及疫苗接种和治疗成本最小化的最优控制，并推导了最优性的必要条件。表明在选定区域集中接种疫苗可大幅减轻疾病传播，还给出了数值模拟。
英文摘要
This paper investigates a regional optimal control problem for a nonlinear spatio-temporal epidemiological model involving fractional diffusion on a bounded domain. In this work, we consider a general form of disease transmission, and two types of control, vaccination and treatment. We establish the existence and uniqueness of global-in-time solutions to our proposed system. We also prove the existence of an optimal control that minimizes the infected individuals as well as the cost of vaccination and treatment. The necessary conditions for optimality are derived. We show that concentrating vaccination in a selected region of the domain can substantially mitigate the spread of the disease. Numerical simulations are given.
