Population Biology of Microparasitic Infections

  • Robert M. May
Part of the Biomathematics book series (BIOMATHEMATICS, volume 17)


Much, though not all, of the material in my chapter has already been published in journals that are likely to be as accessible as this book. There is a constant temptation to repeat oneself in print; with the aim of avoiding this temptation, I have kept most of my presentation to the bare bones, adding flesh in those places where the work is not already published or where new avenues of investigation seem to me to be ready for study. The emphasis here is on the mathematical development of the subject; various kind of applications are discussed in the light of available data elsewhere (and references are given to these works, without repeating the presentation here).


Host Population Vaccination Coverage Population Biology Immunization Program Demographic Stochasticity 
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  1. Anderson, R.M., Jackson, H., May, R.M., Smith, T. (1981). The population dynamics of fox rabies in Europe. Nature 289, 765–771CrossRefGoogle Scholar
  2. Anderson, R.M., May, R.M. (1979). Population biology of infectious diseases: Part I. Nature 280, 361–367Google Scholar
  3. Anderson, R.M., May, R.M. (1981). The population dynamics of microparasites and their invertebrate hosts. Phil. Trans. Roy. Soc. B 291, 451–524Google Scholar
  4. Anderson, R.M., May, R.M. (1982a). The population dynamics and control of human helminth infections. Nature 297, 557–563CrossRefGoogle Scholar
  5. Anderson, R.M., May, R.M. (1982b). Directly transmitted infectious diseases: control by vaccination. Science 215, 1053–1060MathSciNetCrossRefGoogle Scholar
  6. Anderson, R.M., May, R.M. (eds.) (1982c). Population Biology of Infectious Diseases. Springer-Verlag: Berlin and New YorkGoogle Scholar
  7. Anderson, R.M. May, R.M. (1983). Vaccination against rubella and measles: quantitative investigations of different policies. J. Hyg. 90, 259–325CrossRefGoogle Scholar
  8. Anderson, R.M., May, R.M. (1986). The Dynamics of Human Host-Parasite Systems. Princeton University Press: PrincetonGoogle Scholar
  9. Aron, J.L., Schwartz, I.B. (1984). Seasonality and period doubling bifurcations in an epidemic model. J. Theor. Biol. 110, 665–679Google Scholar
  10. Bailey, N.J.T. (1975). The Mathematical Theory of Infectious Diseases ( 2nd edn. ). Macmillan: New YorkMATHGoogle Scholar
  11. Bartlett, M.S. (1957). Measles periodicity and community size. J. Roy. Stat. Soc. Ser. A120, 48–70Google Scholar
  12. Bartlett, M.S. (1960). Stochastic Population Models. Methuen and Co.: LondonMATHGoogle Scholar
  13. Becker, N., Angulo, J. (1981). On estimating the contagiousness of a disease transmitted from person to person. Math. Biosci. 54, 137–154Google Scholar
  14. Cooke, K.L. (1982). Models for epidemic infections with asymptotic cases, I: one group. Math. Modelling 3, 1–15Google Scholar
  15. Dietz, K. (1975). Transmission and control of arbovirus diseases. In: Epidemiology (eds. D. Ludwig and K. L. Cooke ), pp. 104–121. Society for Industrial and Applied Mathematics; PhiladelphiaGoogle Scholar
  16. Dietz, K. (1976). The incidence of infectious diseases under the influence of seasonal fluctuations. In: Mathematical Models in Medicine; Lecture Notes in Biomathematics, II (eds. J. Berger, W. Buhlen, R. Regges, and P. Tautu ), pp. 1–15. Springer-Verlag: BerlinGoogle Scholar
  17. Dietz, K. (1981). The evaluation of rubella vaccination strategies. In: The Mathematical Theory of the Dynamics of Biological Populations, II (eds. R. W. Hiorns and D. Cooke ), pp. 81–97. Academic Press: LondonGoogle Scholar
  18. Fine, P.E.M. (1975). Vectors and vertical transmission: an epidemiological perspective. Ann. N.Y. Acad. Sci. 266, 173–195Google Scholar
  19. Fine, P.E.M., Clarkson, J.A. (1982). Measles in England and Wales, II. The impact of the measles vaccination programme on the distribution of immunity in the population. Int. J. Epidemiol. 11, 15–25Google Scholar
