메뉴 건너뛰기




Volumn 69, Issue 5, 2009, Pages 1205-1227

The complete classification for dynamics in a nine-dimensional west nile virus model

Author keywords

Compound matrices; Differential equations; Global stability; Switch phenomena; West Nile virus

Indexed keywords

ASYMPTOTIC ANALYSIS; DYNAMICS; STRUCTURES (BUILT OBJECTS); SYSTEM STABILITY; VIRUSES;

EID: 62249170555     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/070709438     Document Type: Article
Times cited : (14)

References (30)
  • 1
    • 1042298863 scopus 로고    scopus 로고
    • Global results for an epidemic model with vaccination that exhibits backward bifurcation
    • J. ARINO, C. C. Mccluskey, and P. Van den Driessche, Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64 (2003), pp. 260-276.
    • (2003) SIAM J. Appl. Math , vol.64 , pp. 260-276
    • ARINO, J.1    Mccluskey, C.C.2    Van den Driessche, P.3
  • 2
    • 0036130937 scopus 로고    scopus 로고
    • Global dynamics of an epidemic model with time delay, Nonlinear Anal
    • W. D. WANG and Z. Ma, Global dynamics of an epidemic model with time delay, Nonlinear Anal. Real World Application, 3 (2002), pp. 365-373.
    • (2002) Real World Application , vol.3 , pp. 365-373
    • WANG, W.D.1    Ma, Z.2
  • 3
    • 2542463400 scopus 로고    scopus 로고
    • An epidemic model in a patchy environment
    • W. D. WANG and X. Q. Zhao, An epidemic model in a patchy environment, Math. Biosci., 190 (2004), pp. 97-112.
    • (2004) Math. Biosci , vol.190 , pp. 97-112
    • WANG, W.D.1    Zhao, X.Q.2
  • 4
    • 3242806195 scopus 로고    scopus 로고
    • CENTERS FOR DISEASE CONTROL AND PREVENTION
    • CENTERS FOR DISEASE CONTROL AND PREVENTION, West Nile Virus: Fact Sheet, http://www. cdc.gov/ncidod/dvbid/westnile/wnv factSheet.htm.
    • West Nile Virus: Fact Sheet
  • 6
    • 0035789896 scopus 로고    scopus 로고
    • Simulation studies of St. Louis encephalitis and West Nile viruses: The impact of bird mortality
    • C. C. LORD and J. F. DAY, Simulation studies of St. Louis encephalitis and West Nile viruses: The impact of bird mortality, Vector Borne and Zoonotic Diseases, 1 (2001), pp. 317-329.
    • (2001) Vector Borne and Zoonotic Diseases , vol.1 , pp. 317-329
    • LORD, C.C.1    DAY, J.F.2
  • 7
    • 0034817375 scopus 로고    scopus 로고
    • A model describing the evolution of West Nile-like encephalitis in New York City
    • D. M. THOMAS and B. URENA, A model describing the evolution of West Nile-like encephalitis in New York City, Math. Comput. Modelling, 34 (2001), pp. 771-781.
    • (2001) Math. Comput. Modelling , vol.34 , pp. 771-781
    • THOMAS, D.M.1    URENA, B.2
  • 8
    • 1442308380 scopus 로고    scopus 로고
    • An epidemiological model for West Nile virus: Invasion analysis and control applications
    • M. J. WONHAM, T. DE-CAMINO-BECK, and M. LEWIS, An epidemiological model for West Nile virus: Invasion analysis and control applications, Proc. R. Soc. Lond. Ser. B, 1538 (2004), pp. 501-507.
    • (2004) Proc. R. Soc. Lond. Ser. B , vol.1538 , pp. 501-507
    • WONHAM, M.J.1    DE-CAMINO-BECK, T.2    LEWIS, M.3
  • 9
    • 26844431555 scopus 로고    scopus 로고
    • A theoretical framework for the analysis of the West Nile virus epidemic
    • V. M. KENKRE, R. R. PARMENTER, I. D. PEIXOTO, and L. SADASIV, A theoretical framework for the analysis of the West Nile virus epidemic, Math. Comput. Modelling, 42 (2005), pp. 313-324.
    • (2005) Math. Comput. Modelling , vol.42 , pp. 313-324
