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Population biology of infectious diseases: Part II

Abstract

In the first part of this two-part article (Nature 280, 361–367), mathematical models of directly transmitted microparasitic infections were developed, taking explicit account of the dynamics of the host population. The discussion is now extended to both microparasites (viruses, bacteria and protozoa) and macroparasites (helminths and arthropods), transmitted either directly or indirectly via one or more intermediate hosts. Consideration is given to the relation between the ecology and evolution of the transmission processes and the overall dynamics, and to the mechanisms that can produce cyclic patterns, or multiple stable states, in the levels of infection in the host population.

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References

  1. Anderson, R. M. & May, R. M. Nature 280, 361–367 (1979).

    ADS  CAS  PubMed  Google Scholar 

  2. Hoagland, K. E. & Schad, G. A. Exp. Parasit. 44, 36–49 (1978).

    CAS  PubMed  Google Scholar 

  3. Anderson, R. M. & May, R. M. J. Anim. Ecol. 47, 219–247 (1978).

    Google Scholar 

  4. May, R. M. and Anderson, R. M. J. Anim. Ecol. 47, 249–267 (1978).

    Google Scholar 

  5. Anderson, R. M. in Ecological Stability (eds Usher, M. B. & Williamson, M. H.) (Chapman and Hall, London, 1974).

    Google Scholar 

  6. Fine, P.E.M. Ann. N.Y. Acad. Sci. 266, 173–194 (1975).

    ADS  CAS  PubMed  Google Scholar 

  7. Crofton, H. D. Parasitology 63, 179–193 (1971).

    Google Scholar 

  8. Crofton, H. D. Parasitology 63, 343–364 (1971).

    CAS  PubMed  Google Scholar 

  9. May, R. M. J. Anim. Ecol. 47, 833–844 (1978).

    Google Scholar 

  10. Bradley, D. J. & May, R. M. Trans. R. Soc. trop. Med. Hyg. 72, 262–273 (1978).

    CAS  PubMed  Google Scholar 

  11. Tallis, G. M. & Leyton, M. K. Math. Biosci. 4, 39–48 (1969).

    Google Scholar 

  12. Anderson, R. M. in Mathematical Models in Medicine (eds Berger, J. et al.) (Springer, NewYork, 1976).

    Google Scholar 

  13. Anderson, R. M. Parasitology 76, 119–157 (1978).

    CAS  PubMed  Google Scholar 

  14. May, R. M. Parasitology 75, 259–276 (1977).

    Google Scholar 

  15. Barruzzi, R. G., Macopito, L. F., Serra, M. L. C., Souza, F. A. A. & Stabile, C. in Health and Disease in Tribal Socieities (CIBA Fdn. Symp. 49) (NorthHolland, Amsterdam, 1977).

    Google Scholar 

  16. Campbell, A. D. Proc. R. Soc. Edinb. B74, 347–369 (1972).

    Google Scholar 

  17. Macdonald, G. The Epidemiology and Control of Malaria (Oxford University Press, 1957).

    Google Scholar 

  18. Ross, R. Br. med. J. i, 546–547 (1915).

    Google Scholar 

  19. Nasell, I. & Hirsch, W. M. Commun. pure appl. Math. 26, 395–453 (1973).

    Google Scholar 

  20. Dietz, K. in Epidemiology (eds Ludwig, D. & Cooke, K. L.) 104–121 (Society for Industrial and Applied Mathematics, Philadelphia, 1975).

    Google Scholar 

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

    MATH  Google Scholar 

  22. Hairston, N. G. Bull. Wld Hlth Org. 33, 163–175 (1965).

    CAS  Google Scholar 

  23. Cohen, J. E. in Theoretical Ecology : Principles and Applications (ed. May, R. M.) (Blackwell, Oxford, 1976).

    Google Scholar 

  24. Cohen, J. E. A. Rev. Ecol. Syst. 8, 207–233 (1977).

    Google Scholar 

  25. Fine, P. E. M. Proc. R. Soc. Med. 68, 547–551 (1975).

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Dietz, K., Molineaux, L. & Thomas, A. Bull. Wld Hlth Org. 50, 347–357 (1974).

    CAS  Google Scholar 

  27. Macdonald, G. Dynamics of Tropical Disease (eds Bruce-Chwatt, L. J. & Glanville, V. J.) (Oxford University Press, 1973).

