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.How to predict and control mutually cooperative epidemics on a networked system is an outstanding problem of much interest. Previous attempts in this problem have assumed well-mixed populations and focused on the meanfield analysis. A full analysis of the cooperativity in epidemics at the level of single node is still lacking. In this work, we provide a message-passing approach in order to fully analyze cooperative epidemics on complex networks. We confirm the great accuracy of our theory with numerical simulations for both homogeneous and heterogeneous network structures. In addition, we reveal how to identify precisely influential spreaders in cooperative epidemics by using the message-passing equations.

Interplay between degree and Boolean rules in the stability of Boolean networks

“…Note that Eq. 2 can be interpreted as a percolation process with an occupation probability of q i [32][33][34].…”

Identifying influential subpopulations in metapopulation epidemic models using message-passing theory

“…We regard that the higher the probability and size of causing global epidemics, the higher the influential spreading nodes (e.g., cities) are. We propose a systematic way to identify the most influential subpopulations in a metapopulation model based on a message-passing (MP) approach [34,42,43]. With regard to advantages, the MP approach can be applied to a single network rather than an ensemble of networks, include a node-level analysis, and is based on a solid theoretical background [42].…”

Double transitions and hysteresis in heterogeneous contagion processes

“…Because the characteristics of individuals significantly vary in reality, the heterogeneity of adoption threshold can be widespread for many contagion phenomena. In addition, such a unified contagion model can be useful for analyzing the spread of epidemics of multiple interacting pathogens because interacting epidemics is indistinguishable from social complex contagion [34][35][36]. Therefore, generalized contagion processes integrating simple and complex contagions are crucial phenomena.…”