A re-entrant phase transition in the survival of secondary infections on networks

TL;DR

This paper investigates how secondary infections spread on networks, revealing that their survival depends on a timescale matching the primary infection's dynamics, with implications for understanding layered epidemic processes.

Contribution

It introduces a model linking secondary infection survival to primary infection dynamics on networks, highlighting the importance of timescale matching for epidemic persistence.

Findings

Secondary infection survival requires matching timescales with primary infection.

The model maps to a branching process in a time-sensitive environment.

Survival conditions depend on the interplay between primary and secondary epidemic dynamics.

Abstract

We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped to a branching process spreading in a random time-sensitive environment, determined by the dynamics of the underlying primary infection. When both epidemics follow the Susceptible-Infective-Recovered model, we show that in order to survive, it is necessary for the secondary infection to evolve on a timescale that is closely matched to that of the primary infection on which it depends.