    Google Scholar 

  28. Macdonald, G. Trans. R. Soc. trop. Med. Hyg. 59, 489–506 (1965).

    CAS  PubMed  Google Scholar 

  29. Anderson, R. M. & May, R. M. Parasitology (in the press).

  30. Lewis, T. Math. Biosci. 30, 205–210 (1976).

    Google Scholar 

  31. Macdonald, G. Public Health Reports Washington D.C. 76, 753–764 (1961).

    CAS  Google Scholar 

  32. Keymer, A. E. & Anderson, R. M. Parasitology (in the press).

  33. Yorke, J. A., Hethcote, H. W. & Nold, A. J. sex. Trans. Dis. 5, 51–56 (1978).

    CAS  Google Scholar 

  34. May, R. M. Math. Biosci. 35, 301–343 (1977).

    Google Scholar 

  35. Anderson, R. M. in Population Dynamics (eds Anderson, R. M., Turner, B. D. & Taylor, L. R.) (Blackwell, Oxford, 1979).

    Google Scholar 

  36. Anderson, R. M. Nature 279, 150–152 (1979).

    ADS  Google Scholar 

  37. Bradley, D. J. in Origins of Pest, Parasite, Disease and Weed Problems (eds Cherrit, J. M. & Sagar, G. R.) (Blackwell, Oxford, 1977).

    Google Scholar 

  38. Fenner, F. & Ratcliffe, F. N. Myxomatosis (Cambridge University Press, 1965).

    Google Scholar 

  39. Gillespie, J. H. Ecology 56, 493–495 (1975).

    Google Scholar 

  40. Price, P. W. Evolution 31, 405–420 (1977).

    PubMed  Google Scholar 

  41. Price, P. W. Evolutionary Biology of Parasites (Princeton University Press, 1979).

    Google Scholar 

  42. Black, F. L. et al. Am. J. Epidem. 100, 230–250 (1974).

    CAS  Google Scholar 

  43. Eshel, I. Theor. Pop. Biol. 11, 410–424 (1977).

    CAS  Google Scholar 

  44. London, W. P. & Yorke, J. A. Am. J. Epidem. 98, 453–468 (1973).

    CAS  Google Scholar 

  45. Davis, J. W., Karstad, L. H. and Trainer, D. O. (eds) Infectious Diseases of Wild Mammals (Iowa State University Press, Ames, 1970).

