Bifurcations of an SIRS epidemic model with nonlinear
incidence rate
Pages: 93  112,
Volume 15,
Issue 1,
January
2011
doi:10.3934/dcdsb.2011.15.93 Abstract
References
Full text (1841.6K)
Related Articles
Zhixing Hu  Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China (email)
Ping Bi  Department of Mathematics, East China Normal University, Shanghai 200062, China (email)
Wanbiao Ma  Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China (email)
Shigui Ruan  Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, Florida 33124, United States (email)
1 
M. E. Alexander and S. M. Moghadas, Periodicity in an epidemic model with a generalized nonlinear incidence, Math. Biosci., 189 (2004), 7596. 

2 
M. E. Alexander and S. M. Moghadas, Bifurcation analysis of an SIRS epidemic model with generalized incidence, SIAM J. Appl. Math., 65 (2005), 17941816. 

3 
V. Capasso and G. Serio, A generalization of the KermackMcKendrick deterministic epidemic model, Math. Biosci., 42 (1978), 4361. 

4 
W. R. Derrick and P. van den Driessche, Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population, Discrete Contin. Dyn. Syst. Ser. B, 2 (2003), 299309. 

5 
Z. Feng and H. R. Thieme, Recurrent outbreaks of childhood disease revisited: The impact of isolation, Math. Biosci., 128 (1995), 93130. 

6 
P. Glendinning, "Stability, Instability and Chaos," Cambridge University Press, Cambridge, 1994. 

7 
B. D. Hassard, N. D. Kazarinoff and Y. H. Wan, "Theory and Applications of Hopf Bifurcation," Lecture Notes Series, vol. 41, Cambridge University Press, Cambridge, 1981. 

8 
H. W. Hethcote, The mathematics of infectious disease, SIAM Rev., 42 (2000), 599653. 

9 
H. W. Hethcote and S. A. Levin, Periodicity in epidemiological models, in "Applied Mathematical Ecology" (Trieste, 1986), Biomathematics 18, SpringerVerlag, Berlin, 1989, pp. 193211. 

10 
H. W. Hethcote and P. van den Driessche, Some epidemiological models with nonlinear incidence, J. Math. Biol., 29 (1991), 271287. 

11 
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory," 3rd edition, Appl. Math. Sci. 112, SpringerVerlag, New York, 2004. 

12 
G. Li and W. Wang, Bifurcation analysis of an epidemic model with nonlinear incidence, Appl. Math. Comput., 214 (2009), 411423. 

13 
W. M. Liu, H. W. Hetchote and S. A. Levin, Dynamical behavior of epidemiological models with nonlinear incidence rates, J. Math. Biol., 25 (1987), 359380. 

14 
W. M. Liu, S. A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol., 23 (1986), 187204. 

15 
M. Lizana and J. Rivero, Multiparametric bifurcations for a model in epidemiology, J. Math. Biol., 35 (1996), 2136. 

16 
S. M. Moghadas, Analysis of an epidemic model with bistable equilibria using the PoincarĂ© index, Appl. Math. Comput., 149 (2004), 689702. 

17 
S. M. Moghadas and M. E. Alexander, Bifurcations of an epidemic model with nonlinear incidence and infectiondependent removal rate, Math. Med. Biol., 23 (2006), 231254. 

18 
S. Ruan and W. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations, 188 (2003), 135163. 

19 
Y. Tang, D. Huang, S. Ruan and W. Zhang, Coexistence of limit cycles and homoclinic loops in a SIRS model with a nonlinear incidence rate, SIAM J. Appl. Math., 69 (2008), 621639. 

20 
W. Wang, Epidemic models with nonlinear infection forces, Math. Biosci. Eng., 3 (2006), 267279. 

21 
S. Wiggins, "Introduction to Applied Nonlinear Dynamical Systems and Chaos," 2nd edition, SpringerVerlag, New York, 2004. 

22 
D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208 (2007), 419429. 

Go to top
