论文标题
对隔室流行的传输速率的最佳控制
Optimal control of the transmission rate in compartmental epidemics
论文作者
论文摘要
我们引入了一个普通微分方程的通用系统，其中包括一些在有限的时间范围内没有重要动态的封闭人群中流行病的经典和最新模型。该模型是矢量的，从某种意义上说，它是一个矢量值的状态函数，其组件代表各种暴露/感染的亚群，其控制函数的相应向量可能有所不同。在一般环境中，我们证明了状态方程系统的初始价值问题的适合性和积极性，以及在非常一般的成本功能下，对系统非线性部分系数的最佳控制问题的存在解决方案。当在所有控制变量中成本是超线性的，在间隔中可能不同的指数可能不同的指数时，我们还证明了最佳解决方案的独特性（1,2]。然后，我们考虑控制变量的线性成本并研究奇异弧的线性成本。在情况下给出了完整的详细信息n = 1 = 1，结果通过某些数字模拟来说明结果。
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the sense that it accounts for a vector valued state function whose components represent various kinds of exposed/infected subpopulations, with a corresponding vector of control functions possibly different for any subpopulation. In the general setting, we prove well-posedness and positivity of the initial value problem for the system of state equations and the existence of solutions to the optimal control problem of the coefficients of the nonlinear part of the system, under a very general cost functional. We also prove the uniqueness of the optimal solution for a small time horizon when the cost is superlinear in all control variables with possibly different exponents in the interval (1,2]. We consider then a linear cost in the control variables and study the singular arcs. Full details are given in the case n=1 and the results are illustrated by the aid of some numerical simulations.
