Hostname: page-component-7b9c58cd5d-dlb68 Total loading time: 0 Render date: 2025-03-15T09:28:50.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Vaccination against rubella and measles: quantitative investigations of different policies

Published online by Cambridge University Press:  15 May 2009

R. M. Anderson  and
R. M. May
R. M. Anderson
Affiliation:
Department of Pure and Applied Biology, Imperial College, London University, London 5W7 2BB, England
R. M. May
Affiliation:
Biology Department, Princeton University, Princeton, New Jersey 08544, U.S.A.
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper uses relatively simple and deterministic mathematical models to examine the impact that different immunization policies have on the age-specific incidence of rubella and measles. Following earlier work by Knox (1980) and others, we show that immunization programmes can, under some circumstances, increase the total number of cases among older age groups; the implications for the overall incidence of measles encephalitis and of congenital rubella syndrome are examined, paying attention both to the eventual equilibrium and to the short-term effect in the first few decades after immunization is initiated. Throughout, we use data (from the U.K., and U.S.A. and other countries) both in the estimation of the epidemiological parameters in our models, and in comparison between theoretical predictions and observed facts. The conclusions defy brief summary and are set out at the end of the paper.

Type
Research Article
Information
Journal of Hygiene , Volume 90 , Issue 2 , April 1983 , pp. 259 - 325
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

Anderson, R. M. &May, R. M. (1982). Directly transmitted infectious diseases: control by vaccination. Science 215, 1053–60.CrossRefGoogle ScholarPubMed
Aron, J. L. (1983). A stochastic model of infection boosted by re-infection, In preparation.Google Scholar
Aron, J. L. &Schwartz, I. B. (1983). Seasonality and period doubling bifurcations in an epidemic model. Journal of Theoretical Biology (In the Press.)Google Scholar
Bailey, N. T. J. (1975). The Mathematical Theory of Infectious Diseases and its Applications. London: Griffin.Google Scholar
Bartlett, M. S. (1957). Measles periodicity and community size. Journal of the Royal Statistical Society, A 120, 48–70.CrossRefGoogle Scholar
Bartlett, M. S. (1960). The critical community size for measles in the United States. Journal of the Royal Statistical Society. B. 123, 37–44.CrossRefGoogle Scholar
Becker, N. (1979). The uses of epidemic models. Biometrics, 35, 295–305.CrossRefGoogle ScholarPubMed
Benenson, A. S. (1975). Control of Communicable Diseases in Man, 12th ed.Washington, D.C.: American Public Health Association.Google Scholar
Black, F. L. (1966). Measles endemicity in insular populations: critical community size and its evolutionary implications. Journal of Theoretical Biology 11, 207–211.CrossRefGoogle Scholar
Center For Disease Control (1981 a). Rubella—United States, 1978–1981. Morbidity and Mortality Weekly Report 30, 513–515.Google Scholar
Center For Disease Control (1981 b). Measles encephalitis — United States 1962–1979. Morbidity and Morality Weekly Report 31, 217–224.Google Scholar
Center For Disease Control (1982 a). Measles prevention. Morbidity and Mortality Weekly Report 31, 217–224.Google Scholar
Center For Diseasecontrol (1982 b). Measles-El Paso, Texas, 1981. Morbidity and Mortality Weekly Report 31, 182–183.Google Scholar
Center For Disease Control (1982 c). School immunization requirements for measles—United States, 1982. Morbidity and Mortality Weekly Report 31, 65–67.Google Scholar
