Open AccessApplications of occupancy urn models to epidemiology
Author(s) -
Carlos Hernandez-Suarez,
Oliver Mendoza-Cano
Publication year - 2009
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2009.6.509
Subject(s) - occupancy , poisson distribution , basic reproduction number , interval (graph theory) , point process , distribution (mathematics) , computer science , poisson process , field (mathematics) , epidemic model , statistics , mathematics , demography , ecology , combinatorics , mathematical analysis , biology , population , sociology , pure mathematics
This paper shows how occupancy urn models can be used to derive useful results 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, R0 . We show that this construction does not require that the underlying SIR model be a homogeneous Poisson process, leading to a geometric distribution for the number of contacts before removal, but instead it supports a general distribution. The urn model construction is easy to handle and represents a rich field for further exploitation.