地方性感染的最优长期控制：随机SIS模型中的bang-bang阈值策略
Optimal long-run control of endemic infections: bang-bang threshold policies in a stochastic SIS model
AI总结：
针对随机SIS模型，研究地方性感染长期最优控制，提出bang-bang阈值策略以最小化社会成本，并严格验证其最优性。
AI中文摘要：
我们研究了随机易感-感染-易感（SIS）模型中地方性感染的长期最优干预策略。感染者比例作为一个带有随机波动的扩散过程演化，而控制变量$\zeta_t\in[0,\tilde{\zeta}_{max}]$代表公共卫生干预的强度，该干预在某个干预阈值$\tilde{\zeta}_{max}\in (0,1]$下减少传播。目标是最小化长期平均社会成本，在感染负担与干预成本之间取得平衡。在凹干预成本结构下，该问题可表述为一个遍历随机控制问题，其结构（在若干附加条件下）意味着最优干预属于bang-bang类型，即在感染水平的一个单一切换阈值处，在无干预与最大允许干预之间切换。我们构造候选值函数，严格验证了该单阈值情形下的最优性，并将结果与无控制时基础SIS动力学的灭绝和持续性质联系起来。在我们的框架中，该分析为流行病管理中常用的基于阈值的干预规则提供了严格的理论依据。
英文摘要：
We study long-run optimal intervention strategies for endemic infections in a stochastic susceptible-infected-susceptible (SIS) model. The proportion of infected individuals evolves as a diffusion process with random fluctuations, while a control variable $ζ_t\in[0,\tildeζ_{max}]$ represents the intensity of public health interventions that reduce transmission for some intervention threshold $\tildeζ_{max}\in (0,1]$. The objective is to minimize the long-run average societal cost, balancing the burden of infection against the costs of interventions. Under a concave intervention cost structure the problem can be formulated as an ergodic stochastic control problem, whose structure implies (under certain additional conditions) that optimal interventions are of bang-bang type, switching between no intervention and the maximal admissible intervention at a single switching threshold in the infection level. We construct candidate value functions, rigorously verify optimality in this single-threshold case, and relate the results to extinction and persistence properties of the underlying SIS dynamics in the absence of control. In our framework, the analysis provides a rigorous justification for the threshold-based intervention rules commonly used in epidemic management.
