SIS model of disease extinction on heterogeneous directed population networks

TL;DR

This paper investigates how heterogeneity in susceptibility and infectiousness affects disease extinction times on directed networks, revealing complex effects depending on correlation patterns and heterogeneity strength.

Contribution

It provides the first detailed analysis of how contact heterogeneity influences disease extinction dynamics on directed networks, combining analytical and numerical methods.

Findings

Heterogeneity can both accelerate and delay disease extinction.

Weak anticorrelation in heterogeneity increases disease stability.

Strong heterogeneity leads to different effects depending on correlation patterns.

Abstract

Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact patterns affect the emergence and stability of (meta)stable endemic states in networks. On the other hand, much less is known about longer time scale dynamics, such as disease extinction, whereby inherent process stochasticity and contact heterogeneity interact to produce large fluctuations that result in the spontaneous clearance of infection. Here we show that heterogeneity in both susceptibility and infectiousness (incoming and outgoing degree, respectively) has a non-trivial effect on extinction in directed contact networks, both speeding-up and slowing-down extinction rates depending on the relative proportion of such edges in a network, and on whether the heterogeneities in the incoming and outgoing degrees are correlated or anticorrelated. In particular, we show that weak anticorrelated heterogeneity can increase the disease stability, whereas strong heterogeneity gives rise to markedly different results for correlated and anticorrelated heterogeneous networks. All analytical results are corroborated through various numerical schemes including network Monte-Carlo simulations.