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RANDOM DISPERSAL IN A PREDATOR-PREY-PARASITE SYSTEM

SOPHIA R.-J. JANG

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA

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JAMES BAGLAMA

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

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, and

LI WU

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

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https://doi.org/10.1142/S0218339010003536Cited by:1 (Source: Crossref)

Abstract

We propose predator-prey-parasite models to study the effects of parasites upon the predator-prey interaction. There are two parameters that are used to model the effectiveness of the infected prey and infected predator. For the spatial homogeneous system, the asymptotic dynamics depend on the reproductive number of the parasite. The parasite can persist in the population if this reproductive number is larger than one. Numerical simulations suggest that less competitiveness of the infected predator can make the predator-prey interaction less stable. The dynamics may move from coexisting steady state to oscillations. For the spatial heterogeneous system, diffusion may destabilize the homogeneous interior steady state for a particular set of diffusion coefficients. However, both systems do not exhibit complicated dynamical behavior.

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References

W. O. Kermack and A. G. McKendrick, Proc. R. Soc. Lond. A 115, 700 (1927). Crossref, Google Scholar
R. M. Anderson and R. M. May, Philos. Trans. R. Soc. B 314, 533 (1986). Crossref, Web of Science, Google Scholar
F. Brauer and C. Castillo-Chavez , Mathematical Models in Population Biology and Epidemiology ( Springer , New York , 2001 ) . Crossref, Google Scholar
O. Diekmann and J. Heesterbeek , Mathematical Epidemiology of Infectious Diseases ( Wiley , Chichester , 2000 ) . Google Scholar
H. Hethcote, SIAM Rev. 42, 599 (2000). Crossref, Web of Science, Google Scholar
H. R. Thieme , Mathematics in Population Biology ( Princeton Press , 2005 ) . Google Scholar
J. Chattophadhyay and O. Arino, Non. Anal. 36, 747 (1999). Crossref, Web of Science, Google Scholar
A. Fenton and S. A. Rands, Ecology 87, 2832 (2006). Crossref, Web of Science, Google Scholar
K. P. Hadeler and H. I. Freedman, J. Math. Biol. 27, 609 (1989). Crossref, Web of Science, Google Scholar
L. Han, Z. Ma and H. W. Hethcote, Math. Compu. Mod. 34, 849 (2001). Crossref, Web of Science, Google Scholar
A. Dobson and A. Keymer, Biology of the Acanthocephala, eds. D. Crompton and B. Nickol (Cambridge University Press, Cambridge, 1985) pp. 347–384. Google Scholar
R. D. Holt and J. Pickering, Amer. Natur. 126, 196 (1985). Crossref, Web of Science, Google Scholar
P. J. Hudson, A. Dobson and D. Newborn, Science 282, 2256 (1998). Crossref, Web of Science, Google Scholar
S. R.-J. Jang and J. Baglama, J. Biol. Dyn. 3, 87 (2009). Crossref, Google Scholar
C. Castillo-Chavez and B. Song, Math. Biosci. & Eng. 1, 361 (2004). Crossref, Web of Science, Google Scholar
N. F. Britton , Reaction-Diffusion Equations and Their Applications to Biology ( Academic Press , New York , 1986 ) . Google Scholar
J. D. Murray , Mathematical Biology ( Springer-Verlag , New York , 1989 ) . Crossref, Google Scholar
H. R. Thieme, J. Math. Biol. 30, 755 (1992). Web of Science, Google Scholar