Allocating limit medicine resources by mathematical modeling to control spreading of epidemic diseases is a very promising approach. Especially, how to use the existing partial data to efficiently control epidemic diseases is a interesting problem. When an epidemic disease is spreading, it is very urgent and essential to build a prediction and control model based on the real-time and partial data in order that decision makers find and implement the optimal strategy timely. In this paper, we developed a new framework for solving the problem. Our nonlinear model predictive control (NMPC) based on a discrete time susceptible-infected-removed dynamics (SIR) gave an attempt that aims at timely dealing with the condition. Our NMPC model minimizes the total number of infectious cases and the total cost, with the treatment beds capacity constraints and other constraints, especially, with a state observer based on the system output which can be sampled more easily and more accurately. Our control policy can be updated timely according to the current statistical data because our NMPC is a kind of closed-loop control algorithm based on our observer. We also presented some theoretical results on the state observer. Finally, we gave a numerical example to illustrate our algorithm.

通过数学模型分配有限的药物资源来控制流行病的传播是一种非常有前景的方法。特别是如何利用现有的部分数据有效控制流行病是一个有趣的问题。当一种流行病蔓延时，建立基于实时和局部数据的预测和控制模型是非常紧迫和必要的，以便决策者及时发现并实施最佳策略。在本文中，我们开发了一个新的框架来解决这个问题。我们的非线性模型预测控制 (NMPC) 基于离散时间易感-感染-去除动力学 ( SIR)) 进行了旨在及时处理情况的尝试。我们的 NMPC 模型最大限度地减少了感染病例的总数和总成本，具有治疗床容量约束和其他约束，特别是基于系统输出的状态观察器，可以更容易、更准确地采样。我们的控制策略可以根据当前的统计数据及时更新，因为我们的 NMPC 是一种基于我们的观察者的闭环控制算法。我们还介绍了一些关于状态观察器的理论结果。最后，我们给出了一个数值例子来说明我们的算法。