Bifurcations for a deterministic SIR epidemic model in discrete time

Advances in Difference Equations

Volumn 2014, Issue 1, 2014, Pages

  Zhou, Xiaoliang ^a   Li, Xiaopei ^a   Wang, Wu Sheng ^b  

^a LINGNAN NORMAL UNIVERSITY   (China)

^b HECHI UNIVERSITY   (China)

Author keywords

Center manifold; Discrete time; Epidemic model; Flip bifurcation; Transcritical bifurcation

Indexed keywords

EID: 84904459934     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2014-168     Document Type: Article

References (20)

1. Kermack, WO, McKendrick, AG: Contributions to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700-721 (1927)
2. Anderson, RM, May, RM: Infections Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1991)
3. Diekmann, O, Heersterbeek, JAP: Mathematical Epidemiology of Infectious Diseases: Model Building Analysis, and Interpretation. Wiley, New York (2000)
4. Murray, JD: Mathematical Biology II, 3rd edn. Springer, Berlin (2003)
5. Ma, Z, Zhou, Y, Wang, W, Jin, Z: Mathematical Modelling and Research of Epidemic Dynamical Systems. Science Press, Beijing (2004)
6. Hethcote, HW, Stech, HW, van den Driessche, P: Periodicity and stability in epidemic models. In: Busenberg, SN, Cooke, KL (eds.) Differential Equations and Applications in Ecology, Epidemics and Population Problems, pp. 65-82. Academic Press, New York (1981)
7. Takeuchi, Y, Ma, W, Beretta, E: Global asymptotic properties of a delay SIR epidemic model with finite incubation times. Nonlinear Anal. 42, 931-947 (2000)
8. Castillo-Chavez, C, Yakubu, A-A: Disperal, disease and life-history evolution. Math. Biosci. 173, 35-53 (2001)
9. Medlock, J, Kot, M: Spreading disease: integro-differential equations old and new. Math. Biosci. 184, 201-222 (2003) (Pubitemid 36876938)
10. Song, M, Ma, W: Asymptotic properties of a revised SIR epidemic model with density dependent birth rate and time delay. Dyn. Contin. Discrete Impuls. Syst. 13, 199-208 (2006) (Pubitemid 44965433)
11. Yoshida, N, Hara, T: Global stability of a delayed SIR epidemic model with density dependent birth and death rates. J. Comput. Appl. Math. 201, 339-347 (2007) (Pubitemid 46176486)
12. Robinson, RC: An Introduction to Dynamical Systems: Continuous and Discrete. Pearson Prentice Hall, Upper Saddle River (2004)
13. May, RM: Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976)
14. Rasband, SN: Chaotic Dynamics of Nonlinear Systems. Wiley-Interscience, New York (1990)
15. Allen, LJS: Some discrete-time SI, SIR and SIS epidemic models. Math. Biosci. 124, 83-105 (1994) (Pubitemid 24348343)
16. Allen, LJS, Burgin, AM: Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math. Biosci. 163, 1-33 (2000) (Pubitemid 30054048)
17. Kuznetsov, YA: Elements of Applied Bifurcation Theory. Springer, New York (1995)
18. Wiggins, S: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York (1990)
19. Guckenheimer, J, Holmes, P: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York (1983)
20. Carr, J: Applications of Center Manifold Theory. Springer, New York (1981)