Calculation of disease dynamics in a population of households

PloS One
J V RossM 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 (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 g...Continue Reading

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Citations

Mar 26, 2011·Interdisciplinary Perspectives on Infectious Diseases·Leon DanonMatthew C Vernon
Dec 2, 2010·Journal of Mathematical Biology·Lorenzo PellisChristophe Fraser
Feb 8, 2013·Journal of the Royal Society, Interface·Andrew J BlackJ V Ross
Jan 1, 2016·Journal of Theoretical Biology·Ben Adams
Apr 7, 2015·Epidemics·Frank BallGianpaolo Scalia Tomba
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Sep 10, 2011·Journal of Theoretical Biology·J V Ross
Jun 13, 2014·Bulletin of Mathematical Biology·Thomas House
Mar 1, 2011·Theoretical Population Biology·Kieran J Sharkey
Oct 25, 2011·Theoretical Population Biology·J R Artalejo, M J Lopez-Herrero
Sep 25, 2016·Epidemics·T M KinyanjuiT House
Jun 10, 2014·Journal of Theoretical Biology·Andrew J BlackJoshua V Ross
Apr 29, 2015·Mathematical Biosciences·Lorenzo PellisThomas House
Oct 19, 2017·PloS One·James N WalkerAndrew J Black
Nov 23, 2018·Proceedings of the National Academy of Sciences of the United States of America·Quan-Hui LiuAlessandro Vespignani
Jan 22, 2014·Reports on Progress in Physics·Kat RockMatt J Keeling
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Jan 7, 2021·Proceedings. Mathematical, Physical, and Engineering Sciences·Gabriele Pisano, Gianni Royer-Carfagni

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