Weakening connections in heterogeneous mean-field models

TL;DR

This paper analyzes two variants of the SIS epidemic model on weighted scale-free networks, revealing how weakened connections influence epidemic thresholds and prevalence decay, with implications for epidemic mitigation strategies.

Contribution

It introduces a heterogeneous mean-field analysis of two SIS models with different transmission rules on weighted networks, highlighting conditions for positive infection thresholds.

Findings

Both models can have a positive infection threshold under certain parameters.

When the threshold vanishes, models show different algebraic decay behaviors.

Shared critical exponents indicate similar behavior near the threshold.

Abstract

Two versions of the susceptible-infected-susceptible epidemic model, which have different transmission rules, are analysed. Both models are considered on a weighted network to simulate a mitigation in the connection between the individuals. The analysis is performed through a heterogeneous mean-field approach on a scale-free network. For a suitable choice of the parameters, both models exhibit a positive infection threshold, when they share the same critical exponents associated with the behaviour of the prevalence against the infection rate. Nevertheless, when the infection threshold vanishes, the prevalence of these models display different algebraic decays to zero for low values of the infection rate.