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Volumn 18, Issue 7, 2013, Pages 1873-1887

Long-time behaviour of a perturbed sir model by white noise

Author keywords

Asymptotic stability; Diffusion process; Markov semigroups; Stationary distribution

Indexed keywords


EID: 84879092827     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2013.18.1873     Document Type: Article
Times cited : (56)

References (28)
  • 1
    • 0002340980 scopus 로고
    • On the support of wiener functionals in Asymptotic Problems in Probability Theory: Wiener Functionals and Asymptotic
    • K. D. Elworthy, N. Ikeda)
    • S. Aida, S. Kusuoka and D. Strook, On the support of Wiener functionals, in Asymptotic Problems in Probability Theory: Wiener Functionals and Asymptotic (eds. K. D. Elworthy, N. Ikeda), Longman Scient. Tech., (1993), 3-34.
    • (1993) Longman Scient. Tech. , pp. 3-34
    • Aida, S.1    Kusuoka, S.2    Strook, D.3
  • 3
    • 0018656345 scopus 로고
    • Population biology of infectious diseases, part i
    • R. M. Anderson and R. M. May, Population biology of infectious diseases, part I, Nature, 280 (1979), 361-367.
    • (1979) Nature , vol.280 , pp. 361-367
    • Anderson, R.M.1    May, R.M.2
  • 4
    • 33847299320 scopus 로고
    • D'ecroissance exponentielle du noyau de la chaleur sur la diag-onale (II)
    • G. B. Arous and R. eandre, D'ecroissance exponentielle du noyau de la chaleur sur la diag-onale (II), Probab. Theory Relat. Fields, 90 (1991), 377-402.
    • (1991) Probab. Theory Relat. Fields , vol.90 , pp. 377-402
    • Arous, G.B.1    Eandre, R.2
  • 6
    • 0035425156 scopus 로고    scopus 로고
    • Global asymptotic stability of an SIR epidemic model with distributed time delay
    • 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.
    • (2001) Nonlinear Anal. , vol.47 , pp. 4107-4115
    • Beretta, E.1    Hara, T.2    Ma, W.3    Takeuchi, Y.4
  • 7
    • 0030561585 scopus 로고    scopus 로고
    • Dynamical complexity in age-structured models of the transmission of measles virus
    • N. M. Ferguson, D. J. Nokes and R. M. Anderson, Dynamical complexity in age-structured models of the transmission of measles virus, Math. BioSci., 138 (1996), 101-130.
    • (1996) Math. BioSci. , vol.138 , pp. 101-130
    • Ferguson, N.M.1    Nokes, D.J.2    Anderson, R.M.3
  • 8
    • 79960370338 scopus 로고    scopus 로고
    • A stochastic differential equation SIS epidemic model
    • A. Gray, D. Greenhalgh, L. Hu, X. Mao and J. Pan, A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math., 71 (2011), 876-902.
    • (2011) SIAM J. Appl. Math. , vol.71 , pp. 876-902
    • Gray, A.1    Greenhalgh, D.2    Hu, L.3    Mao, X.4    Pan, J.5
  • 10
    • 38049037455 scopus 로고    scopus 로고
    • Global stability of the endemic equilibrium of multigroup SIR epidemic models
    • H. B. Guo, M. Y. Li and Z. S. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Q., 14 (2006), 259-284.
    • (2006) Can. Appl. Math. Q. , vol.14 , pp. 259-284
    • Guo, H.B.1    Li, M.Y.2    Shuai, Z.S.3
  • 11
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001), 525-546.
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.J.1
  • 12
    • 79952616171 scopus 로고    scopus 로고
    • Multigroup SIR epidemic model with stochastic perturbation
    • C. Y. Ji, D. Q. Jiang and N. Z. Shi, Multigroup SIR epidemic model with stochastic perturbation, Physica A, 390 (2011), 1747-1762.
    • (2011) Physica A , vol.390 , pp. 1747-1762
    • Ji, C.Y.1    Jiang, D.Q.2    Shi, N.Z.3
  • 13
    • 84355161643 scopus 로고    scopus 로고
    • Dynamics of a multigroup SIR epidemic model with stochastic perturbation
    • C. Y. Ji, D. Q. Jiang, Q. S. Yang and N. Z. Shi, Dynamics of a multigroup SIR epidemic model with stochastic perturbation, Automatica, 48 (2012), 121-131.
    • (2012) Automatica , vol.48 , pp. 121-131
    • Ji, C.Y.1    Jiang, D.Q.2    Yang, Q.S.3    Shi, N.Z.4
  • 14
    • 0031015249 scopus 로고    scopus 로고
    • Disease extinction and community size: Modeling the persistence of measles
    • M. J. Keeling and B. T. Grenfell, Disease extinction and community size: modeling the persistence of measles, Science, 275 (1997), 65-67.
    • (1997) Science , vol.275 , pp. 65-67
    • Keeling, M.J.1    Grenfell, B.T.2
  • 15
    • 0000998185 scopus 로고
    • Contributions to the mathematical theory of epidemics (part I)
    • W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics (part I), Proc. R. Soc. Lond. Ser. A, 115 (1927), 700-721.
