Zhou Yinggao, Yang Kuan, Zhou Kai, Liang Yiting
School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People's Republic of China,
Acta Biotheor. 2014 Jun;62(2):171-81. doi: 10.1007/s10441-014-9216-x. Epub 2014 Apr 11.
The purpose of the paper is to use analytical method and optimization tool to suggest a vaccination program intensity for a basic SIR epidemic model with limited resources for vaccination. We show that there are two different scenarios for optimal vaccination strategies, and obtain analytical solutions for the optimal control problem that minimizes the total cost of disease under the assumption of daily vaccine supply being limited. These solutions and their corresponding optimal control policies are derived explicitly in terms of initial conditions, model parameters and resources for vaccination. With sufficient resources, the optimal control strategy is the normal Bang-Bang control. However, with limited resources, the optimal control strategy requires to switch to time-variant vaccination.
本文的目的是使用分析方法和优化工具，针对疫苗接种资源有限的基本SIR传染病模型，提出一个疫苗接种计划强度。我们表明，最优疫苗接种策略存在两种不同情况，并在每日疫苗供应有限的假设下，获得了使疾病总成本最小化的最优控制问题的解析解。这些解及其相应的最优控制策略是根据初始条件、模型参数和疫苗接种资源明确推导出来的。在资源充足的情况下，最优控制策略是常规的Bang-Bang控制。然而，在资源有限的情况下，最优控制策略需要切换为随时间变化的疫苗接种。