    • KENKRE, V.M.1    PARMENTER, R.R.2    PEIXOTO, I.D.3    SADASIV, L.4
  • 10
    • 33745451069 scopus 로고    scopus 로고
    • Modeling spatial spread of West Nile virus and impact of directional dispersal of birds
    • R. S. LIU, J. P. SHUAI, J. WU, and H. Zhu, Modeling spatial spread of West Nile virus and impact of directional dispersal of birds, Math. Biosci. Eng., 3 (2006), pp. 145-160.
    • (2006) Math. Biosci. Eng , vol.3 , pp. 145-160
    • LIU, R.S.1    SHUAI, J.P.2    WU, J.3    Zhu, H.4
  • 11
    • 21444451814 scopus 로고    scopus 로고
    • C. BOWMAN, A. B. GUMEL, J. WU, P. VAN DEN DRIESSCHE, AND H. ZHU, A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol., 67 (2005), pp. 1107-1133.
    • C. BOWMAN, A. B. GUMEL, J. WU, P. VAN DEN DRIESSCHE, AND H. ZHU, A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol., 67 (2005), pp. 1107-1133.
  • 12
    • 62149101085 scopus 로고    scopus 로고
    • Threshold conditions for West Nile virus outbreaks
    • DOI 10.1007/s11538-008-9374-6
    • J. F. JIANG, Z. P. QIU, J.WU, AND H. ZHU, Threshold conditions for West Nile virus outbreaks, Bull. Math. Biol., 2008, DOI 10.1007/s11538-008-9374-6.
    • (2008) Bull. Math. Biol
    • JIANG, J.F.1    QIU, Z.P.2    WU, J.3    ZHU, H.4
  • 13
    • 84959812821 scopus 로고
    • On the global stability of cooperative systems
    • J. F. JIANG, On the global stability of cooperative systems, Bull. London Math. Soc., 6 (1994), pp. 455-458.
    • (1994) Bull. London Math. Soc , vol.6 , pp. 455-458
    • JIANG, J.F.1
  • 14
    • 0030128038 scopus 로고    scopus 로고
    • Competitive exclusion in gonorrhea models and other sexually transmitted diseases
    • C. CASTILLO-CHAVEZ, W. HUANG, AND J. LI, Competitive exclusion in gonorrhea models and other sexually transmitted diseases, SIAM J. Appl. Math., 56 (1996), pp. 494-508.
    • (1996) SIAM J. Appl. Math , vol.56 , pp. 494-508
    • CASTILLO-CHAVEZ, C.1    HUANG, W.2    LI, J.3
  • 15
    • 62249104975 scopus 로고    scopus 로고
    • C. CASTILLO-CHAVEZ AND H. R. THIEME, Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity, 1, O. Arino, D. Axelrod, M. Kimmel, M. Langlais, eds., Wuerz, Winnipeg, 1995, pp. 33-50.
    • C. CASTILLO-CHAVEZ AND H. R. THIEME, Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity, Vol. 1, O. Arino, D. Axelrod, M. Kimmel, M. Langlais, eds., Wuerz, Winnipeg, 1995, pp. 33-50.
  • 16
    • 77952672921 scopus 로고
    • Convergence results and a Poincar'e-Bendixson trichotomy for asymptotically autonomous differential equations
    • H. R. THIEME, Convergence results and a Poincar'e-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), pp. 755-763.
    • (1992) J. Math. Biol , vol.30 , pp. 755-763
    • THIEME, H.R.1
  • 17
    • 84881166951 scopus 로고
    • Asymptotically autonomous differential equations in the plane
    • H. R. THIEME, Asymptotically autonomous differential equations in the plane, Rocky Mountain J. Math., 24 (1994), pp. 351-380.
    • (1994) Rocky Mountain J. Math , vol.24 , pp. 351-380
    • THIEME, H.R.1
  • 18
    • 0036845274 scopus 로고    scopus 로고
    • P. VAN DEN DRIESSCHE AND J. WATMOUGH, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), pp. 29-48.
    • P. VAN DEN DRIESSCHE AND J. WATMOUGH, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), pp. 29-48.
  • 19
    • 35348982202 scopus 로고
    • Monotone Dynamical Systems: An Introduction to Theory of Competitive and Cooperative Systems, Math
    • AMS, Providence, RI
