Simulation of Epidemic Spreading in Scale-free Networks

This post is part of a report I wrote for Complexity Science course offered by Professor Allen Downey at Olin College of Engineering. Full report is available here on Github.

Abstract

How do viruses in scale-free networks spread? What is the probability that a strain of virus survives over a period time? We answer these questions by replicating an experiment by Pastor-Satorras and Vespignani [1] which involves running the susceptible-infected-susceptible (SIS) model on Barabasi and Albert’s (BA) power law graphs. We apply their methodology to a Facebook dataset [4] to further explore their model on a real-world network. We show that viruses with any spreading rate reach a steady state of prevalence of ρ ~ exp(-C/λ) on scale-free networks. We conclude that scale-free networks are prone to epidemic spreading regardless of the spreading rate because there exists a finite prevalence for all network sizes, but the prevalence is kept low for a wide range of spreading rates because the prevalence decays exponentially as the spreading rate increases.