论文标题
SIR模型的根除时间问题
An eradication time problem for the SIR model
论文作者
论文摘要
我们考虑了一种易感，感染和恢复的感染疾病模型，该模型纳入了疫苗接种率。特别是，我们研究了选择疫苗接种率的问题，以便尽可能快地将受感染个体的数量减少到给定的阈值。这自然是时间优势控制的问题。我们将最佳时间解释为两个动态编程方程的解决方案，并为疫苗接种率提供最佳的必要条件。
We consider a susceptible, infected, and recovered infectious disease model which incorporates a vaccination rate. In particular, we study the problem of choosing the vaccination rate in order to reduce the number of infected individuals to a given threshold as quickly as possible. This is naturally a problem of time-optimal control. We interpret the optimal time as a solution of two dynamic programming equations and give necessary and sufficient conditions for a vaccination rate to be optimal.
