Please use this identifier to cite or link to this item:
Scopus Web of Science® Altmetric
Type: Journal article
Title: Hybrid Markov chain models of S-I-R disease dynamics
Author: Rebuli, N.
Bean, N.
Ross, J.
Citation: Journal of Mathematical Biology, 2017; 75(3):521-541
Publisher: Springer
Issue Date: 2017
ISSN: 0303-6812
Statement of
Nicolas P. Rebuli, N. G. Bean, J. V. Ross
Abstract: Deterministic epidemic models are attractive due to their compact nature, allowing substantial complexity with computational efficiency. This partly explains their dominance in epidemic modelling. However, the small numbers of infectious individuals at early and late stages of an epidemic, in combination with the stochastic nature of transmission and recovery events, are critically important to understanding disease dynamics. This motivates the use of a stochastic model, with continuous-time Markov chains being a popular choice. Unfortunately, even the simplest Markovian S-I-R model-the so-called general stochastic epidemic-has a state space of order [Formula: see text], where N is the number of individuals in the population, and hence computational limits are quickly reached. Here we introduce a hybrid Markov chain epidemic model, which maintains the stochastic and discrete dynamics of the Markov chain in regions of the state space where they are of most importance, and uses an approximate model-namely a deterministic or a diffusion model-in the remainder of the state space. We discuss the evaluation, efficiency and accuracy of this hybrid model when approximating the distribution of the duration of the epidemic and the distribution of the final size of the epidemic. We demonstrate that the computational complexity is [Formula: see text] and that under suitable conditions our approximations are highly accurate.
Keywords: Diffusion approximation
Fluid approximation
Markov population processes
Rights: © Springer-Verlag Berlin Heidelberg 2016
DOI: 10.1007/s00285-016-1085-2
Appears in Collections:Aurora harvest 3
Mathematical Sciences publications

Files in This Item:
File Description SizeFormat 
hdl_115564.pdfAccepted version671.24 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.