Communications in Nonlinear Science and

Numerical Simulation

19 (2014) 1301-1312

Xiao-Pu Han, Zhi-Dan Zhao, Tarik Hadzibeganovic,

and Bing-Hong Wang

Epidemic spreading on hierarchical

geographical networks

with mobile agents

Hierarchical geographical traffic networks are critical for our understanding of  scaling laws in human trajectories. Here, we investigate the susceptible-infected epidemic process evolving on hierarchical networks in which agents randomly walk along the edges and establish contacts in network nodes. We employ a metapopulation modeling framework that allows us to explore the contagion spread patterns in relation to multi-scale mobility behaviors. A series of computer simulations revealed that a shifted power-law-like negative relationship between the peak timing of epidemics  $tau_0$  and population density, and a logarithmic positive relationship between  $tau_0$ and the network size,  can both be explained by the gradual enlargement of fluctuations in the spreading process. We employ a semi-analytical method to better understand the nature of these relationships and the role of pertinent demographic factors. Additionally, we provide a quantitative discussion of the efficiency of a border screening procedure in delaying epidemic outbreaks on hierarchical  networks, yielding a rather limited feasibility of this mitigation strategy but also its nontrivial dependence on population density, infector  detectability ,  and the  diversity of the susceptible region. Our results suggest that the interplay between the human spatial dynamics, network topology, and demographic factors can have important consequences for the global spreading and control of infectious diseases. These findings provide novel insights into the combined effects of human mobility and the organization of geographical networks on spreading processes, with important implications for both epidemiological research and health policy.

可动个体系统在层次性地理网络

上的流行病扩散研究

在传统流行病传播研究中，常常把社会网络视作稳定不变的静态结构。在此文中，作者基于对实际人们日常出行行为的实证研究结果，通过构建层次性地理网络来模拟强烈影响日常出行的交通系统结构，并假设大量个体在这个层次性网络中做随机运动并就近接触。在这样的假设下，这一复合种群模型可以再现出和实际高度一致的个体运动统计特性。基于这一框架，文章全面讨论了影响传播过程的各种因素，包括层次影响，传染源位置影响，人口密度影响和相应控制效应。研究发现，在这一系统中，对传播早期过程的微小扰动，其效应会随着传播进程而逐步放大，从而使对未来传播趋势的预测变得困难。

原文下载

CommunNonlinearSciNumerSimulat 19(2014)1301-1312 HanXP ZhaoZD Hadzibeganovic Wan.pdf