新型冠状病毒肺炎(COVID-19)疫情在全球范围传播, 给人们的健康带来了严重的威胁。面对疫情发展预期数据, 我们需要在有限医疗资源的情况下确定疫情传播参数, 以指导主要防疫措施的实施力度。本文采用SIR类型的模型描述新冠肺炎疫情发展, 并建立多阶段最优控制模型确定疫情传播参数。为了高效确定参数取值, 我们建立多项式时间可计算的半定规划近似模型。基于世界卫生组织发布的数据, 我们求解近似模型, 得到描述给定时段内美国新冠肺炎疫情发展态势的疫情传播参数, 并分析疫情防控策略。

The coronavirus disease 2019 (COVID-19) spreads all over the world, and it makes serious threat to people's health. Being faced with the data of anticipated development of COVID-19, we need to determine the epidemic spreading parameters under limited medical resources to give guidance for implementation intensities of the main epidemic prevention and control measures. In this paper, we describe the development of COVID-19 based on the SIR model. What's more, we propose a multi-stage optimal control model to determine the epidemic spreading parameters. In order to determine the values of parameters efficiently, we construct an SDP approximation model which is a polynomial-time computable problem. Based on the data of COVID-19 published by WHO, we apply our approximation model to obtain the epidemic spreading parameters which describe the development of COVID-19 in the USA within a given period of time, and analyze the epidemic prevention and control strategies.