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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 852631, 24 pages
http://dx.doi.org/10.1155/2012/852631
Research Article

The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate

1Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
2Department of Mathematics, College of Science, University of Sulaimania, Sulaimania, Iraq

Received 5 May 2012; Accepted 10 August 2012

Academic Editor: Junjie Wei

Copyright © 2012 Raid Kamel Naji and Arkan N. Mustafa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. I. Freedman and P. Waltman, “Persistence in models of three interacting predator-prey populations,” Mathematical Biosciences, vol. 68, no. 2, pp. 213–231, 1984. View at Google Scholar · View at Scopus
  2. S. Gakkhar and R. K. Naji, “Chaos in three species ratio dependent food chain,” Chaos, Solitons and Fractals, vol. 14, no. 5, pp. 771–778, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. N. T. J. Bailey, The Mathematical Theory of Infectious Diseases, Griffin, London, UK, 1975.
  4. J. D. Murray, Mathematical Biology, vol. 19 of Biomathematics, Springer, Berlin, Germany, 2nd edition, 1993. View at Publisher · View at Google Scholar
  5. R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, UK, 1998.
  6. M. Haque and E. Venturino, “Modelling disease spreading in symbiotic communities,” in Wildlife: Destruction, Conservation and Biodiversity, J. D. Harris and P. L. Brownin, Eds., pp. 135–179, Nova Science, New York, NY, USA, 2009. View at Google Scholar
  7. R. M. Anderson and R. M. May, “The invasion, persistence and spread of infections disease within animal and plant communities,” Philosophical Transactions of the Royal Society B, vol. 314, no. 1167, pp. 533–570, 1986. View at Google Scholar
  8. K. P. Hadeler and H. I. Freedman, “Predator-prey populations with parasitic infection,” Journal of Mathematical Biology, vol. 27, no. 6, pp. 609–631, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. P. J. Hudson, A. P. Dobson, and D. Newborn, “Do parasites make prey vulnerable to predation? Red grouse and parasites,” Journal of Animal Ecology, vol. 61, no. 3, pp. 681–692, 1992. View at Google Scholar · View at Scopus
  10. J. Chattopadhyay and O. Arino, “A predator-prey model with disease in the prey,” Nonlinear Analysis: Theory, Methods & Applications, vol. 36, no. 6, pp. 747–766, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J. Moore, Parasites and the Behavior of Animals, Oxford University Press, Oxford, UK, 2002.
  12. Y. Xiao and L. Chen, “A ratio-dependent predator-prey model with disease in the prey,” Applied Mathematics and Computation, vol. 131, no. 2-3, pp. 397–414, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. H. W. Hethcote, W. Wang, L. Han, and Z. Ma, “A predator—prey model with infected prey,” Theoretical Population Biology, vol. 66, no. 3, pp. 259–268, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Haque and E. Venturino, “The role of transmissible diseases in the Holling-Tanner predator-prey model,” Theoretical Population Biology, vol. 70, no. 3, pp. 273–288, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Kundu and J. Chattopadhyay, “A ratio-dependent eco-epidemiological model of the Salton Sea,” Mathematical Methods in the Applied Sciences, vol. 29, no. 2, pp. 191–207, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. D. Greenhalgh and M. Haque, “A predator-prey model with disease in the prey species only,” Mathematical Methods in the Applied Sciences, vol. 30, no. 8, pp. 911–929, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. Haque and J. Chattopadhyay, “Role of transmissible disease in an infected prey-dependent predator-prey system,” Mathematical and Computer Modelling of Dynamcial Systems. Methods, Tools and Applications in Engineering and Related Sciences, vol. 13, no. 2, pp. 163–178, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. M. Haque and E. Venturino, “Effect of parasitic infection in the Leslie-Gower predator-prey model,” Journal of Biological Systems, vol. 16, no. 3, pp. 425–444, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Sinha, O. P. Misra, and J. Dhar, “Study of a prey-predator dynamics under the simultaneous effect of toxicant and disease,” Journal of Nonlinear Science and Its Applications, vol. 1, no. 2, pp. 102–117, 2008. View at Google Scholar · View at Zentralblatt MATH
  20. K. P. Das, S. Roy, and J. Chattopadhyay, “Effect of disease-selective predation on prey infected by contact and external sources,” BioSystems, vol. 95, no. 3, pp. 188–199, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Haque, J. Zhen, and E. Venturino, “An ecoepidemiological predator-prey model with standard disease incidence,” Mathematical Methods in the Applied Sciences, vol. 32, no. 7, pp. 875–898, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. B. Mukhopadhyay and R. Bhattacharyya, “Role of predator switching in an eco-epidemiological model with disease in the prey,” Ecological Modelling, vol. 220, no. 7, pp. 931–939, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. A. K. Pal and G. P. Samanta, “Stability analysis of an eco-epidemiological model incorporating a prey refuge,” Nonlinear Analysis: Modelling and Control, vol. 15, no. 4, pp. 473–491, 2010. View at Google Scholar
  24. M. Haque and D. Greenhalgh, “When a predator avoids infected prey: a model-based theoretical study,” Mathematical Medicine and Biology, vol. 27, no. 1, pp. 75–94, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. M. Haque and E. Venturino, “An ecoepidemiological model with disease in predator: the ratio-dependent case,” Mathematical Methods in the Applied Sciences, vol. 30, no. 14, pp. 1791–1809, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. M. Haque, “A predator-prey model with disease in the predator species only,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2224–2236, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. M. Haque, S. Sarwardi, S. Preston, and E. Venturino, “Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species,” Mathematical Biosciences, vol. 234, no. 1, pp. 47–57, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. A. B. Gumel and S. M. Moghadas, “A qualitative study of a vaccination model with non-linear incidence,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 409–419, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH