Optimal Control of Epidemiological SEIR models with L1-Objectives and Control-State Constraints
Optimal Control of Epidemiological SEIR models with L1-Objectives and Control-State Constraints
复制标题
具有 L1 目标和控制状态约束的流行病学 SEIR 模型的最优控制
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Pinho
中科院分区：
文献类型：
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作者：
H. Maurer;M. Pinho
最优控制是确定传染病疫苗接种策略的重要工具。对于水平传播的疾病，使用了SEIR com-bridges模型。大多数关于SEIR模型的文献都是关于控制变量（疫苗接种率）的二次成本函数。在本文中，我们认为L1型目标是线性的控制变量。施加了各种纯控制、混合控制状态和纯状态约束。对于所有的约束条件，我们讨论了最大值原理的必要最优性条件，并确定了满足必要最优性条件的最优控制策略，具有较高的精度。由于控制变量在哈密顿量中线性出现，最优控制是一个bang-bang弧，奇异弧和边界弧的串联。对于纯bang-bang控制，我们能够检查二阶充分条件。
Optimal control is an important tool to determine vaccination poli-cies for infectious diseases. For diseases transmitted horizontally, SEIR com-partment models have been used. Most of the literature on SEIR models deals with cost functions that are quadratic with respect to the control variable, the rate of vaccination. In this paper, we consider L 1 –type objectives that are linear with respect to the control variable. Various pure control, mixed control–state and pure state constraints are imposed. For all constraints, we discuss the necessary optimality conditions of the Maximum Principle and determine optimal control strategies that satisfy the necessary optimality con-ditions with high accuracy. Since the control variable appears linearly in the Hamiltonian, the optimal control is a concatenation of bang-bang arcs, singu-lar arcs and boundary arcs. For pure bang-bang controls, we are able to check second-order sufficient conditions.