Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-22T15:15:22.138Z Has data issue: false hasContentIssue false

Age-related changes in the rate of disease transmission: implications for the design of vaccination programmes

Published online by Cambridge University Press:  19 October 2009

R. M. Anderson
Affiliation:
Department of Pure and Applied Biology, Imperial College, London University, London SW7 2BB
R. M. May
Affiliation:
Biology Department, University of Princeton, Princeton, New Jersey 08540, 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.

Mathematical models are developed to aid in the investigation of the implications of heterogeneity in contact with infection within a community, on the design of mass vaccination programmes for the control of childhood viral and bacterial infections in developed countries. Analyses are focused on age-dependency in the rate at which individuals acquire infection, the question of ‘who acquires infection from whom’, and the implications of genetic variability in susceptibility to infection. Throughout, theoretical predictions are based on parameter estimates obtained from epidemiological studies and are compared with observed temporal trends in disease incidence and age-stratified serological profiles.

Analysis of case notification records and serological data suggest that the rate at which individuals acquire many common infections changes from medium to high and then to low levels in the infant, child and teenage plus adult age groups respectively. Such apparent age-dependency in attack rate acts to reduce slightly the predicted levels of herd immunity required for the eradication of infections such as measles, when compared with the predictions of models based on age-independent transmission. The action of maternally derived immunity in prohibiting vaccination in infants, and the broad span of age classes over which vaccination currently takes place in the U.K., however, argue that levels of herd immunity of between 90 and 94 % would be required to eliminate measles.

Problems surrounding the interpretation of apparent age-related trends in the acquisition of infection and their relevance to the design of vaccination programmes, are discussed in relation to the possible role of genetically based variation in susceptibility to infection and observations on epidemics in “virgin” populations. Heterogeneous mixing models provide predictions of changes in serology and disease incidence under the impact of mass vaccination which well mirror observed trends in England and Wales.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

