Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Population dynamics of fox rabies in Europe

Abstract

A simple mathematical model for the overall dynamics of the interaction between fox populations and rabies is presented. The model helps to explain epidemiological patterns observed in Europe, including the 3 to 5 year cycle in fox populations infected with rabies, threshold densities and average levels of prevalence of infection. We give a quantitative discussion of the possibilities of controlling rabies by culling or vaccinating foxes (or by a mixture of the two).

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

  1. Baer, G.M. The Natural History of Rabies Vols I, II (Academic, New York 1975).

    Google Scholar 

  2. Sikes, P. K. Am. J. vet. Res. 23, 1041–1047 (1962).

    CAS  PubMed  Google Scholar 

  3. Parker, R. L. & Wilsnack, R. E. Am. J. vet. Res. 27, 33–46 (1966).

    CAS  PubMed  Google Scholar 

  4. Constantino, D. G. Am. J. vet. Res. 27, 13–32.(1966).

    Google Scholar 

  5. Henschen, F. The History of Diseases (Longman, London, 1966).

    Google Scholar 

  6. Nikolitsch, M. Blue Book for the Veterinary Profession Vol. 10, 7–12 (1965).

    Google Scholar 

  7. Nageno, Y. & Davenport, F.M. (eds) Rabies (University Park Press, Baltimore, 1971).

  8. Kaplan, C. (ed.) Rabies: The Facts (Oxford University Press, 1977).

  9. Steele, J. H. Scand. J. infect. Dis. 5, 299–312 (1973).

    CAS  PubMed  Google Scholar 

  10. Schwabe, C. W. Rep. 1st Wld Hlth Org. Semin. on Veterinary Public Health (Mukteswar, New Delhi, 1971).

    Google Scholar 

  11. Fenner, F., McAuslan, B. R., Mims, C. A., Sambrook, J. & White, P. O. The Biology of Animal Viruses (Academic, New York, 1974).

    Google Scholar 

  12. Features 1, 1–4 (1971).

  13. Rabies Bull. Europe Vol. 3, 5 (WHO Collaborating Centre for Rabies Surveillance and Research, Tubingen, 1980).

  14. Wandeler, A. et al. Zentbl. vet. med. B21, 735–56, 757–64, 765–73 (1974).

    CAS  Google Scholar 

  15. Johnston, D. H. & M. Bull Wildl. Dis. Ass. 5, 357–70 (1969).

    CAS  Google Scholar 

  16. Steele, J. H. Scand. J. infect. Dis. 5, 299–312 (1973).

    CAS  PubMed  Google Scholar 

  17. Chalmers, A. W. & Scott, G. R. Trop. Anim. Hlth Prod. 1, 33–55 (1969).

    Google Scholar 

  18. Lloyd, H. G. Trans. R. Soc. trop. Med. Hyg. 70, 179–87 (1976).

    CAS  PubMed  Google Scholar 

  19. MacDonald, D. W. Rabies and Wildlife. A Biologist's Perspective (Oxford University Press, 1980).

  20. Lloyd, H. G. The Red Fox (Batsford, London, 1980).

    Google Scholar 

  21. Winkler, W. G. J. infect. Dis. 125, 674–675 (1972).

    CAS  PubMed  Google Scholar 

  22. Sikes, R. K. in Infectious Diseases of Wild Mammals (eds Davis, J. W., Karstad, L. H. & Trainer, D. O.) 3–19 (Iowa State University Press, Ames, 1970).

