School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China.
Peking University Shenzhen Graduate School, Shenzhen 518055, China.
Chaos. 2023 Jul 1;33(7). doi: 10.1063/5.0151777.
Investigations on spreading dynamics based on complex networks have received widespread attention these years due to the COVID-19 epidemic, which are conducive to corresponding prevention policies. As for the COVID-19 epidemic itself, the latent time and mobile crowds are two important and inescapable factors that contribute to the significant prevalence. Focusing on these two factors, this paper systematically investigates the epidemic spreading in multiple spaces with mobile crowds. Specifically, we propose a SEIS (Susceptible-Exposed-Infected-Susceptible) model that considers the latent time based on a multi-layer network with active nodes which indicate the mobile crowds. The steady-state equations and epidemic threshold of the SEIS model are deduced and discussed. And by comprehensively discussing the key model parameters, we find that (1) due to the latent time, there is a "cumulative effect" on the infected, leading to the "peaks" or "shoulders" of the curves of the infected individuals, and the system can switch among three states with the relative parameter combinations changing; (2) the minimal mobile crowds can also cause the significant prevalence of the epidemic at the steady state, which is suggested by the zero-point phase change in the proportional curves of infected individuals. These results can provide a theoretical basis for formulating epidemic prevention policies.
近年来，由于 COVID-19 疫情的爆发，基于复杂网络的传播动力学研究受到了广泛关注，这有助于制定相应的预防政策。就 COVID-19 疫情本身而言，潜伏期和流动人群是导致其显著流行的两个重要且不可避免的因素。本文重点关注这两个因素，系统地研究了具有流动人群的多空间中的疫情传播。具体来说，我们提出了一个 SEIS（易感-暴露-感染-易感）模型，该模型基于具有活动节点的多层网络考虑了潜伏期，活动节点表示流动人群。推导出并讨论了 SEIS 模型的稳态方程和传染病阈值。通过综合讨论关键模型参数，我们发现：（1）由于潜伏期的存在，感染人群存在“累积效应”，导致感染曲线出现“峰”或“肩”，系统可以随着相对参数组合的变化而在三种状态之间切换；（2）即使最小规模的流动人群也可能导致疫情在稳态时显著流行，这可以通过感染人群的比例曲线中的零点相变来表明。这些结果可以为制定疫情防控政策提供理论依据。
