Susceptible-Infected-Susceptible Model with Mitigation on Scale-Free Networks

TL;DR

This paper models infectious disease spread on scale-free networks using a mean-field approach that includes mitigation effects, revealing complex behaviors like non-monotonic infection probabilities and reversed prevalence trends.

Contribution

It introduces a nonlinear mitigation mechanism into the SIS model on scale-free networks, uncovering new epidemic dynamics and behaviors not seen in standard models.

Findings

Mitigation causes a maximum in the probability of links to infected nodes at finite infection rates.

Overall prevalence increases monotonically with transmission rate despite mitigation effects.

High transmission rates reverse the usual prevalence trend related to degree exponent.

Abstract

We investigate infectious disease spreading on scale-free networks using a heterogeneous mean-field approach applied to the susceptible-infected-susceptible model, incorporating a mitigation factor. Individual heterogeneity is incorporated through a power-law distribution, while a mitigation factor accounts for behavioral responses and external effects that effectively reduce transmission from infected individuals. This mechanism, inspired by Malthus-Verhulst-type constraints, introduces a nonlinear saturation effect that encodes self-limiting dynamics in a tractable way. Analytical results are supported by stochastic simulations. We find that the mitigation factor induces a nontrivial behavior in the probability that a link points to an infected node, which develops a maximum at finite infection rates. In contrast, the overall prevalence remains a monotonically increasing function of the transmission rate. Additionally, the mitigation mechanism leads to an inversion in the dependence of epidemic observables on the degree exponent at sufficiently high transmission rates. While in the standard model smaller exponents yield higher endemic prevalence, in the modified model this trend reverses, with larger exponents producing higher prevalence and increased infection probability along network links.