    Google Scholar 

  23. Tierkel, E. Symp. Ser. Immunbiol. Stand. 1, 245–258 (1966).

    Google Scholar 

  24. Toma, B. & Andral, L. Adv. Virus. Res. 21, 1–36 (1977).

    CAS  PubMed  Google Scholar 

  25. Bisseuru, B. Rabies (Heinemann, London, 1972).

    Google Scholar 

  26. Blancou, J., Aubert, M. F. A., Andral, L. & Artois, M. Rev. Med. Vet. 130, 1001–1015 (1979).

    Google Scholar 

  27. Kauker, E. & Zettl, K. Dt. tierarztl. Wschr. 67, 463–467 (1960).

    Google Scholar 

  28. Klob, H. H. & Hewson, R. J. appl. Ecol. 17, 7–19 (1980).

    Google Scholar 

  29. Harris, S. Mammal. Rev. 7, 25–39 (1977).

    Google Scholar 

  30. Layne, J. N. & Mckeon, W. H. N. Y. Fish Game J. 3, 44–74 (1956).

    Google Scholar 

  31. Englund, J. Viltrevy 8, 1–82 (1970).

    Google Scholar 

  32. Hewson, R. & Klob, H. H. J. Zool. 171, 285–92 (1973).

    Google Scholar 

  33. Bogel, K., Moegle, H., Knorpp, F., Arata, A., Dietz, K. & Detthelm, P. Bull. Wld Hlth Org. 54, 433–47 (1976).

    CAS  Google Scholar 

  34. Berger, J. Lecture Notes in Biomaths Vol. 11, 75–88 (Springer, Berlin, 1976).

    Google Scholar 

  35. Mollison, D. J. R. statist. Soc. B39, 283–326 (1977).

    MathSciNet  Google Scholar 

  36. Preston, E. M. J. Wildl. Mgmt 37, 501–12 (1973).

    Google Scholar 

  37. Sayers, B., Men Mansourian, B. G., Phan Tan, T. & Bogal, K. Med. Inform. 1, 11–34 (1977).

    Google Scholar 

  38. Frerichs, R. K. & J. Mgmt Sci. 22, 411–21 (1975).

    Google Scholar 

  39. Smart, C. W. & Giles, R. H. Wildl. Dis. 61, 1–89 (1973).

    Google Scholar 

  40. Stellman, C. & Beranger, G. Revue med. vet. 125, 45–64 (1974).

    Google Scholar 

  41. Lambinet, D., Boisvieux, J. F. Mallet, A., Artois, M. & Andral, L. Rev. Epidem. Sante. 26, 9–28 (1978).

    CAS  Google Scholar 

  42. Bacon, P.J. & MacDonald, D.W. New Scient. 87, 640–645 (1980).

    Google Scholar 

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

    ADS  CAS  PubMed  Google Scholar 

  44. May, R. M. & Anderson, R. M. Nature 280, 455–461 (1979).

    ADS  CAS  PubMed  Google Scholar 

  45. Scott, T. G. Iowa State Coll. J. Sci. 14, 155–9 (1941).

    Google Scholar 

  46. Schoefield, R. D. J. Wildl Mgmt 24, 432–4 (1960).

    Google Scholar 

  47. Fairley, J. S. Proc. R. Ir. Acad. 69, 103–37 (1970); Ir. Nat. J. 16, 392–3 (1970).

    Google Scholar 

  48. Jensen, B. Dan. Rev. Game Biol. 8, 1–20 (1973).

    Google Scholar 

  49. MacDonald, D. W. Mammal. Rev. 7, 7–23 (1977).

    Google Scholar 

  50. Storm, G. L. J. Wildl. Mgmt 29, 1–13 (1965).

    Google Scholar 

  51. Lloyd, H. G. et al. Zentbl. VetMed. 23, 580–9 (1976).

    CAS  Google Scholar 

  52. Lloyd, H. G. & Englund, J. J. Reprod. Fert. Suppl 19, 119–130 (1973).

    CAS  Google Scholar 

  53. Ables, E. D. in The Wild Canids-Their Systematics, Behavioural Ecology and Evolution (ed. Fox M. V.) (Van Nostrand Reinhold, New York, 1975).

    Google Scholar 

  54. Wandeler, A. Proc. Symp. Adv. Rabies Res. (US Dept NIH Education and Welfare, Atlanta, 1976).

  55. Englund, J. Viltrevy 3, 377–485 (1965).

    Google Scholar 

  56. Verhulst, P. F. Corresp. Math. Phys. 10, 113 (1938).

    Google Scholar 

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

    MATH  Google Scholar 

  58. Black, J. G. & Lawson, K. F. Can. J. comp. Med. 34, 309–311.

  59. Anderson, R. M. & May, R. M. Phil. Trans. R. Soc. (in the press).

  60. Dietz, K. in Epidemiology (eds Ludwig, D. & Cooke, K. L.) 104–121 (Society for Industrial and Applied Mathematics, Philadelphia, 1974).

    Google Scholar 

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

    ADS  Google Scholar 

  62. Wld Hlth Org. Report on a Conference Frankfurt-am-Main WHO Regional Office for Europe, Copenhagen, 1978).

  63. Muller, J. Bull Off. int. épizoot. 75, 763–776 (1971).

    ADS  CAS  PubMed  Google Scholar 

  64. Dean, D. J. Publ. Hlth Rep., Wash. 70, 564–569 (1955).

    Google Scholar 

  65. Jennings, W. L., Schneider, N. J., Lewis, A. L. & Scatterday, J. E. J. Wildl. Mgmt 24, 171–179 (1960).

    Google Scholar 

  66. Carey, A. B., Giles, R. H. & McLean, R. G. Am. J. trap. Med. Hyg. 27, 573–80 (1978).

    CAS  Google Scholar 

  67. Schelgel, van H. L. Dt. tierärztl Wschr. 83, 311–350 (1976).

    Google Scholar 

  68. Kauker, E. & Zettl, K. Berl. Munch, tierdrztl Wschr. 16, 301 (1969).

    Google Scholar 

  69. May, R. M. (ed.) Theoretical Ecology: Principles and Applications (Blackwell, Oxford, 1976).

  70. Anderson, R. M. in The Mathematical Theory of Biological Populations (eds Hiorns, R. W. & Cooke, D. L.) (Academic, London, in the press).

