Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 5, 2012, Pages 2120-2133

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

^a WASEDA UNIVERSITY   (Japan)

^b BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

Author keywords

Distributed delays; Global asymptotic stability; Lyapunov functional; Nonlinear incidence rate; SIRS epidemic model

Indexed keywords

DISTRIBUTED DELAYS; GLOBAL ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONALS; NONLINEAR INCIDENCE RATES; SIRS EPIDEMIC MODEL;

LYAPUNOV FUNCTIONS;

EPIDEMIOLOGY;

EID: 84859101715     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2012.01.007     Document Type: Article

References (23)

1. E. Beretta, and Y. Takeuchi Convergence results in SIR epidemic models with varying population size Nonlinear Anal. 28 1997 1909 1921
2. E. Beretta, T. Hara, W. Ma, and Y. Takeuchi Global asymptotic stability of an SIR epidemic model with distributed time delay Nonlinear Anal. 47 2001 4107 4115
3. V. Capasso, and G. Serio A generalization of the KermackMckendrick deterministic epidemic model Math. Biosci. 42 1978 43 61
4. J. Chen An SIRS epidemic model Appl. Math. J. Chinese Univ. 19 2004 101 108
5. Y. Enatsu, Y. Nakata, and Y. Muroya Global stability for a class of discrete SIR epidemic models Math. Biosci. Eng. 2 2010 347 361
6. Y. Enatsu, Y. Nakata, and Y. Muroya Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays Discrete Contin. Dyn. Syst. Ser. B 15 2011 61 74
7. Y. Enatsu, E. Messina, Y. Nakata, Y. Muroya, E. Russo, A. Vecchio, Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates, J. Appl. Math. Comput. doi:10.1007/s12190-011-0507-y.
8. G. Huang, and Y. Takeuchi Global analysis on delay epidemiological dynamics models with nonlinear incidence J. Math. Biol. 63 2011 125 139
9. G. Huang, Y. Takeuchi, W. Ma, and D. Wei Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate Bull. Math. Biol. 72 2010 1192 1207
10. A. Korobeinikov Global properties of infectious disease models with nonlinear incidence Bull. Math. Biol. 69 2007 1871 1886
11. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press San Diego
12. C.C. McCluskey Complete global stability for an SIR epidemic model with delay-distributed or discrete Nonlinear Anal. RWA 11 2010 55 59
13. C.C. McCluskey Global stability for an SIR epidemic model with delay and nonlinear incidence Nonlinear Anal. RWA 11 2010 3106 3109
14. C.C. McCluskey Global stability of an SIR epidemic model with delay and general nonlinear incidence Math. Biosci. Eng. 7 2010 837 850
15. 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
16. Y. Nakata, Y. Enatsu, and Y. Muroya On the global stability of an SIRS epidemic model with distributed delays Discrete Contin. Dyn. Syst. Supplement 2011 1119 1128
17. 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
18. W. Wang Global behavior of a SEIRS epidemic model with time delays Appl. Math. Lett. 15 2002 423 428
19. D. Xiao, and S. Ruan Global analysis of an epidemic model with nonmonotone incidence rate Math. Biosci. 208 2007 419 429
20. R. Xu, and Z. Ma Stability of a delayed SIRS epidemic model with a nonlinear incidence rate Chaos Solitons Fractals 41 2009 2319 2325
21. Y. Yang, and D. Xiao Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models Discrete Contin. Dyn. Syst. Ser. B 13 2010 195 211
22. T. Zhang, and Z. Teng Global behavior and permanence of SIRS epidemic model with time delay Nonlinear Anal. RWA 9 2008 1409 1424
23. J. Zhen, Z. Ma, and M. Han Global stability of an SIRS epidemic model with delays Acta Math. Sci. 26B 2006 291 306