Epidemic spreading on hierarchical geographical networks with mobile agents

Abstract

a b s t r a c tHierarchical 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 s 0 and population density, and a logarithmic positive relationship between s 0 and the network size, can both be explained by the gradual enlargement of fluctuations in the spreading process. We employ a semianalytical 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. human motion, including ultraslow diffusion [3,4] and strikingly high predictability [6]. It is these abnormal properties that actually shape the difference between the natural human movements and the so-called Lévy flights [7,16].Several studies have been conducted so far to address the underlying mechanisms of the discovered abnormal properties of human spatial behavior. For the urban and intercity travels, Song et al. investigated the impact of exploration and preferential return on mobility patterns [8]. For the long-range travels, Han et al. [9] demonstrated that hierarchical geographical organization of traffic systems plays a crucial role in the emergence of scaling in human trajectories.An important, but less studied issue in this context, is the impact of the abnormal features of human motion on the dynamical evolution of spreading processes. For example, based on the mobile phone user data published in Ref.[3], Wang et al. analyzed the spreading of a mobile-phone-virus outbreak [10]. Ni and Weng [11] investigated the effects of heterogeneous spatial properties in metapopulation networks, and more recently, Belik et al. [12,13] reported on the dynamics of a spreading process under bidirectional mobility, that was further investigated by Balcan and Vespignani [14]. All of these studies converge on the finding that spat...

Modelling input-output flows of severe acute respiratory syndrome in mainland China

“…Network models incorporate geographic and social distances into topological networks. For example, Xu et al [19] investigated spatial proximity in epidemic transmission using scalefree networks, and Han et al [20] examined the effects of human mobility and network topology on the spread of infectious diseases using a hierarchical geographic network. Gravity models are used to capture the spatial features of interregional flows and disease transmission strength with regard to the geographic and economic aspects of epidemiology [21][22][23].…”

Randomness in the evolution of cooperation

“…For example, in addition to frequently studied mechanisms for the evolution of cooperation (Nowak, 2006), more realistic aspects, such as detailed psychological mechanisms (Stevens et al, 2011) and higher level of inter-individual variation, e.g. through different types of agent migrations (Fu and Nowak, 2013;Hadzibeganovic et al, 2009;Han et al, 2014;Helbing and Yu, 2009), diversity of reproduction rates and strategyselection time scales (Rong et al, 2013;Wu et al, 2009), varied learning motivation (Zhang et al, 2010), or other random factors (McNamara et al, 2004) need to be included in next model generalizations. Moreover, the influence of individual development (Gottlieb, 2002) and social learning (Laland et al, 2000;Zhang et al, 2012) on behavioral variation and the resulting novel adaptations should more explicitly be addressed in future computational models.…”

Modelling the global spread of diseases: A review of current practice and capability

“…OAG is an air travel intelligence company which has a large network of air travel data, also available for purchase (OAG). [1,2,3,4,5,6,7,10,11,12,14,16,17,18,19,20,22,23,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,48,50,51,52,53…”

“…Twenty articles perform a pragmatic form of validation. Fourteen [10], [49], [58] None 52 [2,3,7,8,9,11,15,16,17,22,25,27,28,29,30,33,35,37,38,39,40,44,46,47,50,52,54,55,56,59,60,61,62,63,64,65,66,71,72,75,78] Future predictions [6,14,24,32,34,41] Unclear [18,31,68,…”