  20. Grossman, Z. (1980). Oscillatory phenomena in a model of infectious diseases. Theor. Pop. Biol. 18, 204–243Google Scholar
  21. Grossman, Z. Gumowski, I., Dietz, K. (1977). The incidence of infectious diseases under the influence of seasonal fluctuations - analytic approach. In: Nonlinear Systems and Applications to Life Sciences, pp. 525–546. Academic Press: New YorkGoogle Scholar
  22. Hethcote, H.W. (1982). Measles and rubella in the United States. Am. J. Epidemiol. 117, 2–13Google Scholar
  23. Hethcote, H.W., Tudor, D.W. (1980). Integral equation models for endemic infectious diseases. J. Math. Biol. 9, 37–47MathSciNetMATHCrossRefGoogle Scholar
  24. Hethcote, H.W., Stech, H.W., Van den Driessche, P. (1981). Nonlinear oscillations in epidemic models. SIAM J. Appl. Math. 40, 1–9Google Scholar
  25. Hethcote, H.W., Yorke, J.A., Nold, A. (1982). Gonorrhea modeling: a comparison of control methods. Math. Biosci. 58, 93–109MATHCrossRefGoogle Scholar
  26. Hoppensteadt, F.C. (1974). An age dependent epidemic model. J. Franklin Inst. 297, 325–333MATHCrossRefGoogle Scholar
  27. Hoppensteadt, F.C. (1975). Mathematical Theories of Populations: Demographics, Genetics, and Epidemics. SIAM (Regional Conference Series and Applied Mathematics 20): PhiladelphiaGoogle Scholar
  28. Kemper, J.T. (1980). On the identification of superspreaders for infectious disease. Math. Biosci. 48, 111–128Google Scholar
  29. Knox, E.G. (1980). Strategy for rubella vaccination. Int. J. Epidemiology 9, 13–23CrossRefGoogle Scholar
  30. London, W.P., Yorke, J.A. (1973). Recurrent outbreaks of measles, chickenpox, and mumps, I. Seasonal variation in contact rates. Amer. J. Epidemiol. 98, 453–468Google Scholar
  31. Macdonald, G. (1952). The analysis of equilibrium in malaria. Trop. Dis. Bull. 49, 813–829Google Scholar
  32. McKeown, T. (1976). The Modern Rise of Population. Edward Arnold: LondonGoogle Scholar
  33. McNeill, W.H. (1976). Plagues and Peoples. Doubleday: New YorkGoogle Scholar
  34. May, R.M. (1974). Stability and Complexity in Model Ecosystems ( second edition ). Princeton University Press: PrincetonGoogle Scholar
  35. May, R.M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459–467CrossRefGoogle Scholar
  36. May, R.M. (1981). The transmission and control of gonorrhea. Nature 291, 376–377CrossRefGoogle Scholar
  37. May, R.M. (1983). Parasitic infections as regulators of animal populations. Amer. Sci. 71, 36–45Google Scholar
  38. May, R.M., Anderson, R.M. (1979). Population biology of infectious diseases: II. Nature 280, 455–461CrossRefGoogle Scholar
  39. Nold, A. (1980). Heterogeneity in disease-transmission modeling. Math. Biosci. 52, 227–240Google Scholar
  40. Smith, C.E.G. (1970). Prospects for the control of infectious disease. Proc. Roy. Soc. Med. 63, 1181–1190Google Scholar
  41. Smith, H.L. (1983). Multiple stable subharmonics for a periodic epidemic model. PreprintGoogle Scholar
  42. Soper, H.E. (1929). Interpretation of periodicity in disease prevalence. J. Roy. Stat. Soc. 92, 34–73Google Scholar
  43. Travis, C.C., Lenhart, S.M. (1985). Smallpox eradication: why was it successful? Submitted to Math. Bio. ScienceGoogle Scholar
  44. Waltman, P. (1974). Deterministic Threshold Models in the Theory of Epidemics. ( Lecture Notes in Biomathematics.) Springer-Verlag: New YorkGoogle Scholar
  45. Yorke, J.A., London, W.P. (1973). Recurrent outbreaks of measles, chickenpox, and mumps, II. Systematic differences in contact rates and stochastic effects. Amer. J. Epidemiol. 98, 469–482Google Scholar
  46. Yorke, J.A., Hethcote, H.W., Nold, A. (1978). Dynamics and control of the transmission of gonorrhea. J. Sex. Trans. Dis. 5, 51–56CrossRefGoogle Scholar
  47. Yorke, J.A., Nathanson, N., Pianigiani, G., Martin, J. (1979). Seasonality and the requirements for perpetuation and eradication of viruses in populations. Am. J. Epidem. 109, 103–123Google Scholar

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© Springer-Verlag Berlin Heidelberg 1986

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  • Robert M. May

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