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Type: Journal article
Title: On methods for studying stochastic disease dynamics
Author: Keeling, M.
Ross, J.
Citation: Journal of the Royal Society Interface, 2008; 5(19):171-181
Publisher: The Royal Society Publishing
Issue Date: 2008
ISSN: 1742-5689
Statement of
M.J Keeling and J.V Ross
Abstract: Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters.
Keywords: stochasticity
disease dynamics
time to extinction
total costs
Kolmogorov forward equations
parameter estimation
Rights: © 2007 The Royal Society
DOI: 10.1098/rsif.2007.1106
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Appears in Collections:Aurora harvest 5
Mathematical Sciences publications

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