Center For Disease Control (1982 d). Measles—United States, first 26 weeks, 1982. Morbidity and Mortality Weekly Report 31, 381–382.Google Scholar
Clarke, M., Schild, G. C., Boustred, J., McGregor, I. A. &Williams, K. (1980). Epidemio logical studies of rubella virus in a tropical African community. Bulletin of the World Health Organisation 58, 931–935.Google Scholar
Clarke, M., Schild, G. C., Boustred, J., Seagroatt, V., Pollock, T. M., Findlay, S. E. &Barbara, J. A. J. (1979). Effect of rubella vaccination programme on the serological states of young adults in the U.K. Lancet i, 1224.CrossRefGoogle Scholar
Collins, S. D. (1929). Age incidence of the common communicable diseases of children. United States Public Health Reports 44, 763–828.CrossRefGoogle Scholar
Cvjetanovic, B., Grab, B. &Dixon, H. (1982). Epidemiological models of poliomyelitis and measles and their application in the planning of immunization programmes. Bulletin of the World Health Organisation 60, 405–422.Google ScholarPubMed
Davis, R. (1982). Measles in the tropics and public health practices. Transactions of the Royal Society of Tropical Medicine and Hygiene 76, 268–275.CrossRefGoogle Scholar
Dietz, K. (1975). Transmission and control of arbovirus diseases. In Epidemiology (ed. Ludwig, D. and Cooke, K. L.), pp. 104–121. Philadelphia: Society for Industrial and Applied Mathematics.Google Scholar
Dietz, K. (1976). The incidence of infectious diseases under the influence of seasonal fluctuations. Lecture Notes in Biomathematics 11, 1–15.CrossRefGoogle Scholar
Dietz, K. (1981). The evaluation of rubella vaccination strategies. In The Mathematical Theory of the Dynamics of Biological Populations, vol. ii (ed. Hiorns, R. W. and Cooke, D.), pp. 81–98. London: Academic Press.Google Scholar
Dietz, K. (1982). Overall population patterns in the transmission cycle of infectious disease agents. In Population Biology of Infectious Disease (ed. Anderson, R. M. and May, R. M.), pp. 87–102.CrossRefGoogle Scholar
Edmond, E., Morton, P., Moffat, M. &Urquhart, G. E. D. (1980). Health Bulletin 38, 54.Google Scholar
Fine, P. E. M. &Clarkson, J. (1982 a). Measles in England and Wales. I. An analysis of the factors underlying seasonal patterns. International Journal of Epidemiology 11, 5–14.CrossRefGoogle ScholarPubMed
Fine, P. E. M. &Clarkson, J. E. (1982 b). Measles in England and Wales. II. The impact of the measles vaccination programme on the distribution of immunity in the population. International Journal of Epidemiology 11, 15–25.CrossRefGoogle ScholarPubMed
Fine, P. E. M. &Clarkson, J. A. (1983). Measles in England and Wales. III. Assessing published predictions of the impact of vaccination on incidence. International Journal of Epidemiology. (In the Press.)CrossRefGoogle Scholar
Fisher, R. A. (1930). The Genetical Theory of Natural Selection. New York: Dover (reprint, 1958).CrossRefGoogle Scholar
Fox, J. P., Elveback, L., Scott, W., Galewood, L. &Ackerman, E. (1971). Herd immunity: basic concept and relevance to public health immunization practices. American Journal of Epidemiology 94, 179–189.CrossRefGoogle ScholarPubMed
Gregg, N. M. (1941). Congenital cataract following German measles in the mother. Transactions of the Ophthalmic Society of Australia 3, 35.Google Scholar
Griffiths, D. A. (1974). A catalytic model of infection for measles. Applied Statistics 23, 330–339.CrossRefGoogle Scholar
Grist, N. R., Reid, D. &Young, A. B. (1981). Herd immunity to infections. Health Bulletin 39, 211–217.Google ScholarPubMed
Grossman, Z. (1980). Oscillatory phenomena in a model of infectious diseases. Theoretical Population Biology 18, 204–243.CrossRefGoogle Scholar
