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### Calculation of disease dynamics in a population of households

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Ross, Joshua V., House, Thomas A. and Keeling, Matthew James.
(2010)
*Calculation of disease dynamics in a population of households.*
PLoS One, Vol.5
(No.3).
Article no. e9666.
ISSN 1932-6203

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Official URL: http://dx.doi.org/10.1371/journal.pone.0009666

## 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 (susceptible-infectious-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.

Item Type: | Journal Article |
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Subjects: | R Medicine > RA Public aspects of medicine |

Divisions: | Faculty of Science > Life Sciences (2010- ) > Biological Sciences ( -2010) Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Households -- Great Britain, Communicable diseases -- Transmission -- Mathematical models, Epidemiology -- Research, Disease susceptibility -- Research, Medical mapping |

Journal or Publication Title: | PLoS One |

Publisher: | Public Library of Science |

ISSN: | 1932-6203 |

Official Date: | 18 March 2010 |

Volume: | Vol.5 |

Number: | No.3 |

Number of Pages: | 9 |

Page Range: | Article no. e9666 |

Identification Number: | 10.1371/journal.pone.0009666 |

Status: | Peer Reviewed |

Access rights to Published version: | Open Access |

Funder: | Medical Research Council (Great Britain) (MRC), Wellcome Trust (London, England) |

Grant number: | G0701256 (MRC) |

References: | 1. Kermack W, McKendrick A (1927) A contribution to the mathematical theory |

URI: | http://wrap.warwick.ac.uk/id/eprint/2994 |

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