Anderson, R. M., Grenfell, B. T. & May, R. M. (1984). Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination. Journal of Hygiene 93, 587608.CrossRefGoogle ScholarPubMed
Anderson, R. M. & May, R. M. (1979). Population biology of infectious diseases: Part I. Nature 280, 361367.CrossRefGoogle ScholarPubMed
Anderson, R. M. & May, R. M. (1982). Directly transmitted infectious diseases: control by vaccination. Science 215, 10531060.CrossRefGoogle ScholarPubMed
Anderson, R. M. & May, R. M. (1983). Vaccination against rubella and measles: quantitative investigations of different policies. Journal of Hygiene 90, 258325.CrossRefGoogle ScholarPubMed
Anderson, R. M. & May, R. M. (1985). Spatial, temporal and genetic heterogeneity in host populations and the design of immunization programmes. Journal of Mathematics Applied in Biology and Medicine (In the Press.)Google Scholar
Baltimore (1963). Baltimore Public Health Reports 1963, Baltimore, U.S.A.Google Scholar
Bartlett, M. S. (1956). Deterministic and stochastic models for recurrent epidemics. In Proceedings of the Third Berkely Symposium on Mathematics, Statistics and Probability, 4, 81109. Berkeley and Los Angeles: University of California Press.Google Scholar
Bartlett, M. S. (1957). Measles periodicity and community size. Journal of the Royal Statistical Society A 120, 4870.CrossRefGoogle Scholar
Black, F. L. (1959). Measles antibodies in the population of New Haven, Connecticut. Journal of Immunology 83, 7483.CrossRefGoogle ScholarPubMed
Bliss, C. I. & Blevins, D. L. (1959). The analysis of seasonal variation in measles. American Journal of Hygiene 70, 328334.Google ScholarPubMed
Broady, J. A., Sever, J. L., McAlister, R., Schiff, G. M. & Cutting, R. (1965). Rubella epidemic on St. Paul island in the Pribilofs, 1963. Journal of American Medical Association 191, 619626.CrossRefGoogle Scholar
Butler, W. (1913). Measles. Proceedings of the Royal Society of Medicine 6, 120137.CrossRefGoogle ScholarPubMed
Chapin, C. V. (1925). Measles in Providence, R. I., 1858–1923. American Journal of Hygiene 5, 635655.Google Scholar
Christensen, P. E., Schmidt, H., Bang, H. O., Anderson, V., Jordal, B. & Jensen, O. (1953). Measles in virgin soil, Greenland, 1951. Danish Medical Bulletin 1, 26.Google Scholar
Collins, S. D. (1929). Age incidence of the common communicable diseases of children. United States Public Health Reports 44, 763828.CrossRefGoogle Scholar
Dietz, K. (1975). Transmission and control of arbovirus diseases. In Epidemiology (ed. Lugwig, D. and Cooke, K. L.) pp. 104121. 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, 115.CrossRefGoogle Scholar
Dietz, K. & Schenzle, D. (1984). Mathematical models for infectious disease statistics. In A Celebration of Statistics (ed. Atkinson, A. C. and Fienberg, S. E.). Springer Verlag: Berlin.Google Scholar
Enderle, J. D. (1980). A stochastic communicable disease model with age-specific states and applications to measles. (Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, U.S.A.)Google Scholar
Fales, W. T. (1928). The age distribution of whooping cough, measles, chicken pox, scarlet fever and diphtheria in various areas in he United States. American Journal of Hygiene 8, 759799.Google Scholar
Fine, P. E. M. & Clarkson, J. A. (1982 a). Measles in England and Wales. I. An analysis of factors underlying seasonal patterns. International Journal of Epidemiology 11, 514.CrossRefGoogle ScholarPubMed
Fine, P. E. M. & Clarkson, J. A. (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, 1525.CrossRefGoogle ScholarPubMed
Fine, P. E. M. & Clarkson, J. A. (1984). Distribution of immunity to pertussis in the population of England and Wales. Journal of Hygiene 92, 2136.CrossRefGoogle ScholarPubMed
Griffiths, D. A. (1974). A catalytic model of infection for measles. Applied Statistics 23, 330339.CrossRefGoogle Scholar
Hedrich, A. W. (1933). Monthly estimates of the child population ‘susceptible’ to measles, 1900–1931, Baltimore, M.D. American Journal of Hygiene 17, 613636.Google Scholar
Henderson, E. C. (1916). A census of the contagious diseases of children. American Journal of Public Health 6, 971981.CrossRefGoogle Scholar
Hethcote, H. (1983). Measles and rubella in the United States. American Journal of Epidomiology.CrossRefGoogle ScholarPubMed
Hinman, A. R., Brandling-Bennett, A. D., Bernier, R. H., Kirby, C. D. & Eddins, D. L. (1980). Current features of measles in the United States: feasibility of measles elimination. Epidemiological reviews 2, 153170.CrossRefGoogle ScholarPubMed
Hoppensteadt, F. C. (1974). An age-dependent epidemic model. Journal of the Franklin Institute 297, 325333.CrossRefGoogle Scholar
Horwitz, O., Grunfeld, K., Lysgaard-Hansen, B. & Kjeldsen, K. (1974). The epidemiology and natural history of measles in Denmark. American Journal of Epidemiology 100, 136149.CrossRefGoogle ScholarPubMed
Knolle, H. (1983). The general age-dependent endemic with age-specific contract rates. Biometrical Journal 25, 468475.CrossRefGoogle Scholar
Knox, E. G. (1980). Strategy for rubella vaccination. International Journal for Epidemiology 9, 1323.CrossRefGoogle ScholarPubMed
Macgregor, J. D., MacDonald, J., Ingram, E. A., McDonnell, M. & Marshall, B. (1981). Epidemic measles in Shetland during 1977 and 1978. British Medical Journal 282, 434436.CrossRefGoogle ScholarPubMed
Marks, J. S., Halpin, T. & Orenstein, W. A. (1978). Measles vaccine efficacy in children previously vaccinated at 12 months of age. Pediatrics 62, 955960.Google ScholarPubMed
May, R. M. (1985). Population biology of microparasitic infections. Lecture Notes in Biomathematics (In the Press).Google Scholar
May, R. M. & Anderson, R. M. (1984). Spatial heterogeneity in the design of immunization programmes. Mathematical Biosciences 72, 83111.CrossRefGoogle Scholar
Miller, D. L. (1963). Frequency of complications of measles. British Medical Journal 2, 7578.CrossRefGoogle Scholar
Office of Population Censuses and Surveys (19741982). Statistics of Infectious Diseases. London: H.M.S.O (for the years 1974–82).Google Scholar
Rand, K. H., Emmons, R. W. & Merigan, T. C. (1976). Measles in adults: an unforseen consequence of immunization? Journal of American Medical Association 236, 10281031.CrossRefGoogle Scholar
Registrar General (19481983). Annual Review of the Registrar General of England and Wales. London, H.M.S.O. (for the years 1950–73).Google Scholar
Roden, A. T. & Heath, W. C. C. (1977). Effects of vaccination against measles in the incidence of the disease and on the immunity of the child population in England and Wales. Health Trends 9, 6972.Google Scholar
Schenzle, D. (1985). Control of virus transmission in age structured populations. In Mathematics in Biological Medicine (ed. Capasso, V.) Lecture Notes in Biomathematics (In the Press.)CrossRefGoogle Scholar
Shelton, J. D., Jacobson, J. E., Orenstein, W. A., Schulz, K. F. & Donnel, H. D. (1978). Measles vaccine efficacy: Influence of age at vaccination vs. duration of time since vaccination. Pediatrics 62, 961964.CrossRefGoogle ScholarPubMed
Sutherland, I. & Fayers, P. M. (1971). Effect of measles vaccination on incidence of measles in the community. British Medical Journal 1, 698702.CrossRefGoogle ScholarPubMed
Wilson, G. N. (1904). Measles: its prevalence and mortality in Aberdeen. Report of the Medical Office of Health, Aberdeen, 4150.Google Scholar
Wilson, E. B. & Worcester, J. (1941). Contact with measles. Proceedings of the National Academy of Sciences, Washington 27, 713.CrossRefGoogle Scholar
Yorke, J. A. & London, W. P. (1973). Recurrent outbreaks of measles, chickenpox and mumps: II systematic differences in contact rates and stochastic effects. American Journal of Epidemiology 98, 469482.CrossRefGoogle ScholarPubMed
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, 103123.CrossRefGoogle ScholarPubMed