Slow epidemic extinction in populations with heterogeneous infection rates

TL;DR

This study investigates how heterogeneity in contact intensities influences epidemic dynamics, revealing that highly interactive groups can cause extremely slow epidemic extinction, akin to Griffiths phases, with implications for disease control.

Contribution

It demonstrates that heterogeneity in contact rates leads to slow epidemic decay and identifies the role of highly interactive groups in prolonging outbreaks, supported by mean-field and percolation models.

Findings

Slow decay of infection due to heterogeneity

Identification of Griffiths-like phases in epidemic spreading

Accurate modeling of transition lines with mean-field and percolation approaches

Abstract

We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is endowed with an infection rate $\beta_{ij} = \lambda w_{ij}$ proportional to the intensity of their contact $w_{ij}$, with a distribution $P(w_{ij})$ taken from face-to-face experiments analyzed in Cattuto $et\;al.$ (PLoS ONE 5, e11596, 2010). We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter $\lambda$. Using a distribution of width $a$ we identify two large regions in the $a-\lambda$ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemic alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small $a$) and strong (large $a$) disorder, respectively.