基于次模函数最小化的广义离散SIS传染病控制
Control of Generalized Discrete-time SIS Epidemics via Submodular Function Minimization
摘要：
本文研究了一类广义SIS传染病过程的一种新的控制方法。特别是，我们使用预测控制来设计最佳的保护资源分配策略，该策略平衡了快速消除流行病的需要和限制保护资源使用率的需要。我们预期，这种控制器可能有助于减轻生物疾病的传播，这些疾病不会使以前感染过的人获得免疫力，性传播感染就是一个突出的例子。从技术上讲，本文提供了一个新的贡献，证明了用于设计资源分配的特定组合最优控制问题有一个目标函数，这是次模块化的，所以可以解决多项式时间，尽管其组合性质。我们测试所提出的控制器的性能与数值模拟，并提供一些意见，为今后的工作方向。
英文摘要：
In this paper, we study a novel control method for a generalized SIS epidemic process. In particular, we use predictive control to design optimal protective resource distribution strategies which balance the need to eliminate the epidemic quickly against the need to limit the rate at which protective resources are used. We expect that such a controller may be useful in mitigating the spread of biological diseases which do not confer immunity to those who have been infected previously, with sexually transmitted infections being a prominent example of such. Technically, this paper provides a novel contribution in demonstrating that the particular combinatorial optimal control problem used to design resource allocations has an objective function which is submodular, and so can be solved in polynomial time despite its combinatorial nature. We test the performance of the proposed controller with numerical simulations, and provide some comments on directions for future work.
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