The spread of infections on evolving scale-free networks

TL;DR

This paper rigorously analyzes how the spread of infections on evolving scale-free networks exhibits a phase transition at a power-law exponent of four, contrasting static networks and mean-field models, highlighting the impact of temporal variability.

Contribution

It provides the first rigorous proof of a phase transition in infection survival on evolving scale-free networks, showing the critical exponent is four, unlike static models.

Findings

Infection survives long for all rates when exponent < 4.

For exponent > 4, infection dies out quickly at low rates.

Temporal variability affects both infection spread and metastability.

Abstract

We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most like the square root of the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast to that of the contact process on the corresponding static model, where there is no phase transition, as well as that of a classical mean-field approximation, which has a phase transition at power-law exponent three. The new observation behind our result is that temporal variability of networks can simultaneously increase the rate at which the infection spreads in the network, and decrease the time which the infection spends in metastable states.