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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 320581, 10 pages
Analysis of a Dengue Disease Model with Nonlinear Incidence
1Department of Mathematics and Information Science, Shaoguan University, Shaoguan 512005, China
2Department of Mathematics, Xinyang Normal University, Xinyang 464000, China
3School of Advanced Sciences, VIT University, Chennai Campus, Chennai 600048, India
Received 10 September 2012; Revised 3 January 2013; Accepted 3 January 2013
Academic Editor: Eric Campos Canton
Copyright © 2013 Shu-Min Guo et al. 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.
- Y. Xiao and S. Tang, “Dynamics of infection with nonlinear incidence in a simple vaccination model,” Nonlinear Analysis. Real World Applications, vol. 11, no. 5, pp. 4154–4163, 2010.
- L.-M. Cai and X.-Z. Li, “Global analysis of a vector-host epidemic model with nonlinear incidences,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3531–3541, 2010.
- Z. Hu, W. Ma, and S. Ruan, “Analysis of SIR epidemic models with nonlinear incidence rate and treatment,” Mathematical Biosciences, vol. 238, no. 1, pp. 12–20, 2012.
- L. Li, G.-Q. Sun, and Z. Jin, “Bifurcation and chaos in an epidemic model with nonlinear incidence rates,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1226–1234, 2010.
- M. Ozair, A. A. Lashari, I. H. Jung, and K. O. Okosun, “Stability analysis and optimal control of a vector-borne disease with nonlinear incidence,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 595487, 21 pages, 2012.
- C. Castillo-Chavez and B. Song, “Dynamical models of tuberculosis and their applications,” Mathematical Biosciences and Engineering, vol. 1, no. 2, pp. 361–404, 2004.
- J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.
- M. Y. Li and J. S. Muldowney, “A geometric approach to global-stability problems,” SIAM Journal on Mathematical Analysis, vol. 27, no. 4, pp. 1070–1083, 1996.
- B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, vol. 14 of Software, Environments, and Tools, SIAM, Philadelphia, Pa, USA, 2002.
- M. Y. Li and J. S. Muldowney, “On R. A. Smith's autonomous convergence theorem,” The Rocky Mountain Journal of Mathematics, vol. 25, no. 1, pp. 365–379, 1995.
- Y. Li and J. S. Muldowney, “On Bendixson's criterion,” Journal of Differential Equations, vol. 106, no. 1, pp. 27–39, 1993.
- C. C. Pugh, “An improved closing lemma and a general density theorem,” American Journal of Mathematics, vol. 89, pp. 1010–1021, 1967.
- C. C. Pugh and C. Robinson, “The closing lemma, including Hamiltonians,” Ergodic Theory and Dynamical Systems, vol. 3, no. 2, pp. 261–313, 1983.
- W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Co., Boston, Mass, USA, 1965.