Yang Bo, Yu Zhenhua, Cai Yuanli
Department of Automation, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of China.
Institute of Systems Security and Control, College of Computer Science and Technology, Xi'an University of Science and Technology, Xi'an, 710054 People's Republic of China.
Nonlinear Dyn. 2022;109(1):265-284. doi: 10.1007/s11071-022-07244-6. Epub 2022 Mar 7.
In the absence of specific drugs and vaccines, the best way to control the spread of COVID-19 is to adopt and diligently implement effective and strict anti-epidemic measures. In this paper, a mathematical spread model is proposed based on strict epidemic prevention measures and the known spreading characteristics of COVID-19. The equilibria (disease-free equilibrium and endemic equilibrium) and the basic regenerative number of the model are analyzed. In particular, we prove the asymptotic stability of the equilibria, including locally and globally asymptotic stability. In order to validate the effectiveness of this model, it is used to simulate the spread of COVID-19 in Hubei Province of China for a period of time. The model parameters are estimated by the real data related to COVID-19 in Hubei. To further verify the model effectiveness, it is employed to simulate the spread of COVID-19 in Hunan Province of China. The mean relative error serves to measure the effect of fitting and simulations. Simulation results show that the model can accurately describe the spread dynamics of COVID-19. Sensitivity analysis of the parameters is also done to provide the basis for formulating prevention and control measures. According to the sensitivity analysis and corresponding simulations, it is found that the most effective non-pharmaceutical intervention measures for controlling COVID-19 are to reduce the contact rate of the population and increase the quarantine rate of infected individuals.
在缺乏特效药物和疫苗的情况下，控制新冠病毒传播的最佳方法是采取并切实执行有效且严格的防疫措施。本文基于严格的防疫措施以及新冠病毒已知的传播特征，提出了一个数学传播模型。分析了该模型的平衡点（无病平衡点和地方病平衡点）以及基本再生数。特别地，我们证明了平衡点的渐近稳定性，包括局部渐近稳定性和全局渐近稳定性。为了验证该模型的有效性，用它对中国湖北省一段时间内新冠病毒的传播进行了模拟。模型参数通过湖北省与新冠病毒相关的实际数据进行估计。为进一步验证模型的有效性，还用它对中国湖南省新冠病毒的传播进行了模拟。用平均相对误差来衡量拟合和模拟的效果。模拟结果表明，该模型能够准确描述新冠病毒的传播动态。还对参数进行了敏感性分析，为制定防控措施提供依据。根据敏感性分析及相应模拟，发现控制新冠病毒最有效的非药物干预措施是降低人群接触率和提高感染者隔离率。
