title: Computation of epidemic final size distributions.
abstract: We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is both computationally efficient and numerically stable. The algorithms we present are also physically transparent and so allow us to extend this method from the basic SIR model to a model with a phase-type infectious period and another with waning immunity. The underlying theory is applicable to many Markovian models where we wish to efficiently calculate hitting probabilities.
authors.affiliation: School of Mathematical Sciences, The University of Adelaide, Adelaide SA 5005, Australia. Electronic address: andrew.black@adelaide.edu.au.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Black
authors.affiliation: School of Mathematical Sciences, The University of Adelaide, Adelaide SA 5005, Australia.
authors.forename: J V
authors.initials: JV
authors.lastname: Ross
mesh_terms: D003141:Communicable Diseases / Q000635:transmission; D003198:Computer Simulation; D004198:Disease Susceptibility; D058872:Epidemics; D006801:Humans; D007109:Immunity; D007700:Kinetics; D008954:Models, Biological; D011336:Probability
keywords: Degree-of-advancement; Hitting probabilities; Markov chain; Waning immunity