An analysis of the coexistence of two host species with a shared pathogen
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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.
KeywordsHolt–Pickering model Host population dynamics Host–host–pathogen interactions Stability and instability analysis
Mathematics Subject Classification (2000)92D25 37C10 37C27
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- 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
- 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
- 18.Price P.W. (1980). Evolutionary Biology of Parasites. Princetion University Press, Princeton Google Scholar