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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 508794, 7 pages
Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method
1Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Batu Pahat, 86400 Johor, Malaysia
2Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
3Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Received 24 October 2012; Accepted 12 December 2012
Academic Editor: Xinguang Zhang
Copyright © 2013 Chang Phang 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.
- L. G. Matallana, A. M. Blanco, and J. Alberto Bandoni, “Estimation of domains of attraction in epidemiological models with constant removal rates of infected individuals,” Journal of Physics: Conference Series, vol. 90, no. 1, Article ID 012052, 2007.
- X. Y. Chen, C. J. Li, J. F. Lü, and Y. W. Jing, “The domain of attraction for a SEIR epidemic model based on sum of square optimization,” Bulletin of the Korean Mathematical Society, vol. 49, no. 3, pp. 517–528, 2012.
- Z. Zhang, J. Wu, Y. Suo, and X. Song, “The domain of attraction for the endemic equilibrium of an SIRS epidemic model,” Mathematics and Computers in Simulation, vol. 81, no. 9, pp. 1697–1706, 2011.
- E. Kaslik, A. M. Balint, and S. Balint, “Methods for determination and approximation of the domain of attraction,” Nonlinear Analysis, Theory, Methods and Applications, vol. 60, no. 4, pp. 703–717, 2005.
- A. Vannelli and M. Vidyasagar, “Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems,” Automatica, vol. 21, no. 1, pp. 69–80, 1985.
- S. Rozgonyi, K. M. Hangos, and G. Szederkényi, “Determining the domain of attraction of hybrid non-linear systems using maximal lyapunov functions,” Kybernetika, vol. 46, no. 1, pp. 19–37, 2010.
- J. Pang, J. A. Cui, and J. Hui, “Rich dynamics of epidemic model with sub-optimal immunity and nonlinear recovery rate,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 440–448, 2011.
- M. G. M. Gomes, L. J. White, and G. F. Medley, “Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives,” Journal of Theoretical Biology, vol. 228, no. 4, pp. 539–549, 2004.
- W. M. Liu, S. A. Levin, and Y. Iwasa, “Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models,” Journal of Mathematical Biology, vol. 23, no. 2, pp. 187–204, 1986.