Distribution of infected mass in disease spreading in scale-free networks

TL;DR

This paper investigates how the distribution of infected mass during disease spreading varies in scale-free networks, revealing a transition from bimodal to smooth distributions depending on network density and infection probability.

Contribution

It provides a detailed analysis of the infected mass distribution in scale-free networks using the SIR model, highlighting the impact of network density and structure on disease dynamics.

Findings

Dense networks exhibit bimodal infected mass distribution.

Sparse networks show a smoothly decreasing infected mass distribution.

The disease can either die out quickly or persist, influenced by network structure.

Abstract

We use scale-free networks to study properties of the infected mass $M$ of the network during a spreading process as a function of the infection probability $q$ and the structural scaling exponent $\gamma$. We use the standard SIR model and investigate in detail the distribution of $M$, We find that for dense networks this function is bimodal, while for sparse networks it is a smoothly decreasing function, with the distinction between the two being a function of $q$. We thus recover the full crossover transition from one case to the other. This has a result that on the same network a disease may die out immediately or persist for a considerable time, depending on the initial point where it was originated. Thus, we show that the disease evolution is significantly influenced by the structure of the underlying population.