论文标题
成本功能对最佳控制和成本效益的影响：控制传播感染作为案例研究
Impact of a cost functional on the optimal control and the cost-effectiveness: control of a spreading infection as a case study
论文作者
论文摘要
在最佳控制理论对医学和生物学问题的应用中，目标对控制本身的依赖性通常是一个争议的问题。在本文中，我们使用合理的简单\ emph {sir}和\ emph {seirs}流行模型探讨了依赖性的影响。为了定性地比较不同目标功能的结果，我们应用成本效益分析。我们的结果表明，至少对于相对廉价的控制，在生物学上可行范围内控制功率的变化不会显着影响最佳控制的形式和相应的最佳状态解决方案。此外，成本和有效性的影响甚至更少。同时，成本对状态变量的依赖性可能非常重要。
In applications of the optimal control theory to problems in medicine and biology, the dependency of the objective functional on the control itself is often a matter of controversy. In this paper, we explore the impact of the dependency using reasonably simple \emph{SIR} and \emph{SEIRS} epidemic models. To qualitatively compare the outcomes for different objective functionals, we apply the cost-effectiveness analysis. Our result shows that, at least for the comparatively inexpensive controls, the variation of the power at the controls in a biologically feasible range does not significantly affect the forms of the optimal controls and the corresponding optimal state solutions. Moreover, the costs and effectiveness are affected even less. At the same time, the dependency of the cost on the state variables can be very significant.
