Persistence time of SIS infections in heterogeneous populations and networks

TL;DR

This paper derives simple asymptotic formulas for the mean persistence time of SIS infections in large heterogeneous populations or networks, showing that heterogeneity accelerates infection extinction.

Contribution

It provides the first explicit asymptotic expressions for SIS persistence time in heterogeneous settings, revealing heterogeneity's impact on infection duration.

Findings

Heterogeneity reduces the mean persistence time compared to homogeneous populations.

Greater heterogeneity leads to faster infection extinction.

Formulas apply to populations with varied susceptibility or network structures.

Abstract

For a susceptible-infectious-susceptible (SIS) infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to extinction of infection. Our model may be interpreted as describing an infection spreading through either (i) a population with heterogeneity in individuals' susceptibility and/or infectiousness; or (ii) a heterogeneous directed network. Using our asymptotic formulae, we show that such heterogeneity can only reduce (to leading order) the mean persistence time compared to a corresponding homogeneous population, and that the greater the degree of heterogeneity, the more quickly infection will die out.