一类单参数不确定性的流感峰值的分布鲁棒最优控制

Distributionally Robust Optimal Control of the Influenza Peak underSingle-Parameter Uncertainty

摘要: 流感是一类典型的季节性传染病，它的传播过程受到多种因素的影响，例如毒株类型、气候、易感 者行为模式、疫苗覆盖率与有效性等等。结合流感传播的不确定性与分布鲁棒优化的特点，本文 提出了一类具有矩约束的Chebyshev目标泛函的分布鲁棒优化控制模型，用于设计最优疫苗接种 策略以降低流感住院人数峰值。利用线性对偶理论，将内层问题与外层问题分别求解。其中内层 用线性规划方法求解，外层通过设计粒子群算法进行求解。最后通过实例验证了算法的有效性。

Abstract: Influenza is a typical seasonal infectious disease whose transmission dynamics are in- fluenced by various factors, such as virus strain type, climate conditions, behavioral patterns of susceptible individuals, vaccine coverage, and vaccine effectiveness. Con- sidering the uncertainty inherent in influenza transmission and the characteristics of distributionally robust optimization, this paper proposes a distributionally robust optimal control model with moment constraints and a Chebyshev-type objective func- tional. The model is designed to determine optimal vaccination strategies aimed at reducing the peak number of influenza-related hospitalizations. By employing linear duality theory, the inner and outer problems of the resulting optimization framework are solved separately. Specifically, the inner problem is solved using linear program- ming, while the outer problem is addressed through a particle swarm optimization algorithm. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach.