Understanding polynomial epidemic spread in social networks

Title: Understanding polynomial epidemic spread in social networks

Abstract: While most epidemics spread exponentially (like COVID-19) in the early stages, some epidemics spread polynomially (like monkeypox or ebola in west Africa). However, most models of epidemic spread on random graphs that model social networks predict either exponential spread or no spread at all, independently of parameters corresponding to e.g. the structure of the network or the virulence of the disease. We propose a graph-theoretic explanation for the phenomenon of polynomial spread with two ingredients. First, we require a random graph model capable of accurately modelling both local structure (e.g. clustering) and global structure (e.g. the small-world phenomenon and a scale-free power-law degree distribution). Second, we require a small transmission penalty on high-degree vertices. With both of these ingredients in place, we are able to rigorously prove phase transitions in average infection time from polynomial spread to (at least quasi-)exponential spread and from exponential spread to unphysical “explosion” in an SI model. The talk will not assume any prior background in the area, and it will begin with a self-contained introduction to both the properties of social networks in general and to the specific family of models we use.