Skip to main content
Proceedings of the Royal Society B: Biological Sciences logoLink to Proceedings of the Royal Society B: Biological Sciences
. 2003 Jul 7;270(1522):1359–1364. doi: 10.1098/rspb.2003.2339

A new method for estimating the effort required to control an infectious disease.

M G Roberts 1, J A P Heesterbeek 1
PMCID: PMC1691377  PMID: 12965026

Abstract

We propose a new threshold quantity for the analysis of the epidemiology of infectious diseases. The quantity is similar in concept to the familiar basic reproduction ratio, R0, but it singles out particular host types instead of providing a criterion that is uniform for all host types. Using this methodology we are able to identify the long-term effects of disease-control strategies for particular subgroups of the population, to estimate the level of control necessary when targeting control effort at a subset of host types, and to identify host types that constitute a reservoir of infection. These insights cannot be obtained by using R0 alone.

Full Text

The Full Text of this article is available as a PDF (105.8 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Diekmann O., Heesterbeek J. A., Metz J. A. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol. 1990;28(4):365–382. doi: 10.1007/BF00178324. [DOI] [PubMed] [Google Scholar]
  2. Dye Christopher, Williams Brian G., Espinal Marcos A., Raviglione Mario C. Erasing the world's slow stain: strategies to beat multidrug-resistant tuberculosis. Science. 2002 Mar 15;295(5562):2042–2046. doi: 10.1126/science.1063814. [DOI] [PubMed] [Google Scholar]
  3. Esteva L., Vargas C. Analysis of a dengue disease transmission model. Math Biosci. 1998 Jun 15;150(2):131–151. doi: 10.1016/s0025-5564(98)10003-2. [DOI] [PubMed] [Google Scholar]
  4. Esteva L., Vargas C. Influence of vertical and mechanical transmission on the dynamics of dengue disease. Math Biosci. 2000 Sep;167(1):51–64. doi: 10.1016/s0025-5564(00)00024-9. [DOI] [PubMed] [Google Scholar]
  5. Feng Z., Velasco-Hernández J. X. Competitive exclusion in a vector-host model for the dengue fever. J Math Biol. 1997 May;35(5):523–544. doi: 10.1007/s002850050064. [DOI] [PubMed] [Google Scholar]
  6. Ferguson N. M., Donnelly C. A., Anderson R. M. The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions. Science. 2001 Apr 12;292(5519):1155–1160. doi: 10.1126/science.1061020. [DOI] [PubMed] [Google Scholar]
  7. Fulford G. R., Roberts M. G., Heesterbeek J. A. P. The metapopulation dynamics of an infectious disease: tuberculosis in possums. Theor Popul Biol. 2002 Feb;61(1):15–29. doi: 10.1006/tpbi.2001.1553. [DOI] [PubMed] [Google Scholar]
  8. Gandon S., Mackinnon M. J., Nee S., Read A. F. Imperfect vaccines and the evolution of pathogen virulence. Nature. 2001 Dec 13;414(6865):751–756. doi: 10.1038/414751a. [DOI] [PubMed] [Google Scholar]
  9. Gani R., Leach S. Transmission potential of smallpox in contemporary populations. Nature. 2001 Dec 13;414(6865):748–751. doi: 10.1038/414748a. [DOI] [PubMed] [Google Scholar]
  10. Haydon Daniel T., Cleaveland Sarah, Taylor Louise H., Laurenson M. Karen. Identifying reservoirs of infection: a conceptual and practical challenge. Emerg Infect Dis. 2002 Dec;8(12):1468–1473. doi: 10.3201/eid0812.010317. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Heesterbeek J. A. P. A brief history of R0 and a recipe for its calculation. Acta Biotheor. 2002;50(3):189–204. doi: 10.1023/a:1016599411804. [DOI] [PubMed] [Google Scholar]
  12. Jackson R. The role of wildlife in Mycobacterium bovis infection of livestock in New Zealand. N Z Vet J. 2002;50(3 Suppl):49–52. [PubMed] [Google Scholar]
  13. Kao Rowland R. The role of mathematical modelling in the control of the 2001 FMD epidemic in the UK. Trends Microbiol. 2002 Jun;10(6):279–286. doi: 10.1016/s0966-842x(02)02371-5. [DOI] [PubMed] [Google Scholar]
  14. Keeling M. J., Gilligan C. A. Metapopulation dynamics of bubonic plague. Nature. 2000 Oct 19;407(6806):903–906. doi: 10.1038/35038073. [DOI] [PubMed] [Google Scholar]
  15. Lloyd A. L., May R. M. Epidemiology. How viruses spread among computers and people. Science. 2001 May 18;292(5520):1316–1317. doi: 10.1126/science.1061076. [DOI] [PubMed] [Google Scholar]
  16. Lord C. C., Woolhouse M. E., Heesterbeek J. A., Mellor P. S. Vector-borne diseases and the basic reproduction number: a case study of African horse sickness. Med Vet Entomol. 1996 Jan;10(1):19–28. doi: 10.1111/j.1365-2915.1996.tb00077.x. [DOI] [PubMed] [Google Scholar]
  17. Prata A. Clinical and epidemiological aspects of Chagas disease. Lancet Infect Dis. 2001 Sep;1(2):92–100. doi: 10.1016/S1473-3099(01)00065-2. [DOI] [PubMed] [Google Scholar]
  18. Rosen L., Shroyer D. A., Tesh R. B., Freier J. E., Lien J. C. Transovarial transmission of dengue viruses by mosquitoes: Aedes albopictus and Aedes aegypti. Am J Trop Med Hyg. 1983 Sep;32(5):1108–1119. doi: 10.4269/ajtmh.1983.32.1108. [DOI] [PubMed] [Google Scholar]
  19. Velasco-Hernández J. X. A model for Chagas disease involving transmission by vectors and blood transfusion. Theor Popul Biol. 1994 Aug;46(1):1–31. doi: 10.1006/tpbi.1994.1017. [DOI] [PubMed] [Google Scholar]

Articles from Proceedings of the Royal Society B: Biological Sciences are provided here courtesy of The Royal Society

RESOURCES