论文标题
通过筛查新囚犯对监狱人口中疾病的最佳控制
Optimal control of diseases in prison populations through screening policies of new inmates
论文作者
论文摘要
在本文中，我们研究了监狱人口中传染病的最佳控制问题。为了控制疾病在监狱中的传播，我们考虑了一种主动的案例调查策略，包括在入口点筛查一定比例的新囚犯，然后根据该程序的结果进行治疗。然后，控制变量在于应用于新囚犯的筛选覆盖范围。疾病动力学是由SIS（易感感染感染）模型建模的，通常用于表示感染后不赋予免疫力的疾病。我们确定了最佳策略，该策略可以最大程度地减少入口处筛查/治疗成本与在给定时间范围内维持受感染者在监狱内的成本。使用Pontryagin的最大原理和汉密尔顿 - 雅各比 - 贝尔曼方程，除其他工具外，我们提供了最佳反馈控制的完整综合，由爆炸式策略组成，最多有两个切换时间，没有奇异的弧形轨迹，表征了不同的配置文件，取决于模型参数。
In this paper, we study an optimal control problem of a communicable disease in a prison population. In order to control the spread of the disease inside a prison, we consider an active case-finding strategy, consisting on screening a proportion of new inmates at the entry point, followed by a treatment depending on the results of this procedure. The control variable consists then in the coverage of the screening applied to new inmates. The disease dynamics is modeled by a SIS (susceptible-infected-susceptible) model, typically used to represent diseases that do not confer immunity after infection. We determine the optimal strategy that minimizes a combination between the cost of the screening/treatment at the entrance and the cost of maintaining infected individuals inside the prison, in a given time horizon. Using the Pontryagin Maximum Principle and Hamilton-Jacobi-Bellman equation, among other tools, we provide the complete synthesis of an optimal feedback control, consisting in a bang-bang strategy with at most two switching times and no singular arc trajectory, characterizing different profiles depending on model parameters.
