Bulletin of Mathematical Biology

, Volume 72, Issue 2, pp 444–468

Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey

Original Article


Invasive species are a significant cause of bio-diversity loss particularly in island ecosystems. It has been suggested to release pathogenic parasites as an efficient control measure of these mostly immune-naïve populations. In order to explore the potential impacts of such bio-control approach, we construct and investigate mathematical models describing disease dynamics in a host population that acts as a predator embedded in a simple food chain. The consequences of Feline Immunodeficiency Virus (FIV) introduction into a closed ecosystem are addressed using a bi-trophic system, comprising an indigenous prey (birds) and an introduced predator (cats). Our results show that FIV is unlikely to fully eradicate cats on sub-Antarctic islands, but it can be efficient in depressing their population size, allowing for the recovery of the endangered prey. Depending on the ecological setting and disease transmission mode (we consider proportionate mixing as well as mass action), successful pathogen invasion can induce population oscillations that are not possible in the disease-free predator–prey system. These fluctuations can be seen as a mixed blessing from a management point of view. On the one hand, they may increase the extinction risk of the birds. On the other hand, they provide an opportunity to eradicate cats more easily in combination with other methods such as trapping or culling.


Eco-epidemiological model Bio-control Invasive species removal Island ecosystem restoration Seabird conservation Pathogen release Reproduction number Forward and backward Hopf bifurcations 


