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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 354287, 11 pages
Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates
1School of Science, Department of Fundamental Mathematics, Jiamusi University, Jiamusi 154007, China
2School of Mathematical Science, Heilongjiang University, Harbin 150080, China
Received 26 January 2013; Revised 16 June 2013; Accepted 22 July 2013
Academic Editor: Pagavathi Balasubramaniam
Copyright © 2013 Ling Zhang 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.
- H. R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton, NJ, USA, 2003.
- H. Guo, M. Y. Li, and Z. Shuai, “Global stability of the endemic equilibrium of multigroup SIR epidemic models,” Canadian Applied Mathematics Quarterly, vol. 14, no. 3, pp. 259–284, 2006.
- H. Guo, M. Y. Li, and Z. Shuai, “A graph-theoretic approach to the method of global Lyapunov functions,” Proceedings of the American Mathematical Society, vol. 136, no. 8, pp. 2793–2802, 2008.
- H. Shu, D. Fan, and J. Wei, “Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1581–1592, 2012.
- J. Wang, Y. Takeuchi, and S. Liu, “A multi-group SVEIR epidemic model with distributed delay and vaccination,” International Journal of Biomathematics, vol. 5, no. 3, Article ID 1260001, 18 pages, 2012.
- P. van den Driessche, L. Wang, and X. Zou, “Modeling diseases with latency and relapse,” Mathematical Biosciences and Engineering, vol. 4, no. 2, pp. 205–219, 2007.
- A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979.
- A. Korobeinikov and P. K. Maini, “A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence,” Mathematical Biosciences and Engineering, vol. 1, no. 1, pp. 57–60, 2004.
- M. Y. Li and J. S. Muldowney, “Global stability for the SEIR model in epidemiology,” Mathematical Biosciences, vol. 125, no. 2, pp. 155–164, 1995.
- G. Huang and Y. Takeuchi, “Global analysis on delay epidemiological dynamic models with nonlinear incidence,” Journal of Mathematical Biology, vol. 63, no. 1, pp. 125–139, 2011.
- P. van den Driessche and X. Zou, “Modeling relapse in infectious diseases,” Mathematical Biosciences, vol. 207, no. 1, pp. 89–103, 2007.
- P. van den Driessche, L. Wang, and X. Zou, “Impact of group mixing on disease dynamics,” Mathematical Biosciences, vol. 228, no. 1, pp. 71–77, 2010.
- S. Liu, S. Wang, and L. Wang, “Global dynamics of delay epidemic models with nonlinear incidence rate and relapse,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 119–127, 2011.
- Z. Yuan and X. Zou, “Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 3479–3490, 2010.
- R. Sun and J. Shi, “Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates,” Applied Mathematics and Computation, vol. 218, no. 2, pp. 280–286, 2011.
- R. K. Miller, Nonlinear Volterra Integral Equations, W. A. Benjamin, New York, NY, USA, 1971.
- P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29–48, 2002.
- J. P. Lasalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1976.
- H. I. Freedman, M. X. Tang, and S. G. Ruan, “Uniform persistence and flows near a closed positively invariant set,” Journal of Dynamics and Differential Equations, vol. 6, no. 4, pp. 583–600, 1994.
- H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, Cambridge, UK, 1995.
- M. Y. Li and Z. S. Shuai, “Global-stability problem for coupled systems of differential equations on networks,” Journal of Differential Equations, vol. 248, no. 1, pp. 1–20, 2010.
- Z. Shuai and P. van den Driessche, “Impact of heterogeneity on the dynamics of an SEIR epidemic model,” Mathematical Biosciences and Engineering, vol. 9, no. 2, pp. 393–411, 2012.