Zhu Cheng-Cheng, Zhu Jiang
School of Science, Jiangnan University, Wuxi, Jiangsu 214122, P.R. China.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, P.R. China.
Chaos Solitons Fractals. 2021 Feb;143:110546. doi: 10.1016/j.chaos.2020.110546. Epub 2020 Dec 5.
As the COVID-19 epidemic has entered the normalization stage, the task of prevention and control remains very arduous. This paper constructs a time delay reaction-diffusion model that is closer to the actual spread of the COVID-19 epidemic, including relapse, time delay, home quarantine and temporal-spatial heterogeneous environment that affect the spread of COVID-19. These factors increase the number of equations and the coupling between equations in the system, making it difficult to apply the methods commonly used to discuss global dynamics, such as the Lyapunov function method. Therefore, we use the global exponential attractor theory in the infinite-dimensional dynamic system to study the spreading trend of the COVID-9 epidemic with relapse, time delay, home quarantine in a temporal-spatial heterogeneous environment. Using our latest results of global exponential attractor theory, the global asymptotic stability and the persistence of the COVID-19 epidemic are discussed. We find that due to the influence of relapse in the in temporal-spatial heterogeneity environment, the principal eigenvalue can describe the spread of the epidemic more accurately than the usual basic reproduction number . That is, the non-constant disease-free equilibrium is globally asymptotically stable when and the COVID-19 epidemic is persisting uniformly when . Combine with the latest official data of the COVID-19 and the prevention and control strategies of different countries, some numerical simulations on the stability and global exponential attractiveness of the spread of the COVID-19 epidemic in China and the USA are given. The simulation results fully reflect the impact of the temporal-spatial heterogeneous environment, relapse, time delay and home quarantine strategies on the spread of the epidemic, revealing the significant differences in epidemic prevention strategies and control effects between the East and the West. The results of this study provide a theoretical basis for the current epidemic prevention and control.
随着新冠疫情进入常态化阶段，防控任务依然十分艰巨。本文构建了一个更贴近新冠疫情实际传播情况的时滞反应扩散模型，其中包括复发、时滞、居家隔离以及影响新冠疫情传播的时空异质环境。这些因素增加了系统中方程的数量以及方程之间的耦合度，使得难以应用诸如李雅普诺夫函数法等常用的讨论全局动力学的方法。因此，我们利用无穷维动力系统中的全局指数吸引子理论，研究在时空异质环境下带有复发、时滞和居家隔离的新冠疫情传播趋势。利用我们在全局指数吸引子理论方面的最新成果，讨论了新冠疫情的全局渐近稳定性和持续性。我们发现，由于时空异质环境中复发的影响，主特征值 比通常的基本再生数 能更准确地描述疫情传播情况。也就是说，当 时，无病非恒定平衡点是全局渐近稳定的，当 时，新冠疫情是一致持续的。结合新冠疫情的最新官方数据以及不同国家的防控策略，给出了关于中国和美国新冠疫情传播稳定性和全局指数吸引性的一些数值模拟。模拟结果充分反映了时空异质环境、复发、时滞和居家隔离策略对疫情传播的影响，揭示了东西方在防疫策略和防控效果上的显著差异。本研究结果为当前的疫情防控提供了理论依据。
