Spreading dynamics on heterogeneous populations: Multitype network approach

Abstract

I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population heterogeneity is taken into account by the agent's subdivision in types and the mixing matrix among them. I introduce a type-network representation for the mixing matrix allowing an intuitive understanding of the mixing patterns and the analytical calculations. Using an iterative approach I obtain recursive equations for the probability distribution of the outbreak size as a function of time. I demonstrate that the expected outbreak size and its progression in time are determined by the largest eigenvalue of the reproductive number matrix and the characteristic distance between agents on the contact-graph. Finally, I discuss the impact of intervention strategies to halt epidemic outbreaks. This work provides both a qualitative understanding and tools to obtain quantitative predictions for the spreading dynamics on heterogeneous populations.

Suppressing cascades of load in interdependent networks

“…Sandpile cascades have been extensively studied on isolated networks (35)(36)(37)(38)(39)(40)(41). On interdependent (or modular) networks, more basic dynamical processes have been studied (42)(43)(44)(45), but sandpile dynamics have not.…”

Epidemic fronts in complex networks with metapopulation structure

“…In some cases, it may be useful to conceptualize the topology as a network of networks, where agent-to-agent interactions and community-tocommunity interactions are both useful representations depending on the scale of resolution [8]. The latter has been successfully developed in ecology, with a network of interconnected populations referred to as a "metapopulation" [17,18].…”

“…In this paper, we expand on a possible avenue for addressing this question using a multitype generalization of random graphs with simple, meta-level topology [8,9], and construct a dynamical mean-field theory for the SIR infection model in multitype configuration model networks. Putting these together, we analyze the average infection dynamics and propagating front profile on a simple metapopulation composed of coupled population centers on a one-dimensional lattice and calculate the phenomenological transport properties of the system as functions of the underlying network's degree distributions.…”

Analysis and perturbation of degree correlation in complex networks

“…In biological and technological networks, high-degree nodes often preferably connect to low-degree nodes, which is referred to as -dissassortative mixing‖. The degree correlation has important influence on the topological properties of networks and may impact related problems on networks such as stability [6], the robustness of networks against attacks [7], the network controllability [8], the traffic dynamics on networks [9,10], the network synchronization [11][12][13], the spreading of information or infections and other dynamic processes [7,[13][14][15][16][17][18][19][20][21][22][23][24].…”

“…In biological and technological networks, high-degree nodes often preferably connect to low-degree nodes, which is referred to as -dissassortative mixing‖. The degree correlation has important influence on the topological properties of networks and may impact related problems on networks such as stability [6], the robustness of networks against attacks [7], the network controllability [8], the traffic dynamics on networks [9,10], the network synchronization [11][12][13], the spreading of information or infections and other dynamic processes [7,[13][14][15][16][17][18][19][20][21][22][23][24].In order to characterize and understand such preference of connections in complex networks, many statistical measures and network models have been introduced and investigated [2,3,[25][26][27][28][29][30][31][32][33][34][35][36]. For example, the average nearest neighbors' degree of nodes (ANND) [3] and the degree correlation coefficient…”