  46. Kaschula, V. R. & Truter, D. E. J. S. Afr. vet. med. Ass. 22, 191–192 (1951).

    Google Scholar 

  47. Warner, R. E. Condor, 101–120 (1968).

  48. Woodrow, A. W. J. Econ. Ent. 35, 892–895 (1942).

    Google Scholar 

  49. Bailey, L. Sci. Progr. (Oxford) 59, 309–323 (1971).

    Google Scholar 

  50. Tinsley, T. W. A. Rev. Ent. 24, 63–87 (1979).

    CAS  Google Scholar 

  51. Henry, J. E. & Oma, E. A. J. Invert. Path. 23, 371–377 (1974).

    CAS  Google Scholar 

  52. Maramorosch, K. Invertebrate Immunity (Academic, New York, 1975).

    Google Scholar 

  53. Smith, K. M. Virus-Insect Relationships (Longman, London, 1976).

    Google Scholar 

  54. Brook, T. D. Microbial Ecology (Prentice Hall, New Jersey, 1966).

    Google Scholar 

  55. Matumota, M. Bact. Rev. 33, 404–418 (1969).

    Google Scholar 

  56. Bartlett, M. S. Stochastic Populations in Ecology and Epidemiology (Methuen, London, 1960).

    MATH  Google Scholar 

  57. Dronen, N. O. Am. Midl. Nat. 99, 330–349 (1978).

    Google Scholar 

  58. Bartlett, M. S. J. R. Stat. Soc. AA20, 48–70 (1957).

    Google Scholar 

  59. Bartlett, M. S. J. R. Stat. Soc. A123, 37–44 (1960).

    Google Scholar 

  60. Nisbet, R. M. & Gurney, W. S. C. Nature 263, 319–320 (1976).

    ADS  CAS  PubMed  Google Scholar 

  61. Anderson, R. M. Parasitology 72, 281–305 (1976).

    CAS  PubMed  Google Scholar 

  62. McNamara, M. J., Pierce, W. C., Cranford, Y. E. & Miller, L. F. Am. Rev. resp. Dis. 86, 485–492 (1962).

    CAS  PubMed  Google Scholar 

  63. Yorke, J. A. & London, W. P. Am. J. Epidem. 98, 469–482 (1973).

    CAS  Google Scholar 

  64. Dietz, K. in Mathematical Models in Medicine (ed. Levin, S. A.) (Springer, New York, 1976).

    Google Scholar 

  65. Yorke, J. A., Nathanson, N., Pianigiani, G. & Martin, J. Am. J. Epidem. 109, 103–123 (1979).

    CAS  Google Scholar 

  66. Bliss, C. I. & Blevins, D. L. Am. J. Hyg. 70, 328–334 (1959).

    CAS  PubMed  Google Scholar 

  67. Soper, H. E. J. R. Stat. Soc. A92, 34–73 (1929).

    Google Scholar 

  68. May, R. M. Nature 269, 471–478 (1977).

    ADS  Google Scholar 

  69. Brooke, M. M. Am. J. Hyg. 41, 81–108 (1945).

    CAS  Google Scholar 

  70. Cole, T. J. & Parkin, J. M. Trans. R. Soc. trop. Med. Hyg. 71, 196–198 (1977).

    CAS  PubMed  Google Scholar 

  71. Steinhaus, E. A. Proc. 10th Int. Cong. Ent. 4, 725–730 (1958).

    Google Scholar 

  72. Geiman, Q. M. Vitam. Horm. 16, 1–33 (1958).

    CAS  PubMed  Google Scholar 

  73. Gibson, T. E. Proc. nutri. Soc. 22, 15–20 (1963).

    CAS  Google Scholar 

  74. Chandler, A.mC. J. Egypt. med. Ass. 36, 533–552 (1953).

    CAS  PubMed  Google Scholar 

  75. Wiger, R. Oikos 29, 598–606 (1977).

    Google Scholar 

  76. Mimms, C. A. The Pathogenesis of Infectious Diseases (Academic, London, 1977).

    Google Scholar 

  77. Roitt, I. M. Essential Immunology (Blackwell, Oxford, 1976).

    Google Scholar 

  78. Scrimshaw, N. S., Taylor, C. E. & Gordon, J. E. Wld. Hlth Ord. Monogr. Ser. 57, (1968).

  79. Gordon, M. H. Proc. Aust. Anim. Prod. 3, 93–104 (1963).

    Google Scholar 

  80. Sheppe, W. A. & Adams, J. R. J. Parasit. 57, 55–59 (1957).

    Google Scholar 

  81. Lack, D. The Natural Regulation of Animal Numbers (Oxford University Press, 1954).

    Google Scholar 

  82. Warren, K. S. J. infect. Dis. 127, 595–609 (1973).

    CAS  PubMed  Google Scholar 

  83. Dietz, K. J. R. Stat. Soc. A130, 505–528 (1967).

    Google Scholar 

  84. Waltman, P. Deterministic Threshold Models in the Theory of Epidemics (Springer, New York, 1974).

    MATH  Google Scholar 

  85. Hoppensteadt, F. C. Mathematical Theories of Populations: Demographics, Genetics and Epidemics (SIAM, Philadelphia, 1976).

    MATH  Google Scholar 

  86. Kermack, W. O. & McKendrick, A. G. Proc. R. Soc. A115, 700–721 (1927).

    ADS  Google Scholar 

  87. Homer, W. H. Lancet i, 733–739 (1906).

  88. Plowright, R. C. & Paloheimo, J. E. Theor. Pop. Biol. 12, 286–297 (1977).

    CAS  Google Scholar 

  89. Anderson, R. M. in Ecological Aspects of Parasitology (ed. Kennedy, C. R.) (North-Holland, Amsterdam, 1976).

    Google Scholar 

  90. Rosenfield, P. L., Smith, R. A. & Wolman, M. G. Am. J. trop. Med. Hyg. 26, 505–516 (1977).

    CAS  PubMed  Google Scholar 

  91. Kositzin, V. A. Symbiose, Parasitisme et Evolution (Hermann, Paris, 1934).

    Google Scholar 

  92. Lewis, T. Adv. appl. Prob. 7, 673–704 (1975).

    Google Scholar 

  93. Lotka, A. J. Am. J. Hyg. 3, 1–121 (1923).

    Google Scholar 

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May, R., Anderson, R. Population biology of infectious diseases: Part II. Nature 280, 455–461 (1979). https://doi.org/10.1038/280455a0

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