Applications of occupancy urn models to epidemiology - Carlos M. Hernández-Suárez; Oliver Mendoza-Cano (Mathematical Biosciences and Engineering)
This paper shows how occupancy urn models can be used to derive usefulresults in epidemiology. First we show how simple epidemic models can be re-interpreted in terms of occupancy problems. We use this reformulation to derive an expression for the expected epidemic size, that is,the total number of infected at the end of an outbreak. We also use this approach to derive point and interval estimates of the Basic Reproduction Ratio, $R_{0}$. We show that this construction does not require that the underlying SIR model be a homogeneousPoisson process, leading to a geometric distribution for the number ofcontacts before removal, but instead it supports a generaldistribution. The urn model construction is easy to handle and represents a rich field for further exploitation.