Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III)

The paper is concerned with the final slate and severity of a number of SIR epidemic models in finite populations. Two different classes of models are considered, namely the classical SIR Markovian models and the collective m odels introduced recently by the authors. First, by applying a simple marti ngale argument, it is shown that in both cases, there exists a common algeb raic structure underlying the exact law of the final state and severity. Th en, a unified approach to these statistics is developed by exploiting the t heory of Abel-Gontcharoff pseudopolynomials (presented in a preceding paper ).