메뉴 건너뛰기




Volumn 12, Issue 1, 2009, Pages 169-186

Threshold dynamics in a time-delayed periodic sis epidemic model

Author keywords

Basic reproduction ratio; Maturation delay; Periodic epidemic model; Periodic solutions; Uniform persistence

Indexed keywords


EID: 69249168996     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.12.169     Document Type: Article
Times cited : (44)

References (21)
  • 3
    • 0033209987 scopus 로고    scopus 로고
    • Interaction of maturation delay and nonlinear birth in population and epidemic models
    • K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 39 (1999), 332-352.
    • (1999) J. Math. Biol , vol.39 , pp. 332-352
    • Cooke, K.1    van den Driessche, P.2    Zou, X.3
  • 5
    • 69249195560 scopus 로고    scopus 로고
    • K. Dietz, The incidence of infectious disease under the influence of seasonal fluctuations, In: J. Berger, W.Bühler, R. Repges and P. Tautu (Eds.), Proceedings of a Workshop on Mathematical Models in Medicine, Mainz. Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 11 (1976), 1-15.
    • K. Dietz, The incidence of infectious disease under the influence of seasonal fluctuations, In: J. Berger, W.Bühler, R. Repges and P. Tautu (Eds.), Proceedings of a Workshop on Mathematical Models in Medicine, Mainz. Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 11 (1976), 1-15.
  • 6
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • D. J. D. Earn, P. Rohani, B. M. Bolker and B. T. Grenfell, A simple model for complex dynamical transitions in epidemics, Science, 287 (2000), 667-670.
    • (2000) Science , vol.287 , pp. 667-670
    • Earn, D.J.D.1    Rohani, P.2    Bolker, B.M.3    Grenfell, B.T.4
  • 7
    • 33748982385 scopus 로고    scopus 로고
    • Seasonal infectious disease epidemiology
    • N. C. Grassly and C. Fraser, Seasonal infectious disease epidemiology, Proc. R. Soc. B, 273 (2006), 2541-2550.
    • (2006) Proc. R. Soc. B , vol.273 , pp. 2541-2550
    • Grassly, N.C.1    Fraser, C.2
  • 8
    • 33748131158 scopus 로고    scopus 로고
    • Epidemic threshold conditions for seasonally forced SEIR models
    • J. Ma and Z. Ma, Epidemic threshold conditions for seasonally forced SEIR models, Mathematical Biosciences and Engineering, 3 (2006), 161-172.
    • (2006) Mathematical Biosciences and Engineering , vol.3 , pp. 161-172
    • Ma, J.1    Ma, Z.2
  • 12
    • 33144473617 scopus 로고    scopus 로고
    • Global attractors and steady states for uniformly persistent dynamical systems
    • P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.
    • (2005) SIAM J. Math. Anal , vol.37 , pp. 251-275
    • Magal, P.1    Zhao, X.-Q.2
  • 13
    • 0003726932 scopus 로고
    • Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Amer Math Soc
    • H. L. Smith, "Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems," Amer Math Soc Math Surveys and Monographs, 41, 1995.
    • (1995) Math Surveys and Monographs , vol.41
    • Smith, H.L.1
  • 14
    • 0025468667 scopus 로고
    • Monotone semiflows in scalar non-quasi-monotone functional differential equations
    • H. Smith and H. Thieme, Monotone semiflows in scalar non-quasi-monotone functional differential equations, J. Math. Anal. Appl., 150 (1990), 289-306.
    • (1990) J. Math. Anal. Appl , vol.150 , pp. 289-306
    • Smith, H.1    Thieme, H.2
  • 15
    • 22444452981 scopus 로고    scopus 로고
    • Perturbation of a globally stable steady state
    • H. L. Smith and P. Waltman, Perturbation of a globally stable steady state, Proc. Amer. Math. Soc, 127 (1999), 447-453.
    • (1999) Proc. Amer. Math. Soc , vol.127 , pp. 447-453
    • Smith, H.L.1    Waltman, P.2
  • 16
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 525-540.
    • (2002) Mathematical Biosciences , vol.180 , pp. 525-540
    • van den Driessche, P.1    Watmough, J.2
  • 17
    • 47149095789 scopus 로고    scopus 로고
    • Threshold dynamics for compartmental epidemic models in periodic environments
    • W. Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, Journal of Dynamics and Differential Equations, 20 (2008), 699-717.
    • (2008) Journal of Dynamics and Differential Equations , vol.20 , pp. 699-717
    • Wang, W.1    Zhao, X.-Q.2
  • 18
    • 25144465899 scopus 로고    scopus 로고
    • Dynamics in a periodic competitive model with stage structure
    • D. Xu and X.-Q. Zhao, Dynamics in a periodic competitive model with stage structure, J. Math. Anal. Appl., 311 (2005), 417-438.
    • (2005) J. Math. Anal. Appl , vol.311 , pp. 417-438
    • Xu, D.1    Zhao, X.-Q.2
  • 20
    • 0037455394 scopus 로고    scopus 로고
    • Global attractivity in monotone and subhomogeneous almost periodic systems
    • X.-Q. Zhao, Global attractivity in monotone and subhomogeneous almost periodic systems, J. Differential Equations, 187 (2003), 494-509.
    • (2003) J. Differential Equations , vol.187 , pp. 494-509
    • Zhao, X.-Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.