Global stability of a SIR epidemic model with nonlinear incidence rate and time delay

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 5, 2009, Pages 3175-3189

  Xu, Rui ^a,b   Ma, Zhien ^b  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Nonlinear incidence; SIR epidemic model; Stability; Time delay

Indexed keywords

BASIC REPRODUCTIVE NUMBERS; CHARACTERISTIC EQUATIONS; DISEASE-FREE EQUILIBRIUMS; ENDEMIC EQUILIBRIUMS; GLOBAL ASYMPTOTIC STABILITIES; GLOBAL STABILITIES; GLOBALLY ASYMPTOTICALLY STABLES; ITERATION TECHNIQUES; LOCAL STABILITIES; LYAPUNOV FUNCTIONAL; NONLINEAR INCIDENCE; NONLINEAR INCIDENCE RATES; SIR EPIDEMIC MODEL; SUFFICIENT CONDITIONS;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; NEURAL NETWORKS; SYSTEM STABILITY; TIME DELAY;

DISEASE CONTROL;

EID: 64049103800     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.10.013     Document Type: Article

References (15)

1. Anderson R.M., and May R.M. Population biology of infectious diseases: Part I. Nature 280 (1979) 361-367
2. Beretta E., Capasso V., and Rinaldi F. Global stability results for a generalized Lotka-Volterra system with distributed delays: Applications to predator-prey and epidemic systems. J. Math. Biol. 26 (1988) 661-668
3. 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
4. Beretta E., and Takeuchi Y. Global stability of an SIR epidemic model with time delays. J. Math. Biol. 33 (1995) 250-260
5. Beretta E., and Takeuchi Y. Convergence results in SIR epidemic model with varying population sizes. Nonlinear Anal. 28 (1997) 1909-1921
6. Capasso V., and Serio G. A generalization of the Kermack-Mckendrick deterministic epidemic model. Math. Biosci. 42 (1978) 41-61
7. Cooke K.L. Stability analysis for a vector disease model. Rocky Mountain J. Math. 9 (1979) 31-42
8. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic, Dordrecht, Norwell, MA
9. Hale J. Theory of Functional Differential Equations (1977), Springer-Verlag, Heidelberg
10. Hethcote H.W. Qualitative analyses of communicable disease models. Math. Biosci. 7 (1976) 335-356
11. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press, New York
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. Takeuchi Y., and Ma W. Stability analysis on a delayed SIR epidemic model with density dependent birth process. Dynam. Cont. Discrete Impul. Syst. 5 (1999) 171-184
15. Takeuchi Y., Ma W., and Beretta E. Global asymptotic properties of a SIR epidemic model with night incubation time. Nonlinear Anal. 42 (2000) 931-947