Epidemic spreading in scale-free networks

TL;DR

A dynamical model for the spreading of infections on scale-free networks is defined, finding the absence of an epidemic threshold and its associated critical behavior and this new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.

Abstract

The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and prevalence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalize data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.

Figures (3)

• Figure 1: Surviving probability for viruses in the wild. The 814 different viruses analyzed have been grouped in three main strains virus: file viruses infect a computer when running an infected application; boot viruses also spread via infected applications, but copy themselves into the boot sector of the hard-drive and are thus immune to a computer reboot; macro viruses infect data files and are thus platform-independent. It is evident in the plot the presence of an exponential decay, with characteristic time $\tau \simeq 14$ months for macro and boot viruses and $\tau \simeq 7$ months for file viruses.
• Figure 2: Persistence $\rho$ as a function of $1/\lambda$ for different network sizes: $N=10^5$ ($+$), $N=5 \times 10^5$ ($\Box$), $N=10^6$ ($\times$), $N=5 \times 10^6$ ($\circ$), and $N=8.5 \times 10^6$ ($\Diamond$). The linear behavior on the semi-logarithmic scale proves the stretched exponential behavior predicted for $\rho$. The full line is a fit to the form $\rho \sim\exp(-C/\lambda)$.
• Figure 3: a) Surviving probability $P_s(t)$ for a spreading rate $\lambda=0.065$ in scale-free networks of size $N=5 \times 10^5$ ($\Box$), $N=2.5 \times 10^4$ ($\Diamond$), $N=1.25 \times 10^4$ ($\triangle$), and $N=6.25 \times 10^3$ ($\circ$). The exponential behavior, following a sharp initial drop, is compatible with the data analysis of Fig. 1. b) Relative density $\rho_k$ versus $k^{-1}$ in a SF network of size $N=5 \times 10^5$ and spreading rate $\lambda=0.1$. The plot recovers the form predicted in Eq.(\ref{['dep']}).