Message-passing theory for cooperative epidemics

Abstract

The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the phenomenology of epidemic spreading, leading for instance to abrupt transitions and hysteresis. Here we consider a simple model for two interacting pathogens on a network and we study it by using the message-passing approach. In this way we are able to provide detailed predictions for the behavior of the model in the whole phase-diagram for any given network structure. Numerical simulations on synthetic networks (both homogeneous and heterogeneous) confirm the great accuracy of the theoretical results. We finally consider the issue of identifying the nodes where it is better to seed the infection in order to maximize the probability of observing an extensive outbreak. The message-passing approach provides an accurate solution also for this problem.

8 pages, 6 figures

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• Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics
• Identifying influential subpopulations in metapopulation epidemic models using message-passing theory
• Interplay between degree and Boolean rules in the stability of Boolean networks
• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• Vaccination with partial transmission and social distancing on contact networks
• Critical behaviors of cascading dynamics on multiplex two-dimensional lattices