title: Bimodal epidemic size distributions for near-critical SIR with vaccination.
abstract: We introduce a recursive algorithm which enables the computation of the distribution of epidemic size in a stochastic SIR model for very large population sizes. In the important parameter region where the model is just slightly supercritical, the distribution of epidemic size is decidedly bimodal. We find close agreement between the distribution for large populations and the limiting case where the distribution is that of the time a Brownian motion hits a quadratic curve. The model includes the possibility of vaccination during the epidemic. The effects of the parameters, including vaccination level, on the form of the epidemic size distribution are explored.
authors.affiliation: Mathematical and Theoretical Biology Institute, Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1801, USA. gordillo@math.uprm.edu
authors.forename: Luis F
authors.initials: LF
authors.lastname: Gordillo
authors.forename: Stephen A
authors.initials: SA
authors.lastname: Marion
authors.forename: Anders
authors.initials: A
authors.lastname: Martin-Löf
authors.forename: Priscilla E
authors.initials: PE
authors.lastname: Greenwood
mesh_terms: D000465:Algorithms; D015331:Cohort Studies; D003141:Communicable Diseases / Q000453:epidemiology; D003198:Computer Simulation; D003430:Cross-Sectional Studies; D004196:Disease Outbreaks / Q000706:statistics & numerical data; D006304:Health Status; D006305:Health Status Indicators; D006801:Humans; D015233:Models, Statistical; D011156:Population Density; D016008:Statistical Distributions; D013269:Stochastic Processes; D014611:Vaccination / Q000706:statistics & numerical data