Journal of Statistical Theory and Practice

, Volume 2, Issue 2, pp 145–158 | Cite as

The Impact of Dispersion in the Number of Secondary Infections on the Probability of an Epidemic

  • Belinda BarnesEmail author
  • Niels G. Becker


Heterogeneity in communities is a key factor to consider when modelling the transmission of an infection or implementing strategies to control its transmission. Heterogeneity in the level of infectiousness of individuals can arise in a number of ways. For example, it can arise through the structure of a community with, say, households, through the nature of a disease that may include superspreaders and others who are hardly infectious (like SARS), or through mixing and behaviour patterns that can be altered by interventions. Lloyd-Smith et al. (Lloyd-Smith, Schreiber, Kopp and Getz (2005)) observed that, under certain specific assumptions, greater heterogeneity, leads to a greater probability of disease elimination. In this paper we explore the impact of heterogeneity on the probability of disease elimination more generally. We show that, for many commonly arising distributions in ecology and epidemiology, an increase in heterogeneity, when the mean is fixed, leads to a reduction in the probability of a local outbreak. This result has important consequences for health care strategies, such as choosing strategies that increase heterogeneity for the same mean level of infectivity thereby delaying, or possibly preventing, an outbreak. However, while broadly true, including for most offspring distributions common to epidemic and ecological situations, the result is not in general true as we show by counter-examples for each of the types of heterogeneity considered. We conjecture a general principle determining when the result holds, but it remains an open question precisely when greater heterogeneity leads to an increase in the probability of extinction.


Heterogeneity in disease transmission Control of infectious disease Elimination of an infection Epidemic control Superspreaders Variance in disease transmission 

AMS Subject Classification

60J80 60J85 92D30 


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  1. Ball, F., Becker, N. G., 2006. Control of transmission with two types of infection. Mathematical Biosciences 200, 170–187.MathSciNetCrossRefGoogle Scholar
  2. Becker, N., 1974. On parametric estimation for mortal branching processes. Biometrika 61, 393–399.MathSciNetCrossRefGoogle Scholar
  3. Farrington, C. P., Grant, A. D., 1999. The distribution of time to extinction in subcritical branching processes: applications to outbreaks of infectious disease. Journal Applied Probability 36, 771–779.MathSciNetCrossRefGoogle Scholar
  4. James, A., Pitchford, J. W., Plank, M. J., 2007. An event based model of super-spreading in epidemics. Proceedings of the Royal Society B 274 (1610), 741-747.Google Scholar
  5. Johnson, N. L., Kotz, S., Kemp, A. W., 1993. Univariate Discrete Distributions. Wiley-Interscience, New York.zbMATHGoogle Scholar
  6. Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E., Getz, W. M., 2005. Superspreading and the effect of individual variation on disease emergence. Nature 438, 355–359.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  1. 1.National Centre for Epidemiology and Population HealthAustralian National UniversityCanberraAustralia

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