Stochastic SIRS model under regime switching

Nonlinear Analysis: Real World Applications

Volumn 14, Issue 1, 2013, Pages 352-364

  Han, Zhixia ^a   Zhao, Jiandong ^a  

^a LUDONG UNIVERSITY   (China)

Author keywords

Boundedness; It formula; Markov chain; Moment average in time; Stochastic SIRS model

Indexed keywords

ASYMPTOTICALLY STABLE; BOUNDEDNESS; DISEASE-FREE EQUILIBRIUM; ENVIRONMENTAL NOISE; MODEL SOLUTION; MOMENT AVERAGE IN TIME; REGIME SWITCHING;

MARKOV PROCESSES; STOCHASTIC SYSTEMS; WHITE NOISE;

STOCHASTIC MODELS;

EID: 84866406854     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2012.06.008     Document Type: Article

References (19)

1. W.O. Kermack, and A.G. McKendrick A contribution to the mathematical theory of epidemics Proc. R. Soc. Lond. Ser. A 115 1927 700 721
2. Z. Zhang, J. Wu, Y. Suo, and X. Song The domain of attraction for the endemic equilibrium of an SIRS epidemic model Math. Comput. Simul. 81 2011 1697 1706
3. Z. Zhang, Y. Suo, J. Peng, and W. Lin Singular perturbation approach to stability of a SIRS epidemic system Nonlinear Anal. Real World Appl. 10 2009 2688 2699
4. T. Zhang, and Z. Teng Global behavior and permanence of SIRS epidemic model with time delay Nonlinear Anal. Real World Appl. 9 2008 1409 1424 (Pubitemid 351685787)
5. Z. Jin, Z. Ma, and M. Han Global stability of an SIRS epidemic model with delays Acta Math. Sci. 26 2 2006 191 306
6. W.M. Liu, Hethcote, and S.A. Levin Dynamical behavior of epidemiological models with nonlinear incidence rate J. Math. Biol. 25 1987 359 380
7. W.M. Liu, S.A. Levin, and Y. Lwasa Influence of nonlinear incidence rate upon the behavior for a stage-structured SIR infectious disease model Nonlinear Anal. RWA 3 2002 175 190
8. R. Xu, Z. Ma, and Z. Wang Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity Comput. Math. Appl. 59 2010 3211 3221
9. Q. Lu Stability of SIRS system with random perturbations Physica A 388 2009 3677 3686
10. D. Jiang, C. Ji, N. Shi, and J. Yu The long time behavior of DI SIR epidemic model with stochastic perturbation J. Math. Anal. Appl. 372 2010 162 180
11. X. Mao, G. Sabanis, and R. Renshaw Asymptotic behavior of the stochastic Lotka-Volterra model J. Math. Anal. Appl. 287 2003 141 156 (Pubitemid 37374125)
12. X. Mao, G. Marion, and E. Renshaw Environmental Brownian noise suppresses explosions in population dynamics Stochastic Process. Appl. 97 2002 95 110 (Pubitemid 40030718)
13. C. Yuan, D. Jiang, D. O'Regan, and R.P. Agarwal Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation Commun. Nonlinear Sci. Numer. Simul. 17 6 2012 2501 2516
14. Q. Luo, and X. Mao Stochastic population dynamics under regime switching J. Math. Anal. Appl. 334 2007 69 84
15. C. Zhu, and G. Yin On competitive Lotka-Volterra model in random environments J. Math. Anal. Appl. 357 2009 154 170
16. R.L. Stratonovich A new representation for stochastic integral and equations SIAM J. Control Optim. 4 1966 362 371
17. M. Slatkin The dynamics of a population in a Markovian environment Ecology 59 1978 249 256
18. C. Zhu, and G. Yin On hybrid competitive Lotka-Volterra ecosystems Nonlinear Anal. 71 2009 e1370 e1379
19. W.J. Anderson Continuous-Time Markov Chains 1991 Springer-Verlag New York