A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes

Abstract

This paper provides a global treatment of the final size distribution of Reed–Frost epidemic processes. Exact and asymptotic results are derived for both single and multipopulation situations. The key tool is a non-standard family of polynomials, introduced initially by Gontcharoff (1937) for one variable, revisited and extended here for several variables. The attractiveness of these polynomials will be enhanced in forthcoming works in the epidemic context as well as in other fields.