Feng Shanshan, Luo Xiao-Feng, Pei Xin, Jin Zhen, Lewis Mark, Wang Hao
Department of Mathematics, North University of China, Taiyuan, Shanxi, 030 051, China.
College of Mathematics, Taiyuan University of Technology, Shanxi, Taiyuan, 030 024, China.
Infect Dis Model. 2022 Mar;7(1):212-230. doi: 10.1016/j.idm.2021.12.009. Epub 2022 Jan 5.
Classical epidemiological models assume mass action. However, this assumption is violated when interactions are not random. With the recent COVID-19 pandemic, and resulting shelter in place social distancing directives, mass action models must be modified to account for limited social interactions. In this paper we apply a pairwise network model with moment closure to study the early transmission of COVID-19 in New York and San Francisco and to investigate the factors determining the severity and duration of outbreak in these two cities. In particular, we consider the role of population density, transmission rates and social distancing on the disease dynamics and outcomes. Sensitivity analysis shows that there is a strongly negative correlation between the clustering coefficient in the pairwise model and the basic reproduction number and the effective reproduction number. The shelter in place policy makes the clustering coefficient increase thereby reducing the basic reproduction number and the effective reproduction number. By switching population densities in New York and San Francisco we demonstrate how the outbreak would progress if New York had the same density as San Francisco and vice-versa. The results underscore the crucial role that population density has in the epidemic outcomes. We also show that under the assumption of no further changes in policy or transmission dynamics not lifting the shelter in place policy would have little effect on final outbreak size in New York, but would reduce the final size in San Francisco by 97%.
经典流行病学模型假定为群体行为。然而，当互动并非随机时，这一假设就不成立了。随着近期新冠疫情的爆发以及随之而来的就地避难社交距离指令，必须对群体行为模型进行修正，以考虑有限的社交互动。在本文中，我们应用一种带有矩量闭合的成对网络模型来研究新冠病毒在纽约和旧金山的早期传播，并调查决定这两个城市疫情严重程度和持续时间的因素。具体而言，我们考虑人口密度、传播率和社交距离对疾病动态和结果的作用。敏感性分析表明，成对模型中的聚类系数与基本再生数和有效再生数之间存在强烈的负相关。就地避难政策使聚类系数增加，从而降低了基本再生数和有效再生数。通过交换纽约和旧金山的人口密度，我们展示了如果纽约拥有与旧金山相同的密度，疫情将如何发展，反之亦然。结果强调了人口密度在疫情结果中所起的关键作用。我们还表明，在政策或传播动态不再发生进一步变化的假设下，不解除就地避难政策对纽约最终疫情规模影响不大，但会使旧金山的最终规模减少97%。
