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Population Biology of Microparasitic Infections

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Mathematical Ecology

Part of the book series: Biomathematics ((BIOMATHEMATICS,volume 17))

Abstract

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).

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References

  • Anderson, R.M., Jackson, H., May, R.M., Smith, T. (1981). The population dynamics of fox rabies in Europe. Nature 289, 765–771

    Article  Google Scholar 

  • Anderson, R.M., May, R.M. (1979). Population biology of infectious diseases: Part I. Nature 280, 361–367

    Google Scholar 

  • Anderson, R.M., May, R.M. (1981). The population dynamics of microparasites and their invertebrate hosts. Phil. Trans. Roy. Soc. B 291, 451–524

    Google Scholar 

  • Anderson, R.M., May, R.M. (1982a). The population dynamics and control of human helminth infections. Nature 297, 557–563

    Article  Google Scholar 

  • Anderson, R.M., May, R.M. (1982b). Directly transmitted infectious diseases: control by vaccination. Science 215, 1053–1060

    Article  MathSciNet  Google Scholar 

  • Anderson, R.M., May, R.M. (eds.) (1982c). Population Biology of Infectious Diseases. Springer-Verlag: Berlin and New York

    Google Scholar 

  • Anderson, R.M. May, R.M. (1983). Vaccination against rubella and measles: quantitative investigations of different policies. J. Hyg. 90, 259–325

    Article  Google Scholar 

  • Anderson, R.M., May, R.M. (1986). The Dynamics of Human Host-Parasite Systems. Princeton University Press: Princeton

    Google Scholar 

  • Aron, J.L., Schwartz, I.B. (1984). Seasonality and period doubling bifurcations in an epidemic model. J. Theor. Biol. 110, 665–679

    Google Scholar 

  • Bailey, N.J.T. (1975). The Mathematical Theory of Infectious Diseases ( 2nd edn. ). Macmillan: New York

    MATH  Google Scholar 

  • Bartlett, M.S. (1957). Measles periodicity and community size. J. Roy. Stat. Soc. Ser. A120, 48–70

    Google Scholar 

  • Bartlett, M.S. (1960). Stochastic Population Models. Methuen and Co.: London

    MATH  Google Scholar 

  • Becker, N., Angulo, J. (1981). On estimating the contagiousness of a disease transmitted from person to person. Math. Biosci. 54, 137–154

    Google Scholar 

  • Cooke, K.L. (1982). Models for epidemic infections with asymptotic cases, I: one group. Math. Modelling 3, 1–15

    Google Scholar 

  • 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; Philadelphia

    Google Scholar 

  • 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: Berlin

    Google Scholar 

  • 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: London

    Google Scholar 

  • Fine, P.E.M. (1975). Vectors and vertical transmission: an epidemiological perspective. Ann. N.Y. Acad. Sci. 266, 173–195

    Google Scholar 

  • 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, 15–25

    Google Scholar 

  • Grossman, Z. (1980). Oscillatory phenomena in a model of infectious diseases. Theor. Pop. Biol. 18, 204–243

    Google Scholar 

  • 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 York

    Google Scholar 

  • Hethcote, H.W. (1982). Measles and rubella in the United States. Am. J. Epidemiol. 117, 2–13

    Google Scholar 

  • Hethcote, H.W., Tudor, D.W. (1980). Integral equation models for endemic infectious diseases. J. Math. Biol. 9, 37–47

    Article  MathSciNet  MATH  Google Scholar 

  • Hethcote, H.W., Stech, H.W., Van den Driessche, P. (1981). Nonlinear oscillations in epidemic models. SIAM J. Appl. Math. 40, 1–9

    Google Scholar 

  • Hethcote, H.W., Yorke, J.A., Nold, A. (1982). Gonorrhea modeling: a comparison of control methods. Math. Biosci. 58, 93–109

    Article  MATH  Google Scholar 

  • Hoppensteadt, F.C. (1974). An age dependent epidemic model. J. Franklin Inst. 297, 325–333

    Article  MATH  Google Scholar 

  • Hoppensteadt, F.C. (1975). Mathematical Theories of Populations: Demographics, Genetics, and Epidemics. SIAM (Regional Conference Series and Applied Mathematics 20): Philadelphia

    Google Scholar 

  • Kemper, J.T. (1980). On the identification of superspreaders for infectious disease. Math. Biosci. 48, 111–128

    Google Scholar 

  • Knox, E.G. (1980). Strategy for rubella vaccination. Int. J. Epidemiology 9, 13–23

    Article  Google Scholar 

  • London, W.P., Yorke, J.A. (1973). Recurrent outbreaks of measles, chickenpox, and mumps, I. Seasonal variation in contact rates. Amer. J. Epidemiol. 98, 453–468

    Google Scholar 

  • Macdonald, G. (1952). The analysis of equilibrium in malaria. Trop. Dis. Bull. 49, 813–829

    Google Scholar 

  • McKeown, T. (1976). The Modern Rise of Population. Edward Arnold: London

    Google Scholar 

  • McNeill, W.H. (1976). Plagues and Peoples. Doubleday: New York

    Google Scholar 

  • May, R.M. (1974). Stability and Complexity in Model Ecosystems ( second edition ). Princeton University Press: Princeton

    Google Scholar 

  • May, R.M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459–467

    Article  Google Scholar 

  • May, R.M. (1981). The transmission and control of gonorrhea. Nature 291, 376–377

    Article  Google Scholar 

  • May, R.M. (1983). Parasitic infections as regulators of animal populations. Amer. Sci. 71, 36–45

    Google Scholar 

  • May, R.M., Anderson, R.M. (1979). Population biology of infectious diseases: II. Nature 280, 455–461

    Article  Google Scholar 

  • Nold, A. (1980). Heterogeneity in disease-transmission modeling. Math. Biosci. 52, 227–240

    Google Scholar 

  • Smith, C.E.G. (1970). Prospects for the control of infectious disease. Proc. Roy. Soc. Med. 63, 1181–1190

    Google Scholar 

  • Smith, H.L. (1983). Multiple stable subharmonics for a periodic epidemic model. Preprint

    Google Scholar 

  • Soper, H.E. (1929). Interpretation of periodicity in disease prevalence. J. Roy. Stat. Soc. 92, 34–73

    Google Scholar 

  • Travis, C.C., Lenhart, S.M. (1985). Smallpox eradication: why was it successful? Submitted to Math. Bio. Science

    Google Scholar 

  • Waltman, P. (1974). Deterministic Threshold Models in the Theory of Epidemics. ( Lecture Notes in Biomathematics.) Springer-Verlag: New York

    Google Scholar 

  • 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, 469–482

    Google Scholar 

  • Yorke, J.A., Hethcote, H.W., Nold, A. (1978). Dynamics and control of the transmission of gonorrhea. J. Sex. Trans. Dis. 5, 51–56

    Article  Google Scholar 

  • 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, 103–123

    Google Scholar 

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Authors
  1. Robert M. May
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Editors and Affiliations

  1. Department of Mathematics and Program in Ecology, University of Tennessee, 37996-1300, Knoxville, TN, USA

    Thomas G. Hallam

  2. Section of Ecology & Systematics and Ecosystems Research Center, Cornell University, 14853-0239, Ithaca, NY, USA

    Simon A. Levin

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© 1986 Springer-Verlag Berlin Heidelberg

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May, R.M. (1986). Population Biology of Microparasitic Infections. In: Hallam, T.G., Levin, S.A. (eds) Mathematical Ecology. Biomathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69888-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-69888-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69890-3

  • Online ISBN: 978-3-642-69888-0

  • eBook Packages: Springer Book Archive

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