- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 314958, 9 pages
Rich Dynamics of an Epidemic Model with Saturation Recovery
1Jiangsu Key Laboratory for NSLSCS, School of Mathematics, Nanjing Normal University, Nanjing 210046, China
2School of Sciences, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
Received 18 January 2013; Accepted 26 March 2013
Academic Editor: Xinyu Song
Copyright © 2013 Hui Wan and Jing-an Cui. 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.
- M. E. Alexander and S. M. Moghadas, “Periodicity in an epidemic model with a generalized non-linear incidence,” Mathematical Biosciences, vol. 189, no. 1, pp. 75–96, 2004.
- X. Shi, J. Cui, and X. Zhou, “Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 4, pp. 1088–1106, 2011.
- H. W. Hethcote, “The mathematics of infectious diseases,” SIAM Review, vol. 42, no. 4, pp. 599–653, 2000.
- Z. Hu, Z. Teng, and H. Jiang, “Stability analysis in a class of discrete SIRS epidemic models,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2017–2033, 2012.
- J. Pang, J. 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.
- H. Wan and H. Zhu, “The backward bifurcation in compartmental models for West Nile virus,” Mathematical Biosciences, vol. 227, no. 1, pp. 20–28, 2010.
- W. Wang, “Backward bifurcation of an epidemic model with treatment,” Mathematical Biosciences, vol. 201, no. 1-2, pp. 58–71, 2006.
- X. Zhang and X. Liu, “Backward bifurcation of an epidemic model with saturated treatment function,” Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 433–443, 2008.
- W. Wang and S. Ruan, “Bifurcation in an epidemic model with constant removal rate of the infectives,” Journal of Mathematical Analysis and Applications, vol. 291, no. 2, pp. 775–793, 2004.
- J. D. Murray, Mathematical Biology, Springer, New York, NY, USA, 1998.
- P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002.
- L. Perko, Differential Equations and Dynamical Systems, Springer, New York, NY, USA, 1996.
- W. M. Liu, H. W. Hethcote, and S. A. Levin, “Dynamical behavior of epidemiological models with nonlinear incidence rates,” Journal of Mathematical Biology, vol. 25, no. 4, pp. 359–380, 1987.
- J. Lin, V. Andreasen, and S. A. Levin, “Dynamics of influenza A drift: the linear three-strain model,” Mathematical Biosciences, vol. 162, no. 1-2, pp. 33–51, 1999.