Hanshaw, J. B. &Dudgeon, J. A. (1978). Viral Diseases of the Fet us and Newborn. W. B. Saunders Company, London.Google Scholar
Haydon, G. F., Modlin, J. F. &Wittle, J. J. (1977). Current status of rubella in the United States 1969–75. Journal of Infectious Diseases 185, 337–340.Google Scholar
Hethcote, H. W. (1978). An immunization model for the heterogeneous population. Theoretical Population Biology 14, 338–349.CrossRefGoogle ScholarPubMed
Hethcote, H. W. (1983). Measles and rubella in the United States. American Journal of Epidemiology. (In the Press.)CrossRefGoogle ScholarPubMed
Hethcote, H. W., Stech, H. W. &Van Den Driesche, P. (1981). Nonlinear oscillations in epidemic models. SIAM Journal of Applied Mathematics 40, 1–9.CrossRefGoogle Scholar
Hethcote, H. W. &Tudor, D. W. (1980). Integral equation models for endemic infectious diseases. Journal of Mathematical Biology 9, 37–47.CrossRefGoogle ScholarPubMed
H.M.S.O. (1981). Whooping Cough. London: Her Majesty's Stationery Office.Google Scholar
Hoppensteadt, F. C. (1974). An age dependent epidemic model. Journal of the Franklin Institute 297, 325–333.CrossRefGoogle Scholar
Hoppensteadt, F. C. (1975). Mathematical Theories of Populations. Demographics, Genetics and Epidemics. Philadelphia: SIAM (Regional Conference Series in Applied Mathematics, 20).CrossRefGoogle Scholar
Kermack, W. O. &McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A 115, 13–23.Google Scholar
Knox, E. G. (1980). Strategy for rubella vaccination. International Journal for Epidemiology 9. 13–23.CrossRefGoogle ScholarPubMed
Macdonald, G. (1952). The analysis of equilibrium in malaria. Tropical Diseases Bulletin 49, 813–829.Google ScholarPubMed
McCartney, A. &Ross, C. A. C. (1979). Communicable Diseases, Scotland Weekly Report No. 15.Google Scholar
May, R. M. (1974). Stability and Complexity in Model Ecosystems, 2nd ed.Princeton: Princeton University Press.Google Scholar
Morley, D. C. (1969). Severe measles in the tropics. 1. British Medical Journal i, 293–300.Google Scholar
Muench, H. (1959). Catalytic Models in Epidemiology. Cambridge, Mass.: Harvard University Press.CrossRefGoogle Scholar
Nold, A. (1979). The infectee number at equilibrium for a communicable disease. Mathematical Biosciences 46, 131–138.CrossRefGoogle Scholar
Preblud, S. R., Serdula, M. K., Frank, J. A. Jr., Brandling-Bennett, A. D. &Hinman, A. R. (1980). Rubella vaccination in the United States: a ten year review. Epidemiological Reviews 2, 171–194.CrossRefGoogle ScholarPubMed
Smith, H. L. (1983). Multiple stable subharmonics for a periodic epidemic model. (Preprint.)CrossRefGoogle Scholar
Soper, H. E. (1929). Interpretation of periodicity in disease prevalence. Journal of the Royal Statistical Society 92, 34–73.CrossRefGoogle Scholar
Starr, C. &Whipple, C. (1980). Risks of risk decisions. Science 208, 1114–1119.CrossRefGoogle ScholarPubMed
Urquhart, G. E. D. (1980). Communicable Diseases Scotland Weekly Report No. 24.Google Scholar
Waltman, P. (1974.). Deterministic Threshold Models in the Theory of Epidemics (Lecture Notes in Biomathetics). New York: Springer-Verlag.CrossRefGoogle Scholar
Wickwire, K. (1977). Mathematical models for the control of pests and infectious diseases: a survey. Theoretical Population Biology 11, 182–238.CrossRefGoogle ScholarPubMed
Wilson, E. B. &Worcester, J. (1941). Contact with measles. Proceedings of the National Academy of Sciences, Washington 27, 7–13.CrossRefGoogle Scholar
Yorke, J. A., Nathanson, N., Pianingiani, G. &Martin, J. (1979). Seasonality and the requirements for perpetuation and eradication of viruses. American Journal of Epidemiology 109, 103–123.CrossRefGoogle ScholarPubMed