Stability of a delayed SIRS epidemic model with a nonlinear incidence rate

Chaos, Solitons and Fractals

Volumn 41, Issue 5, 2009, Pages 2319-2325

  Xu, Rui ^a,b,c   Ma, Zhien ^c  

^a MECHANICAL ENGINEERING COLLEGE   (China)

^b YUNCHENG UNIVERSITY   (China)

^c XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ITERATIVE METHODS;

BASIC REPRODUCTIVE NUMBER; CHARACTERISTIC EQUATION; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; GLOBAL ASYMPTOTIC STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; ITERATION TECHNIQUES; NON-LINEAR INCIDENCE RATES;

EPIDEMIOLOGY;

EID: 67649304819     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2008.09.007     Document Type: Article

References (19)

1. Beretta E., Hara T., Ma W., and Takeuchi Y. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal 47 (2001) 4107-4115
2. Beretta E., and Takeuchi Y. Global stability of an SIR epidemic model with time delays. J Math Biol 33 (1995) 250-260
3. Beretta E., and Takeuchi Y. Convergence results in SIR epidemic model with varying population sizes. Nonlinear Anal 28 (1997) 1909-1921
4. Capasso V., and Serio G. A generalization of the Kermack-Mckendrick deterministic epidemic model. Math Biosci 42 (1978) 41-61
5. Cooke K.L. Stability analysis for a vector disease model. Rocky Mount J Math 9 (1979) 31-42
6. Gakkhar S., and Negi K. Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate. Chaos Solitons & Fractals 35 (2008) 626-638
7. Hale J. Theory of functional differential equations (1977), Springer-Verlag, Heidelberg
8. Jin Y., Wang W., and Xiao S. An SIRS model with a nonlinear incidence rate. Chaos Solitons & Fractals 34 (2007) 1482-1497
9. Liu J., and Zhou Y. Global stability of an SIRS epidemic model with transport-related infection. Chaos, Solitons & Fractals 40 1 (2009) 145-158
10. Liu W.M., Hethcote H.W., and Levin S.A. Dynamical behavior of epidemiological models with nonlinear incidence rates. J Math Biol 25 (1987) 359-380
11. Liu W.M., Levin S.A., and Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J Math Biol 23 (1986) 187-204
12. Ma W., Song M., and Takeuchi Y. Global stability of an SIR epidemic model with time delay. Appl Math Lett 17 (2004) 1141-1145
13. Ma W., Takeuchi Y., Hara T., and Beretta E. Permanence of an SIR epidemic model with distributed time delays. Tohoku Math J 54 (2002) 581-591
14. Mena-Lorca J., and Hethcote H.W. Dynamic models of infectious diseases as regulators of population size. J Math Biol 30 (1992) 693-716
15. Pang G., and Chen L. A delayed SIRS epidemic model with pulse vaccination. Chaos Solitons & Fractals 34 (2007) 1629-1635
16. Song X., and Chen L. Optimal harvesting and stability for a two-species competitive system with stage structure. Math Biosci 170 (2001) 173-186
17. Takeuchi Y., and Ma W. Stability analysis on a delayed SIR epidemic model with density dependent birth process. Dynam Cont Discrete Impul Sys 5 (1999) 171-184
18. Takeuchi Y., Ma W., and Beretta E. Global asymptotic properties of a SIR epidemic model with nite incubation time. Nonlinear Anal 42 (2000) 931-947
19. Wen L., and Yang X. Global stability of a delayed SIRS model with temporary immunity. Chaos Solitons & Fractals 38 (2008) 221-226