  71. Gross, E. C. J. Mammal. 21, 294–306 (1940).

    Google Scholar 

  72. Elton, C. S. Voles Mice and Lemmings (Clarendon, Oxford, 1942).

    Google Scholar 

  73. Taper, S. C. Mammal Rev. 6, 93–117 (1976).

    Google Scholar 

  74. Taper, S. C. J. Anim. Ecol. 48, 603–617 (1979).

    Google Scholar 

  75. Davis, D. E. & Wood, J. E. Publ Hlth Rep. 72, 115–118 (1959).

    Google Scholar 

  76. Moegle, H. et al. Zentbl. Vet. Reihe 21, 647 (1974).

    CAS  Google Scholar 

  77. Andral, L. & Toma, B. Cah. Méd. vét. 42, 203–214 (1973).

    Google Scholar 

  78. Schaefer, M. B. Inter-American Tropical Tuna Commission Bulletin, 126–56 (1954).

  79. May, R. M. Nature 269, 471–477 (1977).

    ADS  Google Scholar 

  80. Beddington, J. R. & May, R. M. Science 197, 463–465 (1977).

    ADS  CAS  PubMed  Google Scholar 

  81. Bogel, K., Arata, A. A., Moegle, H. & Knorpp, F. Zbl vet. med. B21, 401–12 (1974).

    CAS  Google Scholar 

  82. Turner, G. S. Trans. R. Soc. trop. med. Hyg. 70, 175–8 (1976).

    CAS  PubMed  Google Scholar 

  83. Blancou, J. Reel. Med. Vet. 155, 733–41 (1979).

    Google Scholar 

  84. Black, J. G. & Lawson, K. F. Can. Vet. 314, 206–11 (1973).

    Google Scholar 

  85. Ramsden, R. D. & Johnston, P. H. J. Wildl. Dis. 11, 318–24 (1975).

    CAS  PubMed  Google Scholar 

  86. Baer, G. M., Broderson, J. R. & Yega, P. Am. J. Epidemiol 101, 160–4 (1975).

    CAS  PubMed  Google Scholar 

  87. Winkler, W. G. & Baer, G. M. Am. J. Epidemiol 103, 408–15 (1976).

    CAS  PubMed  Google Scholar 

  88. Manz, D. Dt. Vet. Med. Ges., Bad Nauheim 12(4) 75 (1975).

    Google Scholar 

  89. Dubreuil, M., Andral, L., Aubert, M. F. & Blancou, J. Ann. Rech. Vet. 10, 9–21 (1979).

    CAS  PubMed  Google Scholar 

  90. Steck, F., Hafliger, U., Stocker, C. H. & Wandeler, A. I. Experienta 34, 1662 (1978).

    Google Scholar 

  91. Winkler, W. G., McLean, R. G. & Cowart, J. C. J. Wildl Dis. 11, 382–388 (1975).

    CAS  PubMed  Google Scholar 

  92. MacInnes, C. D. & Johnston, D. H. Ontario Fish and Wildl. Rev. 14, 17–20 (1975).

    Google Scholar 

  93. Ministry of Agriculture, Fisheries and Food Rabies Memorandum (Ministry of Agriculture, Fisheries and Food and Department of Agriculture and Fisheries, Scotland, 1977).

  94. Rabies Bull. Europe Vol. 3, Nos. 1–5 (WHO Collaborating Centre for Rabies Surveillance and Research, Tubingen, 1979).

  95. Crick, J. & Brown, F. Vet. Rec. 28 Aug. 6–11 (1976).

  96. Harris, S. J. Zool. Lond. 187, 195–199 (1979).

    Google Scholar 

  97. Harris, S. thesis, University of London (1975).

  98. Bromel, J. & Zettl, K. Zeitschrift Jagdwissenshaft 20, 96–104 (1974).

    Google Scholar 

  99. Hauften, J. Trans. Int. Cong. Game Biologists 9, 539–543 (1970).

    Google Scholar 

  100. Zimen, E. (ed.) The Red Fox. Symposium on Behaviour and Ecology (Junk, The Hague, 1980).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, R., Jackson, H., May, R. et al. Population dynamics of fox rabies in Europe. Nature 289, 765–771 (1981). https://doi.org/10.1038/289765a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/289765a0

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing