Threshold effects for two pathogens spreading on a network

TL;DR

This paper explores how two competing pathogens spread on a network, revealing that their coexistence depends on specific intermediate network connectivity levels, with distinct phase transitions influencing epidemic outcomes.

Contribution

It introduces the concept of a coexistence threshold for two pathogens on networks, highlighting a new topological phase transition affecting epidemic spread.

Findings

Both pathogens spread only within a specific bond probability range.

A second, higher threshold marks a topological phase transition.

Coexistence occurs only between the epidemic and the coexistence thresholds.

Abstract

Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.