Competing epidemics on complex networks

TL;DR

This paper models two competing diseases spreading simultaneously on complex networks, revealing a phase diagram with a transition between dominance and coexistence, influenced by stochastic fluctuations and network size.

Contribution

It introduces a combined analytical and numerical framework to analyze competing epidemics on networks, highlighting a novel dynamical transition and coexistence regimes.

Findings

Unusual dynamical transition between disease dominance and coexistence.

Final outcomes depend strongly on early stochastic fluctuations.

Large networks still exhibit visible effects of early stochasticity.

Abstract

Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance of one disease and dominance of the other as a function of their relative rates of growth. Close to this transition the final outcomes show strong dependence on stochastic fluctuations in the early stages of growth, dependence that decreases with increasing network size, but does so sufficiently slowly as still to be easily visible in systems with millions or billions of individuals. In most regions of the phase diagram we find that one disease eventually dominates while the other reaches only a vanishing fraction of the network, but the system also displays a significant coexistence regime in which both diseases reach epidemic proportions and infect an extensive fraction of the network.