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

Abstract

We study the combined effects of aging and links removal on epidemic dynamics in the Barabási-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 $p\ge p_c$, 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.

8 pages, 3 figures, revtex, corrected Ref.[11]