论文标题
通过有限的非药物干预措施对爵士流行病的最佳控制
Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention
论文作者
论文摘要
我们考虑通过暂时降低人群中的接触率来控制SIR模型流行的问题。该控制采取了传染个体接触率的乘法降低的形式。只能在有限的时间间隔内应用控制，而目的是最大程度地减少长期限制中感染的个体总数，但要遵守对照的某些成本功能。我们首先考虑无成本方案，并通过分析确定最佳控制和解决方案。然后，当包括干预成本以及与可用的医疗资源相关的成本时，我们会研究解决方案。通过相关的Hamilton-Jacobi-Bellman方程的数值解决方案研究了示例。最后，我们提供了一些与当前大流行有关的例子。
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention is included, as well as a cost associated with overwhelming the available medical resources. Examples are studied through the numerical solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we provide some examples related directly to the current pandemic.
