通过对新囚犯的筛查政策对监狱人口的疾病进行最优控制
Optimal control of diseases in prison populations through screening policies of new inmates
摘要：
本文研究了监狱人群传染病的最优控制问题。为了控制疾病在监狱内的传播，我们考虑采取积极的病例发现战略，包括在入境点对一部分新囚犯进行筛查，然后根据这一程序的结果进行治疗。因此，控制变量包括适用于新囚犯的筛查范围。疾病动力学由SIS（易感-感染-易感）模型建模，该模型通常用于表示感染后不赋予免疫力的疾病。我们确定最优策略，在给定的时间范围内，最大限度地减少入口处的筛查/治疗成本和监狱内感染者的维持成本之间的组合。使用庞特里亚金最大值原理和Hamilton-Jacobi-Bellman方程，在其他工具中，我们提供了一个完整的合成的最佳反馈控制，包括在一个bang-bang策略，最多两个开关时间和没有奇异的电弧轨迹，不同的配置文件的特征取决于模型参数。
英文摘要：
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.
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