    • (1927) Proc. R. Soc. Lond. Ser. A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 16
    • 70349785039 scopus 로고    scopus 로고
    • Global-stability problem for coupled systems of differential equations on networks
    • M. Y. Li and Z. S. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Differential Equations, 248 (2010), 1-20.
    • (2010) J. Differential Equations , vol.248 , pp. 1-20
    • Li, M.Y.1    Shuai, Z.S.2
  • 17
    • 0018357820 scopus 로고
    • Population biology of infectious diseases, part II
    • R. M. May and R. M. Anderson, Population biology of infectious diseases, part II, Nature, 280 (1979), 455-461.
    • (1979) Nature , vol.280 , pp. 455-461
    • May, R.M.1    Anderson, R.M.2
  • 18
    • 39449119838 scopus 로고    scopus 로고
    • The dynamics of a new SIR epidemic model concerning pulse vaccination strategy
    • X. Z. Meng and L. S. Chen, The dynamics of a new SIR epidemic model concerning pulse vaccination strategy, Appl. Math. Comput., 197 (2008), 528-597.
    • (2008) Appl. Math. Comput. , vol.197 , pp. 528-597
    • Meng, X.Z.1    Chen, L.S.2
  • 20
    • 0031260781 scopus 로고    scopus 로고
    • Stability of Markov semigroups and applications to parabolic systems
    • K. Pich'or and R. Rudnicki, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., 215 (1997), 56-74.
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 56-74
    • Pich'Or, K.1    Rudnicki, R.2
  • 21
    • 0033615482 scopus 로고    scopus 로고
    • Opposite patterns of synchrony: In sympatric disease metapopulations
    • P. Rohani, D. J. D. Earn and B. T. Grenfell, Opposite patterns of synchrony: In sympatric disease metapopulations, Science, 286 (1999), 968-971.
    • (1999) Science , vol.286 , pp. 968-971
    • Rohani, P.1    Earn, D.J.D.2    Grenfell, B.T.3
  • 22
    • 41149168534 scopus 로고    scopus 로고
    • Effects of predation on host-pathogen dynamics in SIR models
    • M. Roy and R. D. Holt, Effects of predation on host-pathogen dynamics in SIR models, Theor. Popul. Biol., 73 (2008), 319-331.
    • (2008) Theor. Popul. Biol. , vol.73 , pp. 319-331
    • Roy, M.1    Holt, R.D.2
  • 23
    • 0141799906 scopus 로고    scopus 로고
    • Long-time behaviour of a stochastic prey-predator model
    • R. Rudnicki, Long-time behaviour of a stochastic prey-predator model, Stochastic Process. Appl., 108 (2003), 93-107.
    • (2003) Stochastic Process. Appl. , vol.108 , pp. 93-107
    • Rudnicki, R.1
  • 24
    • 33847295610 scopus 로고    scopus 로고
    • Influence of stochastic perturbation on prey-predator systems
    • R. Rudnicki and K. Pich'or, Influence of stochastic perturbation on prey-predator systems, Math. Biosci., 206 (2007), 108-119.
    • (2007) Math. Biosci. , vol.206 , pp. 108-119
    • Rudnicki, R.1    Pich'Or, K.2
  • 25
    • 0000395295 scopus 로고
    • On the support of diffusion processes with applications to the strong maximum principle
    • University of California Press, Berkeley
    • D. W. Stroock and S. R. S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, in Proc. Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. III, University of California Press, Berkeley, (1972), 333-359.
    • (1972) Proc. Sixth Berkeley Symposium on Mathematical Statistics and Probability , vol.3 , pp. 333-359
    • Stroock, D.W.1    Varadhan, S.R.S.2
  • 26
    • 33947105089 scopus 로고    scopus 로고
    • Global behaviour of an SIR epidemic model with time delay
    • J. M. Tchuenche, A. Nwagwo and R. Levins, Global behaviour of an SIR epidemic model with time delay, Math. Methods Appl. Sci., 30 (2007), 733-749.
    • (2007) Math. Methods Appl. Sci. , vol.30 , pp. 733-749
    • Tchuenche, J.M.1    Nwagwo, A.2    Levins, R.3
  • 27
    • 19944381861 scopus 로고    scopus 로고
    • Stability of a stochastic SIR system
    • E. Tornatore, S. M. Buccellato and P. Vetro, Stability of a stochastic SIR system, Physica A, 354 (2005), 111-126.
    • (2005) Physica A , vol.354 , pp. 111-126
    • Tornatore, E.1    Buccellato, S.M.2    Vetro, P.3
  • 28
    • 41949125685 scopus 로고    scopus 로고
    • Global stability of an SIR epidemic model with constant infectious period
    • F. P. Zhang, Z. Z. Li and F. Zhang, Global stability of an SIR epidemic model with constant infectious period, Appl. Math. Comput., 199 (2008), 285-291.
    • (2008) Appl. Math. Comput. , vol.199 , pp. 285-291
    • Zhang, F.P.1    Li, Z.Z.2    Zhang, F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.