    • H. L. SMITH, Monotone Dynamical Systems: An Introduction to Theory of Competitive and Cooperative Systems, Math. Surveys Monogr. 41, AMS, Providence, RI, 1995.
    • (1995) Surveys Monogr , vol.41
    • SMITH, H.L.1
  • 20
    • 0035506703 scopus 로고    scopus 로고
    • The general properties of discrete time competitive dynamical systems
    • Y. WANG AND J. F. JIANG, The general properties of discrete time competitive dynamical systems, J. Differential Equations, 176 (2001), pp. 470-493.
    • (2001) J. Differential Equations , vol.176 , pp. 470-493
    • WANG, Y.1    JIANG, J.F.2
  • 21
    • 4243550804 scopus 로고
    • Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups
    • P. TAKAC, Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups, J. Reine Angew. Math., 423 (1992), pp. 101-173.
    • (1992) J. Reine Angew. Math , vol.423 , pp. 101-173
    • TAKAC, P.1
  • 22
    • 0011409551 scopus 로고
    • On derivations arising in differential equations
    • D. LONDON, On derivations arising in differential equations, Linear Multilinear Algebra, 4 (1976), pp. 179-189.
    • (1976) Linear Multilinear Algebra , vol.4 , pp. 179-189
    • LONDON, D.1
  • 23
    • 84880990802 scopus 로고
    • Compound matrices and ordinary differential equation
    • J. S. MULDOWNEY, Compound matrices and ordinary differential equation, Rocky Mountain J. Math., 20 (1990), pp. 857-872.
    • (1990) Rocky Mountain J. Math , vol.20 , pp. 857-872
    • MULDOWNEY, J.S.1
  • 24
    • 0028817626 scopus 로고
    • Global stability for the SEIR model in epidemiology
    • M. Y. LI AND J. S. MULDOWNEY, Global stability for the SEIR model in epidemiology, Math. Biosci., 125 (1995), pp. 155-164.
    • (1995) Math. Biosci , vol.125 , pp. 155-164
    • LI, M.Y.1    MULDOWNEY, J.S.2
  • 25
    • 0039591930 scopus 로고
    • Persistence under relaxed point-dissipativity (with an application to an endemic model)
    • H. R. THIEME, Persistence under relaxed point-dissipativity (with an application to an endemic model), SIAM J. Math. Anal., 24 (1993), pp. 407-435.
    • (1993) SIAM J. Math. Anal , vol.24 , pp. 407-435
    • THIEME, H.R.1
  • 27
    • 0030544879 scopus 로고    scopus 로고
    • A geometric approach to global-stability problems
    • M. Y. LI AND J. MULDOWNEY, A geometric approach to global-stability problems, SIAM J. Math. Anal., 27 (1996), pp. 1070-1083.
    • (1996) SIAM J. Math. Anal , vol.27 , pp. 1070-1083
    • LI, M.Y.1    MULDOWNEY, J.2
  • 28
    • 0016027180 scopus 로고
    • Logarithmic norms and projections applied to linear differential systems
    • R. H. MARTIN, JR., Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl., 45 (1974), pp. 432-454.
    • (1974) J. Math. Anal. Appl , vol.45 , pp. 432-454
    • MARTIN JR., R.H.1
  • 29
    • 0000875103 scopus 로고
    • Dichotomies and asymptotic behavior for linear differential systems
    • J. S. MULDOWNEY, Dichotomies and asymptotic behavior for linear differential systems, Trans. Amer. Math. Soc., 283 (1984), pp. 465-484.
    • (1984) Trans. Amer. Math. Soc , vol.283 , pp. 465-484
    • MULDOWNEY, J.S.1
  • 30
    • 0000703838 scopus 로고
    • Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions
    • K. MISCHAIKOW, H. SMITH, AND H. R. THIEME, Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions, Trans. Amer. Math. Soc., 347 (1995), pp. 1669-1685.
    • (1995) Trans. Amer. Math. Soc , vol.347 , pp. 1669-1685
    • MISCHAIKOW, K.1    SMITH, H.2    THIEME, H.R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.