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  1. Anderson, R.M., 1982. Theoretical basis for the use of pathogens as biological control agents of pest species. Parasitology 84, 3–33. CrossRefGoogle Scholar
  2. Anderson, R.M., May, R.M., 1981. The population dynamics of microparasites and their invertebrate hosts. Philos. Trans. R. Soc. Lond. B 291, 451–524. CrossRefGoogle Scholar
  3. Anderson, R.M., May, R.M., 1986. The invasion, persistence and spread of infectious diseases within animal and plant communities. Philos. Trans. R. Soc. Lond. B 314, 533–570. CrossRefGoogle Scholar
  4. Atkinson, I.A.E., 1988. Opportunities for ecological restoration. N.Z. J. Ecol. 11, 1–12. Google Scholar
  5. Atkinson, I.A.E., 1989. Introduced animals and extinction. In: Western, D., Pearl, M.C. (Eds.), Conservation for the Twenty-First Century, pp. 54–75. Oxford University Press, Oxford. Google Scholar
  6. Auger, P., Mchich, R., Chowdhury, T., Sallet, G., Tchuente, M., Chattopadhyay, J., 2009. Effects of a disease affecting a predator on the dynamics of a predator–prey system. J. Theor. Biol. doi:10.1016/j.jtbi.2008.10.030. MATHGoogle Scholar
  7. Bax, N., Carlton, J.T., Mathews-Amos, A., Haedrich, R.L., Howarth, F.G., Purcell, J.E., Rieser, A., Gray, A., 2001. The control of biological invasions in the world’s oceans. Conserv. Biol. 15, 1234–1246. CrossRefGoogle Scholar
  8. Begon, M., Bennett, M., Bowers, R.G., French, N.P., Hazel, S.M., Turner, J., 2002. A clarification of transmission terms in host-microparasite models: numbers, densities and areas. Epidemiol. Infect. 129, 147–153. CrossRefGoogle Scholar
  9. Berruti, A., Griffiths, A.M., Imber, M.J., Schramm, M., Sinclair, J.C., 2000. Status of seabirds at Prince Edward Island. S. Afr. J. Antarct. Res. 10, 32–33. Google Scholar
  10. Berthier, K., Langlais, M., Auger, P., Pontier, D., 2000. Dynamics of a feline virus with two transmission modes within exponentially growing host populations. Proc. R. Soc. Lond. B 267, 2049–2056. CrossRefGoogle Scholar
  11. Bester, M.N., Bloomer, J.P., van Aarde, R.J., Erasmus, B.H., van Rensburg, P.J.J., Skinner, J.D., Howell, P.G., Naude, T.W., 2002. A review of the successful eradication of feral cats from sub-Antarctic Marion Island, Southern Indian Ocean. S. Afr. J. Wildl. Res. 32, 65–73. Google Scholar
  12. Brooke, R.K., Cooper, J., Hockey, P.A.R., Ryan, P.G., Sinclair, J.C., Suter, W., Tree, A.J., 1988. Distribution, population size and conservation of the Antarctic tern Sterna vittata in southern Africa. Cormorant 16, 107–113. Google Scholar
  13. Chaphuis, J.L., Boussès, P., Barnaud, G., 1994. Alien mammals, impact and management in the French Subantarctic Islands. Biol. Conserv. 67, 97–104. CrossRefGoogle Scholar
  14. Chornesky, E.A., Randal, J.M., 2003. The threat of invasive alien species to biological diversity: setting a future course. Ann. M. Bot. Gard. 90, 67–76. CrossRefGoogle Scholar
  15. Cleaveland, S., Thirgood, S., Laurenson, K., 1999. Pathogens as allies in island conservation? Trends Ecol. Evol. 14, 83–84. CrossRefGoogle Scholar
  16. Cooper, J., Brown, C.R., 1990. Ornithological research at the sub-Antarctic Prince Edward Islands: a review of achievements. S. Afr. J. Antarct. Res. 20, 40–57. Google Scholar
  17. Cooper, J.A., Marais, A.V.N., Bloomer, J.P., Bester, M.N., 1995. A success story: breeding of burrowing petrels (Procellariidae) before and after the eradication of feral cats Felis catus at subantarctic Marion Island. Mar. Ornithol. 23, 33–37. Google Scholar
  18. Courchamp, F., Sugihara, G., 1999. Modeling the biological control of an alien predator to protect island species from extinction. Ecol. Appl. 9, 112–123. CrossRefGoogle Scholar
  19. Courchamp, F., Pontier, D., Langlais, M., Artois, M., 1995. Population dynamics of Feline Immunodeficiency Virus within cat populations. J. Theor. Biol. 175, 553–560. CrossRefGoogle Scholar
  20. Courchamp, F., Yoccoz, N.G., Artois, M., Pontier, D., 1998. At-risk individuals in Feline Immunodeficiency Virus epidemiology: Evidence from a multivariate approach in a natural population of domestic cats (Felis catus). Epidemiol. Infect. 121, 227–236. CrossRefGoogle Scholar
  21. Courchamp, F., Say, L., Pontier, D., 2000. Transmission of Feline Immunodeficiency Virus in a population of cats (Felis catus). Wildl. Res. 27, 603–611. CrossRefGoogle Scholar
  22. de Castro, F., Bolker, B., 2005. Mechanisms of disease-induced extinction. Ecol. Lett. 8, 117–126. CrossRefGoogle Scholar
  23. Didham, R.K., Tylianakis, J.M., Hutchinson, M.A., Ewers, R.M., Gemmell, N.J., 2005. Are invasive species the drivers of ecological change? Trends Ecol. Evol. 20, 470–474. CrossRefGoogle Scholar
