Spreading of infectious diseases on heterogeneous populations: multi-type 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.

arXiv comment28 pages, 4 figures

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• General and exact approach to percolation on random graphs
• Percolation on random networks with arbitrary k-core structure
• A multi-type branching process method for modelling complex contagion on clustered networks
• Node discovery problem for a social network
• Branching process approach for Boolean bipartite networks of metabolic reactions
• Pandemic Spread in Communities via Random Graphs
• Multiscale modeling of brain network organization
• Sandpile cascades on interacting tree-like networks
• Go Viral, or Not: Rate-Optimal Control for Resource-Constrained Branching Processes
• Aggregate-networks and p-cores of monoflow partially overlapped multilayer systems