标题： 时空SEIQR传染病模型与接种、治疗和社会措施的最优控制 显示英文标题

标题： Spatiotemporal SEIQR Epidemic Modeling with Optimal Control for Vaccination, Treatment, and Social Measures

摘要： 本文介绍了一个由反应扩散偏微分方程组控制的时空SEIQR流行病模型，该模型结合了最优控制策略。 该模型捕捉了传染病在空间和时间上的传播动态。 它包括三个时间相关的控制变量：对易感个体的预防措施，对传染个体的隔离措施，以及对隔离个体的治疗措施。 研究有四个主要目标：(i) 使用分析半群理论证明全局强解的存在性、唯一性和正性，(ii) 通过泛函分析技术展示最优控制策略的存在性，(iii) 通过凸扰动方法和伴随方程推导一阶必要最优性条件，(iv) 进行数值模拟以评估不同控制干预组合的有效性。 模拟结果强调了结合药物和非药物干预措施的优势，以最小化疾病流行程度和控制相关费用。 显示英文摘要

摘要： This paper introduces a spatiotemporal SEIQR epidemic model governed by a system of reaction-diffusion partial differential equations that incorporates optimal control strategies. The model captures the transmission dynamics of an infectious disease across space and time. It includes three time-dependent control variables: preventive measures for susceptible individuals, quarantine for infectious individuals, and treatment for quarantined individuals. The study has four main objectives: (i) to prove the existence, uniqueness, and positivity of global strong solutions using analytic semigroup theory, (ii) to demonstrate the existence of optimal control strategies through functional analysis techniques, (iii) to derive first-order necessary optimality conditions via convex perturbation methods and adjoint equations, and (iv) to perform numerical simulations to assess the effectiveness of different combinations of control interventions. The simulation results emphasize the advantages of combining pharmaceutical and non-pharmaceutical interventions to minimize disease prevalence and control-related expenses.