Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation

TL;DR

This paper studies how saturation effects influence SIS epidemic spreading on heterogeneous networks, revealing a finite epidemic threshold in scale-free networks with degree-dependent transmission rates.

Contribution

It introduces a saturation function reducing infection transmission on highly connected nodes, leading to a finite epidemic threshold in scale-free networks, which contrasts with previous models.

Findings

Finite epidemic threshold in scale-free networks with saturation

Degree-dependent transmission affects epidemic prevalence

Simulation results align with mean field predictions

Abstract

We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution $P(k)$,including scale-free(SF) networks with power law distributions $P(k)\sim k^{-\gamma}$. Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function $C(k)$ which reduces the infection transmission rate $\lambda$ across an edge going from a node with high connectivity $k$. A mean field approximation with the neglect of degree-degree correlation then leads to a finite threshold $\lambda_{c}>0$ for SF networks with $2<\gamma \leq 3$. We also find, in this approximation, the fraction of infected individuals among those with degree $k$ for $\lambda$ close to $\lambda_{c}$. We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree-degree correlations.