Frank Ball: Susceptibility sets and the final outcome of stochastic SIR epidemic models

Abstract: This talk is concerned with exact results for the final outcome of stochastic SIR (Susceptible - Infective - Recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles who ultimately avoid infection by such an epidemic is shown to be intimately related to the concept of a susceptibility set. This connection leads to simple, probabilistically illuminating proofs of exact results concerning the total size and severity of a broad class of such SIR epidemics, in terms of Gontcharoff polynomials. The proofs extend easily to multitype SIR epidemics.