Epidemic threshold for the SIS model on networks

TL;DR

This paper derives an analytical expression for the epidemic threshold in the SIS model on random networks, linking infection probability to network topology and disease parameters.

Contribution

It introduces a novel analytical approach to determine the epidemic threshold by calculating reinfection probability using percolation theory.

Findings

Derived an explicit formula for the critical infection rate r_c

Linked reinfection probability to network topology and disease parameters

Provided insights into how network structure influences epidemic spreading

Abstract

We derive an analytical expression for the critical infection rate r_c of the susceptible-infectious-susceptible (SIS) disease spreading model on random networks. To obtain r_c, we first calculate the probability of reinfection, pi, defined as the probability of a node to reinfect the node that had earlier infected it. We then derive r_c from pi using percolation theory. We show that pi is governed by two effects: (i) The requirement from an infecting node to recover prior to its reinfection, which depends on the disease spreading parameters; and (ii) The competition between nodes that simultaneously try to reinfect the same ancestor, which depends on the network topology.