Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/66428
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Type: Journal article
Title: Calculation of disease dynamics in a population of households
Author: Ross, J.
House, T.
Keeling, M.
Citation: PLoS One, 2010; 5(3):1-9
Publisher: Public Library of Science
Issue Date: 2010
ISSN: 1932-6203
1932-6203
Statement of
Responsibility: 
Joshua V. Ross, Thomas House and Matt J. Keeling
Abstract: Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptibleinfectious- recovered-susceptible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks.
Keywords: Humans; Communicable Diseases; Prevalence; Models, Statistical; Markov Chains; Public Health; Disease Outbreaks; Population Density; Residence Characteristics; Models, Theoretical; Family Health
Rights: Copyright 2010 Ross et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
RMID: 0020110218
DOI: 10.1371/journal.pone.0009666
Appears in Collections:Mathematical Sciences publications

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