  24. Dobson, A.P., 1988. Restoring island ecosystems: the potential of parasites to control introduced mammals. Conserv. Biol. 2, 31–39. CrossRefGoogle Scholar
  25. Fan, M., Kuang, Y., Feng, Z., 2005. Cats protecting birds revisited. Bull. Math. Biol. 67, 1081–1106. CrossRefMathSciNetGoogle Scholar
  26. Fenton, A., Rands, S.A., 2006. The impact of parasite manipulation and predator foraging behavior on predator-prey communities. Ecology 87, 2832–2841. CrossRefGoogle Scholar
  27. Fromont, E., Pontier, D., Langlais, M., 1998. Dynamics of a feline retrovirus (FeLV) in host populations with variable spatial structure. Proc. R. Soc. Lond. B 265, 1097–1104. CrossRefGoogle Scholar
  28. Ginzburg, L.R., 1998. Assuming reproduction to be a function of consumption raises doubts about some popular predator–prey models. J. Anim. Ecol. 67, 325–327. CrossRefGoogle Scholar
  29. Granadeiro, J.P., Dias, M.P., Rebelo, R., Santos, C.D., Catry, P., 2006. Numbers and population trends of Cory’s Shearwater Calonectris diomedea at Selvagem Grande, Northeast Atlantic. Waterbirds 29, 56–60. CrossRefGoogle Scholar
  30. Grenfell, B.T., Dobson, A.P. (Eds.), 1995. Ecology of Infectious Diseases in Natural Populations. Cambridge University Press, Cambridge. MATHGoogle Scholar
  31. Gurevitch, J., Padilla, D.K., 2004. Are invasive species a major cause of extinctions? Trends Ecol. Evol. 19, 470–474. CrossRefGoogle Scholar
  32. Han, L., Ma, Z., Hethcote, H.W., 2001. Four predator prey models with infectious diseases. Math. Comput. Model. 34, 849–858. MATHCrossRefMathSciNetGoogle Scholar
  33. Haque, M., Venturino, E., 2007. An ecoepidemiological model with disease in predator: the ratio-dependent case. Math. Methods Appl. Sci. 30, 1791–1809. MATHCrossRefMathSciNetGoogle Scholar
  34. Hatcher, M.J., Dick, J.T.A., Dunn, A.M., 2006. How parasites affect interactions between competitors and predators. Ecol. Lett. 9, 1253–1271. CrossRefGoogle Scholar
  35. Hilker, F.M., Schmitz, K., 2008. Disease-induced stabilization of predator-prey oscillations. J. Theor. Biol. 255, 299–306. CrossRefGoogle Scholar
  36. Hilker, F.M., Langlais, M., Petrovskii, S.V., Malchow, H., 2007. A diffusive SI model with Allee effect and application to FIV. Math. Biosci. 206, 61–80. MATHCrossRefMathSciNetGoogle Scholar
  37. Hilker, F.M., Langlais, M., Malchow, H., 2009. The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations. Am. Nat. 173, 72–88. CrossRefGoogle Scholar
  38. Holt, R.D., Polis, G.A., 1997. A theoretical framework for intraguild predation. Am. Nat. 149, 745–764. CrossRefGoogle Scholar
  39. Kot, M., 2001. Elements of Mathematical Ecology. Cambridge University Press, Cambridge. Google Scholar
  40. Krajick, K., 2005. Winning the war against island invaders. Science 310, 1410–1413. CrossRefGoogle Scholar
  41. Le Corre, M., 2008. Cats, rats and seabirds. Nature 451, 134–135. CrossRefGoogle Scholar
  42. Liberg, O., Sandell, M., Pontier, D., Natoli, E., 2000. Density, spatial organisation and reproductive tactics in the domestic cat and other felids. In: Turner, D.C., Bateson, P. (Eds.), The Domestic Cat: The Biology of Its Behaviour, 2nd edn., pp. 119–147. Cambridge University Press, Cambridge. Google Scholar
  43. Lockwood, J.L., Hoopes, M.F., Marchetti, M., 2007. Invasion Ecology. Blackwell Publishing, Oxford. Google Scholar
  44. Mack, R.N., Simberloff, D., Lonsdale, W.M., Evans, H., Clout, M., Bazzaz, F.A., 2000. Biotic invasions: causes, epidemiology, global consequences, and control. Ecol. Appl. 10, 689–710. CrossRefGoogle Scholar
  45. May, R.M., Hassell, M.P., 1988. Population dynamics and biological control. Philos. Trans. R. Soc. Lond. B 318, 129–169. CrossRefGoogle Scholar
  46. McCallum, H., Barlow, N., Hone, J., 2001. How should pathogen transmission be modelled? Trends Ecol. Evol. 16, 295–300. CrossRefGoogle Scholar
  47. Moors, P.J., Atkinson, I.A.E., 1984. Predation on seabirds by introduced animals, and factors affecting its severity. In: Croxall, P.J., Evans, P.G.H., Schreiber, R.W. (Eds.), Status and Conservation of the World’s Seabirds, vol. 2, pp. 667–690. ICBP Technical Publications, Cambridge. Google Scholar
  48. Murdoch, W.W., Briggs, C.J., 1996. Theory for biological control: recent developments. Ecology 77, 2001–2013. CrossRefGoogle Scholar
  49. Nogales, M., Martín, A., Tershy, B.R., Josh Donlan, C., Veitch, D., Puerta, N., Wood, B., Alonso, J., 2004. A review of feral cat eradication on islands. Conserv. Biol. 18, 310–319. CrossRefGoogle Scholar
