Effects of aging and links removal on epidemic dynamics in scale-free networks

TL;DR

This study investigates how aging effects and link removal influence epidemic spread in scale-free networks, revealing a threshold for epidemic outbreaks and how it depends on aging and network connectivity.

Contribution

It introduces a model combining node aging and link removal effects on epidemic dynamics in scale-free networks, providing detailed analysis of epidemic thresholds.

Findings

Existence of a critical link removal fraction $p_c$ for epidemic outbreak

Epidemic spread depends on the aging factor $eta$ and link removal fraction $p$

The function $p_c(eta)$ delineates local and global spreading regions

Abstract

We study the combined effects of aging and links removal on epidemic dynamics in the Barab\'{a}si-Albert scale-free networks. The epidemic is described by a susceptible-infected-refractory (SIR) model. The aging effect of a node introduced at time $t_{i}$ is described by an aging factor of the form $(t-t_{i})^{-\beta}$ in the probability of being connected to newly added nodes in a growing network under the preferential attachment scheme based on popularity of the existing nodes. SIR dynamics is studied in networks with a fraction $1-p$ of the links removed. Extensive numerical simulations reveal that there exists a threshold $p_{c}$ such that for $p \geq p_{c}$, epidemic breaks out in the network. For $p < p_{c}$, only a local spread results. The dependence of $p_{c}$ on $\beta$ is studied in detail. The function $p_{c}(\beta)$ separates the space formed by $\beta$ and $p$ into regions corresponding to local and global spreads, respectively.