Hansen Elsa, Day Troy
Department of Mathematics and Statistics, Queen's University, Jeffery Hall, Kingston, ON, Canada.
J Math Biol. 2011 Mar;62(3):423-51. doi: 10.1007/s00285-010-0341-0. Epub 2010 Apr 21.
We extend the existing work on the time-optimal control of the basic SIR epidemic model with mass action contact rate. Previous results have focused on minimizing an objective function that is a linear combination of the cost associated with using control and either the outbreak size or the infectious burden. We instead, provide analytic solutions for the control that minimizes the outbreak size (or infectious burden) under the assumption that there are limited control resources. We provide optimal control policies for an isolation only model, a vaccination only model and a combined isolation-vaccination model (or mixed model). The optimal policies described here contain many interesting features especially when compared to previous analyses. For example, under certain circumstances the optimal isolation only policy is not unique. Furthermore the optimal mixed policy is not simply a combination of the optimal isolation only policy and the optimal vaccination only policy. The results presented here also highlight a number of areas that warrant further study and emphasize that time-optimal control of the basic SIR model is still not fully understood.
我们扩展了关于具有质量作用接触率的基本SIR传染病模型的时间最优控制的现有工作。先前的结果集中在最小化一个目标函数，该目标函数是与使用控制措施相关的成本与爆发规模或感染负担的线性组合。相反，我们在控制资源有限的假设下，为最小化爆发规模（或感染负担）的控制提供解析解。我们为仅隔离模型、仅疫苗接种模型以及联合隔离-疫苗接种模型（或混合模型）提供最优控制策略。这里描述的最优策略包含许多有趣的特征，特别是与先前的分析相比。例如，在某些情况下，仅隔离的最优策略不是唯一的。此外，最优混合策略不仅仅是仅隔离的最优策略和仅疫苗接种的最优策略的简单组合。这里给出的结果还突出了一些值得进一步研究的领域，并强调基本SIR模型的时间最优控制仍未得到充分理解。