  50. Pimm, S.L., 1982. Food Webs. Chapman and Hall, London. Google Scholar
  51. Rosenzweig, M.L., 1969. Why the prey curve has a hump. Am. Nat. 103, 81–87. CrossRefGoogle Scholar
  52. Rounsevell, D.E., Copson, G.R., 1982. Growth rate and recovery of a king penguin, Aptenodytes patagonicus, population after exploitation. Aust. Wildl. Res. 9, 519–525. CrossRefGoogle Scholar
  53. Ryan, P.G., 1987. The distribution, population size and foraging behaviour of Kerguelen terns at the Prince Edwards Islands. S. Afr. J. Antarct. Res. 17(2), 163–166. Google Scholar
  54. Sæther, B.E., Engen, S., 2002. Pattern of variation in avian population growth rates. Philos. Trans. R. Soc. Lond. B 357, 1185–1195. CrossRefGoogle Scholar
  55. Sax, D.F., Brown, J.H., 2000. The paradox of invasion. Glob. Ecol. Biogeogr. 9, 363–371. CrossRefGoogle Scholar
  56. Say, L., Gaillard, J.M., Pontier, D., 2002. Spatio-temporal variation in cat population density in a Sub-Antarctic environment. Polar Biol. 25, 90–95. Google Scholar
  57. Schramm, M., 1986. Burrow densities and nest site preferences of petrels (Procellariidae) at the Prince Edward Islands. Polar Biol. 6, 63–70. CrossRefGoogle Scholar
  58. Siegfried, W.R., 1978. Ornithological research at the Prince Edward islands: a review of progress. S. Afr. Antarktis Nave 8, 30–34. Google Scholar
  59. Strong, D.R., Pemberton, R.W., 2000. Biological control of invading species—risk and reform. Science 288, 1969–1970. CrossRefGoogle Scholar
  60. Tanabe, K., Namba, T., 2005. Omnivory creates chaos in simple food web models. Ecology 86, 3411–3414. CrossRefGoogle Scholar
  61. Turchin, P., 2003. Complex Population Dynamics. A Theoretical/Empirical Synthesis. Princeton University Press, Princeton. MATHGoogle Scholar
  62. Van Aarde, R.J., 1979. Distribution and density of the feral house cat Felis catus at Marion Island. S. Afr. J. Antarct. Res. 9, 14–19. Google Scholar
  63. Van Aarde, R.J., 1980. The diet and feeding behaviour of feral cats, Felis catus at Marion Island. S. Afr. J. Wildl. Res. 10(3/4), 123–128. Google Scholar
  64. Van Aarde, R.J., 1983. Demographic parameters of the feral cat Felis catus population at Marion Island. S. Afr. J. Wildl. Res. 13(1), 12–16. Google Scholar
  65. Van Rensburg, P.J.J., Bester, M.N., 1988. The effect of cat Felis catus predation on three breeding Procellariidae species on Marion Island. S. Afr. J. Zool. 23(4), 301–305. Google Scholar
  66. Van Rensburg, P.J.J., Skinner, J.D., Van Aarde, R.J., 1987. Effects of feline panleucopenia on the population characteristics of feral cats on Marion Island. J. Appl. Ecol. 24, 63–73. CrossRefGoogle Scholar
  67. Venturino, E., 1994. The influence of diseases on Lotka-Volterra systems. Rocky M. J. Math. 24(1), 381–402. MATHCrossRefMathSciNetGoogle Scholar
  68. Venturino, E., 2002. Epidemics in predator-prey models: disease in the predators. IMA J. Math. Appl. Med. Biol. 19, 185–205. MATHCrossRefGoogle Scholar
  69. Volterra, V., 1931. Leçons sur la Théorie Mathématique de la Lutte pour la Vie. Gauthier-Villars, Paris. Google Scholar
  70. Waage, J.K., Greathead, D.J., 1988. Biological control: challenges and opportunities. Philos. Trans. R. Soc. Lond. B 318, 111–128. CrossRefGoogle Scholar
  71. Wilcox, C., Donlan, C.J., 2007. Compensatory mitigation as a solution to fisheries bycatch-biodiversity conservation conflicts. Front. Ecol. Environ. 5, 325–331. CrossRefGoogle Scholar
  72. Williams, A.J., Burger, A.E., Berruti, A., Siegfried, W.R., 1975. Ornithological research on Marion Island 1974–1975. S. Afr. Antarktis Nave 5, 48–50. Google Scholar
  73. Williams, A.J., Siegfried, W.R., Burger, A.E., Berruti, A., 1979. The Prince Edward Islands: a sanctuary for seabirds in the Southern Ocean. Biol. Conserv. 15, 59–71. CrossRefGoogle Scholar
  74. Xiao, Y., Van Den Bosch, F., 2003. The dynamics of an eco-epidemic model with biological control. Ecol. Model. 168, 203–214. CrossRefGoogle Scholar
  75. Zavaleta, E.S., Hobbs, R.J., Mooney, H.A., 2001. Viewing invasive species removal in a whole-ecosystem context. Trends Ecol. Evol. 16, 454–459. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Instituto Gulbenkian de CiênciaOeirasPortugal
  2. 2.Departamento de Biologia Animal, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  3. 3.Centre for Mathematical Biology, Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  4. 4.Centro de Matemática e Aplicações FundamentaisUniversidade de LisboaLisboaPortugal
  5. 5.Department of Mathematical SciencesUniversity of BathBathUK

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