Skip to main content

The effect of heterogeneity on the spread of disease

  • Conference paper
Stochastic Processes in Epidemic Theory

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 86))

Abstract

In the formulations of standard epidemic models it is usually assumed that, as far as the spread of the disease is concerned, the community consists of homogeneous individuals who mix uniformly with one another. This is a simplifying assumption which helps to make the mathematics tractable. Empirical evidence suggests that in real world epidemics there is often variability among individuals. It is therefore important to determine how the introduction of heterogeneity among individuals is likely to affect any conclusions arrived at from consideration of the standard epidemic models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Athreya K. B. & Ney P. E., "Branching Processes," Springer-Verlag, Berlin, 1972.

    Book  MATH  Google Scholar 

  • Bailey N. T. J., The use of chain-binomials with a variable chance of infection for the analysis of intra-household epidemics, Biometrika 40 (1953), 279-286.

    MATH  Google Scholar 

  • Bailey N. T. J., Some problems in the statistical analysis of epidemic data (with discussion), J. R. Statist. Soc. B 17 (1955), 35-68.

    MATH  Google Scholar 

  • Ball F., Deterministic and stochastic epidemics with several kinds of susceptibles, Adv. Appl. Prob. 17 (1985), 1-22.

    Article  Google Scholar 

  • Barbour A. D., MacDonald's model and the transmission of bilharzia, Trans. Roy. Soc. Trop. Med. Hyg. 72 (1978), 6-15.

    Article  Google Scholar 

  • Becker N. G., Carrier-borne epidemics in a community consisting of different groups, J. Appl. Prob. 10 (1973), 491-501.

    Article  MATH  Google Scholar 

  • Becker N. G., On a general epidemic model, Theor. Pop. Bioi. 11 (1977a)), 23-36. (Correction: ibid 14, 498.)

    Article  Google Scholar 

  • Becker N. G., Estimation for the discrete time branching process with applications to epidemics,

    Google Scholar 

  • Biometrics 33 (1977b), 515-522.

    Google Scholar 

  • Becker N. G., An epidemic chain model, Biometrics 36 (1980), 249-254.

    Article  MATH  MathSciNet  Google Scholar 

  • Cane V. & McNamee R., The spread of infection in a heterogeneous population, J. Appl. Prob. 19 A (1982), 173-184.

    Article  MathSciNet  Google Scholar 

  • Dietz K., Models for vector-borne parasitic diseases, in: Vito Volterra Symposium on Mathematical

    Google Scholar 

  • Models in Biology, ed. C. Barigozzi, Lecture Notes in Biomathematics 39 (1980), 264-277. Berlin: Springer-Verlag

    Google Scholar 

  • Griffiths D. A., Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease, Biometrics 29 (1973), 637-648.

    Article  Google Scholar 

  • Hougaard P., Life table methods for heterogeneous populations: Distributions describing the heterogeneity, Biometrika 71 (1984), 75-83.

    Article  MATH  MathSciNet  Google Scholar 

  • Isham V., Mathematical modelling of the transmission dynamics of HIV infection and AIDS: a review, J. R. Statist. Soc. A 151 (1988), 5-30.

    Article  MATH  MathSciNet  Google Scholar 

  • Karlin S. & Taylor H. M. M., “A First Course in Stochastic Processes,” Academic Press, New York, 1975.

    Google Scholar 

  • Lefevre C. & Malice M., Comparisons for carrier-borne epidemics in heterogeneous and homogeneous populations, J. Appl. Pro b. 25 (1988), 663-67 4.

    Google Scholar 

  • Muench H., “Catalytic Models in Epidemiology,” Harvard University Press, 1959. von Bahr B. & Martin-Lof A., Threshold limit theorems for some epidemic processes, Research

    Google Scholar 

  • Report 108, Inst. for Forsiikringsmatematik och Matematisk Statistik, University of Stockholm (1978).

    Google Scholar 

  • Weiss G. H., On the spread of epidemics by carriers, Biometrics 21 (1965), 481-490.

    Article  Google Scholar 

  • Whittle P., The outcome of a stochastic epidemic-a note on Bailey's paper, Biometrika 42 (1955), 116-122.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Becker, N., Marschner, I. (1990). The effect of heterogeneity on the spread of disease. In: Gabriel, JP., Lefèvre, C., Picard, P. (eds) Stochastic Processes in Epidemic Theory. Lecture Notes in Biomathematics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10067-7_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-10067-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52571-4

  • Online ISBN: 978-3-662-10067-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics