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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 262535, 9 pages
Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination
1Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Enshi, Hubei 445000, China
2Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei 445000, China
Received 20 April 2013; Revised 27 December 2013; Accepted 30 December 2013; Published 23 February 2014
Academic Editor: Aura Reggiani
Copyright © 2014 Mei Yan and Zhongyi Xiang. 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.
- G. Jiang and Q. Yang, “Periodic solutions and bifurcation in an SIS epidemic model with birth pulses,” Mathematical and Computer Modelling, vol. 50, no. 3-4, pp. 498–508, 2009.
- T. Zhang and Z. Teng, “Pulse vaccination delayed SEIRS epidemic model with saturation incidence,” Applied Mathematical Modelling, vol. 32, no. 7, pp. 1403–1416, 2008.
- C. Zhang, Y. Zhao, and Y. Wu, “An impulse model for computer viruses,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 260962, 13 pages, 2012.
- T. Zhang and Z. Teng, “Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model,” Chaos, Solitons & Fractals, vol. 39, no. 5, pp. 2411–2425, 2009.
- C. Zhang, Y. Zhao, and Y. Wu, “An impulse dynamic model for computer worms,” Abstract and Applied Analysis, vol. 2013, Article ID 286209, 8 pages, 2013.
- X. Meng, J. Jiao, and L. Chen, “Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination,” Chaos, Solitons & Fractals, vol. 40, no. 5, pp. 2114–2125, 2009.
- T. Zhang, J. Liu, and Z. Teng, “Existence of positive periodic solutions of an SEIR model with periodic coefficients,” Applications of Mathematics, vol. 57, no. 6, pp. 601–616, 2012.
- X. Ji, Y. Pei, and C. Li, “Two patterns of recruitment in an epidemic model with difference in immunity of individuals,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 2078–2090, 2010.
- H.-F. Huo and L.-X. Feng, “Global stability of an epidemic model with incomplete treatment and vaccination,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 530267, 14 pages, 2012.
- X. Liu and P. Stechlinski, “Pulse and constant control schemes for epidemic models with seasonality,” Nonlinear Analysis: Real World Applications, vol. 12, no. 2, pp. 931–946, 2011.
- C. Sun and Y.-H. Hsieh, “Global analysis of an SEIR model with varying population size and vaccination,” Applied Mathematical Modelling, vol. 34, no. 10, pp. 2685–2697, 2010.
- M. de la Sen, A. Ibeas, and S. Alonso-Quesada, “Observer-based vaccination strategy for a true mass action SEIR epidemic model with potential estimation of all the populations,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 743067, 19 pages, 2011.
- W. Wang, J. Xin, and F. Zhang, “Persistence of an SEIR model with immigration dependent on the prevalence of infection,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 727168, 7 pages, 2010.
- Z. Bai and Y. Zhou, “Existence of two periodic solutions for a non-autonomous SIR epidemic model,” Applied Mathematical Modelling, vol. 35, no. 1, pp. 382–391, 2011.
- N. Bacaër and S. Guernaoui, “The epidemic threshold of vector-borne diseases with seasonality. The case of cutaneous leishmaniasis in Chichaoua, Morocco,” Journal of Mathematical Biology, vol. 53, no. 3, pp. 421–436, 2006.
- W. Wang and X.-Q. Zhao, “Threshold dynamics for compartmental epidemic models in periodic environments,” Journal of Dynamics and Differential Equations, vol. 20, no. 3, pp. 699–717, 2008.
- Y. Nakata and T. Kuniya, “Global dynamics of a class of SEIRS epidemic models in a periodic environment,” Journal of Mathematical Analysis and Applications, vol. 363, no. 1, pp. 230–237, 2010.
- T. Zhang and Z. Teng, “On a nonautonomous SEIRS model in epidemiology,” Bulletin of Mathematical Biology, vol. 69, no. 8, pp. 2537–2559, 2007.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, Singapore, 1989.
- J. J. Kim, M. Brisson, W. J. Edmunds, and S. J. Goldie, “Modeling cervical cancer prevention in developed countries,” Vaccine, vol. 26, no. 10, pp. K76–K86, 2008.