On the global stability of an SIRS epidemic model with distributed delays

Discrete and Continuous Dynamical Systems- Series A

Volumn , Issue SUPPL., 2011, Pages 1119-1128

  Nakata, Yukihiko ^a   Enatsu, Yoichi ^b   Muroya, Yoshiaki ^b  

^a BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

^b WASEDA UNIVERSITY   (Japan)

Author keywords

Distributed delays; Global asymptotic stability; Lyapunov functional; SIRS epidemic model

Indexed keywords

EID: 84859102947     PISSN: 10780947     EISSN: 15535231     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. E. Beretta and Y. Takeuchi, Global stability of an SIR epidemic model with time delays, J. Math. Biol. 33 (1995) 250-260.
2. J. Chen, An SIRS epidemic model, Appl. Math. J. Chinese Univ. 19 (2004) 101-108.
3. Y. Enatsu, Y. Nakata and Y. Muroya, Global stability of SIRS epidemic models with a class of nonlinear incidence rates and distributed delays, Acta Math. Sci. To appear.
4. H.W. Hethcote, The mathematics of infectious diseases, SIAM review 42 (2000) 599-653.
5. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics. Academic Press, San Diego, 1993.
6. C.C. McCluskey, Complete global stability for an SIR epidemic model with delay-Distributed or discrete, Nonlinear Anal. RWA. 11 (2010) 55-59.
7. J. Mena-Lorcat and H.W. Hethcote, Dynamic models of infectious diseases as regulators of population sizes, J. Math. Biol. 30 7 (1992) 693-716.
8. Y. Muroya, Y. Enatsu and Y. Nakata, Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate, J. Math. Anal. Appl. 377 (2011) 1-14.
9. Y. Muroya, Y. Enatsu and Y. Nakata, Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays, Nonlinear Anal. RWA. 12 (2011) 1897-1910.
10. Y. Takeuchi, W. Ma and E. Beretta, Global asymptotic properties of a delay SIR epidemic model with finite incubation times, Nonlinear Anal. 42 (2000) 931-947.
11. R. Xu and Z. Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate, Chaos, Solitons and Fractals. 41 (2009) 2319-2325.
12. T. Zhang and Z. Teng, Global behavior and permanence of SIRS epidemic model with time delay, Nonlinear Anal. RWA. 9 (2008) 1409-1424.
13. J. Zhen, Z. Ma and M. Han, Global stability of an SIRS epidemic model with delays, Acta Math. Sci. 26 (2006) 291-306.