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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 656920, 13 pages
Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
Received 13 June 2013; Accepted 5 September 2013
Academic Editor: XianHua Tang
Copyright © 2013 Lianwen Wang and Zhijun Liu. 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.
- R. M. Anderson and R. M. May, Population Biology of Infectious Disease, Springer, Berlin, Germany, 1982.
- Y. Xiao and L. Chen, “Modeling and analysis of a predator-prey model with disease in the prey,” Mathematical Biosciences, vol. 171, no. 1, pp. 59–82, 2001.
- 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.
- G. P. Hu and X. L. Li, “Stability and Hopf bifurcation for a delayed predator-prey model with disease in the prey,” Chaos, Solitons & Fractals, vol. 45, no. 3, pp. 229–237, 2012.
- G. P. Samanta, “Analysis of a delay nonautonomous predator-prey system with disease in the prey,” Nonlinear Analysis: Modelling and Control, vol. 15, no. 1, pp. 97–108, 2010.
- A. J. Nicholson, “An outline of the dynamics of the animal populations,” Australian Journal of Zoology, vol. 2, no. 1, pp. 9–65, 1954.
- A. Lakmeche and O. Arino, “Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 7, no. 2, pp. 265–287, 2000.
- A. D'Onofrio, “On pulse vaccination strategy in the SIR epidemic model with vertical transmission,” Applied Mathematics Letters, vol. 18, no. 7, pp. 729–732, 2005.
- M. Choisy, J. F. Guégan, and P. Rohani, “Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects,” Physica D, vol. 223, no. 1, pp. 26–35, 2006.
- M. Liu, Z. Jin, and M. Haque, “An impulsive predator-prey model with communicable disease in the prey species only,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3098–3111, 2009.
- R. Shi, X. Jiang, and L. Chen, “A predator-prey model with disease in the prey and two impulses for integrated pest management,” Applied Mathematical Modelling, vol. 33, no. 5, pp. 2248–2256, 2009.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989.
- Z. Liu, J. Wu, and R. A. Cheke, “Coexistence and partial extinction in a delay competitive system subject to impulsive harvesting and stocking,” IMA Journal of Applied Mathematics, vol. 75, no. 5, pp. 777–795, 2010.
- W. Wang, J. Shen, and J. J. Nieto, “Permanence and periodic solution of predator-prey system with Holling type functional response and impulses,” Discrete Dynamtics in Nature and Society, vol. 2007, Article ID 521729, 15 pages, 2007.
- Z. Liu, Y. Chen, Z. He, and J. Wu, “Permanence in a periodic delay logistic system subject to constant impulsive stocking,” Mathematical Methods in the Applied Sciences, vol. 33, no. 8, pp. 985–993, 2010.
- W. Wang, J. Shen, and Z. Luo, “Partial survival and extinction in two competing species with impulses,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1243–1254, 2009.