Exploring epidemic thresholds using spectral graph theory

Laura Zager, Department of Electrical Engineering and Computer Science, MIT

Over the last ten years, the field of mathematical epidemiology has piqued the interest of complex systems researchers, which has resulted in a tremendous volume of work exploring the consequences of population structure on disease propagation. Much of this research focuses on computing $R_0$, the basic reproductive ratio of an infection, which provides a structure-dependent threshold on whether a disease will become an epidemic. Computation of $R_0$ from mathematical models is a topic that is fraught with complications, and several different thresholds are often used interchangeably. This poster will clarify the relationship between different threshold criteria, discuss conditions under which topology and infection characteristics can be decoupled in the computation of a threshold, and connect current and classical threshold theorems to results in spectral graph theory.