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An analysis of the coexistence of two host species with a shared pathogen

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Abstract

Population dynamics of two-host species under direct transmission of an infectious disease or a pathogen is studied based on the Holt–Pickering mathematical model, which accounts for the influence of the pathogen on the population of the two-host species. Through rigorous analysis and a numerical scheme of study, circumstances are specified under which the shared pathogen leads to the coexistence of the two-host species in either a persistent or periodic form. This study shows the importance of intrinsic growth rates or the differences between birth rates and death rates of the two host susceptibles in controlling these circumstances. It is also demonstrated that the periodicity may arise when the positive intrinsic growth rates are very small, but the periodicity is very weak which may not be observed in an empirical investigation.

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References

  1. Anderson R.M. and May R.M. (1979). Population biology of infectious deseases: Part I. Nature 280: 361–367

    Article  Google Scholar 

  2. Anderson R.M. and May R.M. (1981). The population dynamics of mioparasites and their invertebrate hosts. Phil. Trans. R. Soc. Lond. B. Biol. Sci. 291: 451–524

    Article  Google Scholar 

  3. Begon M. and Bowers R.G. (1992). Dease and community structure: the importance of host self-regulation in a host-pathogen model. Am. Nat. 139: 1131–1150

    Article  Google Scholar 

  4. Briggs C.J., Hails R.S., Barlow N.D. and Godfray H.C.J. (1995). The dynamics of insect–pathegon interactions. In: Grenfell, B.T. and Dobson, A.P. (eds) Ecology of Infectious Desease in Natural Populations, pp 295–326. Cambridge University Press, Cambridge

    Google Scholar 

  5. Burden R.L. and Faires J.D. (1988). Numerical Analysis. PWS-KENT, Boston

    Google Scholar 

  6. Cantrell R.S., Cosner C. and Fagan W.F. (2001). Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction. J. Math. Biol. 42: 95–119

    Article  MATH  MathSciNet  Google Scholar 

  7. Edelstein-Keshet L. (1988). Mathematical Models in Biology. McGraw-Hill, New York

    MATH  Google Scholar 

  8. Elton C.S. (1927). Animal Ecology. Sidgwick and Jackson, London

    Google Scholar 

  9. Gantmacher F.R. (1960). The Theory of Matrices, vol. II. Chelsea Publishing, New York

    Google Scholar 

  10. Greenman J.V. and Hudson P.J. (1997). Infected coexistence instability with and without density-dependent regulation. J. Theor. Biol. 185: 345–356

    Article  Google Scholar 

  11. Holt R.D. (1977). Predation, apparent competition and the structure of prey communities. Theor. Popul. Biol. 12: 197–229

    Article  MathSciNet  Google Scholar 

  12. Holt R.D. (1984). Spatial heterogeneity, indirect interactions and the coexistence of prey species. Am. Nat. 124: 337–406

    Article  Google Scholar 

  13. Holt R.D. (1993). Apparent competition and enemy-free space in insect host-parasitoid communities. Am. Nat. 142: 623–645

    Article  Google Scholar 

  14. Holt R.D. and Pickering J. (1985). Infectious desease and species coeixstence: a model in Lotka–Volterra form. Am. Nat. 126: 196–211

    Article  Google Scholar 

  15. Jansen V.A.A. and Sigmund K. (1998). Shaken not stirred: on permanence in ecological communities. Theor. Popul. Biol. 54: 195–201

    Article  MATH  Google Scholar 

  16. Liu W.M. (1994). Criterion of Hopf bifurcations without using eigenvalues. J. Math. Anal. Appl. 182: 250–256

    Article  MATH  MathSciNet  Google Scholar 

  17. O’Keefe K.J. (2005). The evolution of virulence in pathogens with frequency-dependent transmission. J. Theor. Biol. 233: 55–64

    Article  MathSciNet  Google Scholar 

  18. Price P.W. (1980). Evolutionary Biology of Parasites. Princetion University Press, Princeton

    Google Scholar 

  19. Rosenzweig M.L. (1971). The paradox of enrichment-destabilization of exploitation ecosystems in ecological time. Science 171: 385–387

    Article  Google Scholar 

  20. Rosenzweig M.L. and MacArthur R.H. (1963). Graphical representation and stability conditions of predator-prey interactions. Am. Nat. 47: 209–223

    Article  Google Scholar 

  21. Schoener T.W. (1983). Field experiments on interspecific competition. Am. Nat. 122: 240–285

    Article  Google Scholar 

  22. Schreiber S.J. (2004). Coexistence for species sharing a predator. J. Diff. Equ. 196: 209–225

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Engineering Sciences, University of Southampton, Southampton, SO17 1BJ, UK

    Zhi-Min Chen & W. G. Price

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  1. Zhi-Min Chen
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  2. W. G. Price
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Correspondence to Zhi-Min Chen.

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Chen, ZM., Price, W.G. An analysis of the coexistence of two host species with a shared pathogen. J. Math. Biol. 56, 841–859 (2008). https://doi.org/10.1007/s00285-007-0141-3

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  • DOI: https://doi.org/10.1007/s00285-007-0141-3

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