Random graphs, infectious diseases and vaccination strategies

Tom Britton, Stockholm University

Abstract: Random graphs of various types can be used to describe the
social structures in a community. Given such a graph a simple epidemic
model can be defined in which individuals may infect a subgroup of its
acquaintances. In order to avoid a major epidemic outbreak the
community might be partly vaccinated. In the present talk we study
these types of problems with focus on graphs where the degree
distribution is heavy-tailed, but other than that completely
random. For such graphs we derive results determining under what
criteria a major outbreak may occur, and for what vaccination policies
such outbreaks are avoided.