Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks

TL;DR

This paper studies how the mobility of infected individuals affects epidemic thresholds on scale-free networks, revealing non-monotonic and monotonic behaviors depending on diffusion type, with thresholds vanishing as network size grows.

Contribution

It introduces a fermionic SIS model with infected mobility on scale-free networks, analyzing the impact of diffusive processes on epidemic thresholds using mean-field theories.

Findings

Non-monotonic epidemic threshold dependence on diffusion rate in standard diffusion.

Monotonic decay of thresholds in biased diffusion.

Thresholds tend to zero as network size increases, influenced by diffusion rule and degree exponent.

Abstract

We investigate a fermionic susceptible-infected-susceptible model with mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions $P (k) \sim k^{-\gamma}$ of exponents $2<\gamma<3$. Two diffusive processes with diffusion rate $D$ of an infected vertex are considered. In the \textit{standard diffusion}, one of the nearest-neighbors is chosen with equal chance while in the \textit{biased diffusion} this choice happens with probability proportional to the neighbor's degree. A non-monotonic dependence of the epidemic threshold on $D$ with an optimum diffusion rate $D_\ast$, for which the epidemic spreading is more efficient, is found for standard diffusion while monotonic decays are observed in the biased case. The epidemic thresholds go to zero as the network size is increased and the form that this happens depends on the diffusion rule and degree exponent. We analytically investigated the dynamics using quenched and heterogeneous mean-field theories. The former presents, in general, a better performance for standard and the latter for biased diffusion models, indicating different activation mechanisms of the epidemic phases that are rationalized in terms of hubs or max $k$-core subgraphs.