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Volumn 15, Issue 1, 2011, Pages 61-74

Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays

Author keywords

Distributed delays; Global asymptotic stability; Lyapunov functional; Nonlinear incidence rate; Permanence; SIR epidemic models

Indexed keywords


EID: 78651244615     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2011.15.61     Document Type: Article
Times cited : (40)

References (22)
  • 1
    • 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
  • 2
    • 0031167217 scopus 로고    scopus 로고
    • Convergence results in SIR epidemic models with varying pop-ulation size
    • E. Beretta and Y. Takeuchi, Convergence results in SIR epidemic models with varying pop-ulation size, Nonlinear Anal., 28 (1997), 1909-1921.
    • (1997) Nonlinear Anal. , vol.28 , pp. 1909-1921
    • Beretta, E.1    Takeuchi, Y.2
  • 3
    • 0006751822 scopus 로고
    • Conidial discharge and transmission efficiency of "neozygites floridana" an entomopathogenic fungus infeccting two-spotted spider mites under laboratory conditions
    • G. C. Brown and R. Hasibuan, Conidial discharge and transmission efficiency of "Neozygites floridana", an entomopathogenic fungus infeccting two-spotted spider mites under laboratory conditions, J. Invertebr. Pathol., 65 (1995), 10-16.
    • (1995) J. Invertebr. Pathol. , vol.65 , pp. 10-16
    • Brown, G.C.1    Hasibuan, R.2
  • 4
    • 0018041874 scopus 로고
    • A generalization of the Kermack-Mckendrick deterministic epidemic model
    • V. Capasso and G. Serio, A generalization of the Kermack-Mckendrick deterministic epidemic model, Math. Biosci., 42 (1978), 43-61.
    • (1978) Math. Biosci. , vol.42 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 5
    • 0003100558 scopus 로고
    • Stability analysis for a vector disease model
    • K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain J. Math., 9 (1979), 31-42.
    • (1979) Rocky Mountain J. Math. , vol.9 , pp. 31-42
    • Cooke, K.L.1
  • 7
    • 0017228276 scopus 로고
    • Qualitative analyses of communicable disease models
    • H. W. Hethcote, Qualitative analyses of communicable disease models, Math. Biosci. 28 (1976), 335-356.
    • (1976) Math. Biosci. , vol.28 , pp. 335-356
    • Hethcote, H.W.1
  • 8
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H. W. Hethcote, The Mathematics of Infectious Diseases, SIAM Rev., 42 (2000), 599-653.
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 9
    • 77954623221 scopus 로고    scopus 로고
    • Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate
    • 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.
    • (2010) Bull. Math. Biol. , vol.72 , pp. 1192-1207
    • Huang, G.1    Takeuchi, Y.2    Ma, W.3    Wei, D.4
  • 10
    • 25144476559 scopus 로고    scopus 로고
    • Nonlinear incidence and stability of infectious disease models
    • A. Korobeinikov and P. K. Maini, Nonlinear incidence and stability of infectious disease models, Math. Med. Biol., 22 (2005), 113-128.
    • (2005) Math. Med. Biol. , vol.22 , pp. 113-128
    • Korobeinikov, A.1    Maini, P.K.2
  • 11
    • 33746594608 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
    • A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 68 (2006), 615-626.
    • (2006) Bull. Math. Biol. , vol.68 , pp. 615-626
    • Korobeinikov, A.1
  • 12
    • 34547655762 scopus 로고    scopus 로고
    • Global properties of infectious disease models with nonlinear incidence
    • A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1871-1886
    • Korobeinikov, A.1
  • 14
    • 55049136942 scopus 로고
    • Stability by liapunov's direct method, with applications
    • Academic Press, New York-London
    • J. LaSalle and S. Lefschetz, "Stability by Liapunov's Direct Method, with Applications," Mathematics in Science and Engineering, 4, Academic Press, New York-London, 1961.
    • (1961) Mathematics in Science and Engineering , vol.4
    • Lasalle, J.1    Lefschetz, S.2
  • 15
    • 0036986139 scopus 로고    scopus 로고
    • Permanence of an SIR epidemic model with distributed delays
    • W. Ma, Y. Takeuchi, T. Hara and E. Beretta, Permanence of an SIR epidemic model with distributed delays, Tohoku. Math. J., 54 (2002), 581-591.
    • (2002) Tohoku. Math. J. , vol.54 , pp. 581-591
    • Ma, W.1    Takeuchi, Y.2    Hara, T.3    Beretta, E.4
  • 16
    • 10644240707 scopus 로고    scopus 로고
    • Global stability of an SIR epidemic model with time delay
    • W. Ma, M. Song and Y. Takeuchi, Global stability of an SIR epidemic model with time delay, Appl. Math. Lett., 17 (2004), 1141-1145.
    • (2004) Appl. Math. Lett. , vol.17 , pp. 1141-1145
    • Ma, W.1    Song, M.2    Takeuchi, Y.3
  • 17
    • 70350722240 scopus 로고    scopus 로고
    • Complete global stability for an SIR epidemic model with delay-Distributed or discrete
    • C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-Distributed or discrete, Nonl. Anal. RWA., 11 (2010), 55-59.
    • (2010) Nonl. Anal. RWA. , vol.11 , pp. 55-59
    • McCluskey, C.C.1
  • 18
    • 77954634545 scopus 로고    scopus 로고
    • Global stability for an SIR epidemic model with delay and nonlinear inci-dence
    • C. C. McCluskey, Global stability for an SIR epidemic model with delay and nonlinear inci-dence, Nonl. Anal. RWA., 11 (2010), 3106-3109.
    • (2010) Nonl. Anal. RWA. , vol.11 , pp. 3106-3109
    • McCluskey, C.C.1
  • 19
    • 33846576177 scopus 로고    scopus 로고
    • Permanence of a delayed SIR epidemic model with density dependent birth rate
    • M. Song, W. Ma and Y. Takeuchi, Permanence of a delayed SIR epidemic model with density dependent birth rate, J. Comp. Appl. Math., 201 (2007), 389-394.
    • (2007) J. Comp. Appl. Math. , vol.201 , pp. 389-394
    • Song, M.1    Ma, W.2    Takeuchi, Y.3
  • 20
    • 0343442479 scopus 로고    scopus 로고
    • Global asymptotic properties of a delay SIR epidemic model with finite incubation times
    • 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.
    • (2000) Nonlinear Anal. , vol.42 , pp. 931-947
    • Takeuchi, Y.1    Ma, W.2    Beretta, E.3
  • 21
    • 31244431921 scopus 로고    scopus 로고
    • Global behavior of an SEIRS epidemic model with time delays
    • W. Wang, Global behavior of an SEIRS epidemic model with time delays, Appl. Math. Lett., 15 (2002), 423-428.
    • (2002) Appl. Math. Lett. , vol.15 , pp. 423-428
    • Wang, W.1
  • 22
    • 64049103800 scopus 로고    scopus 로고
    • Global stability of a SIR epidemic model with nonlinear incidence rate and time delay
    • R. Xu and Z. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonl. Anal. RWA., 10 (2009), 3175-3189.
    • (2009) Nonl. Anal. RWA. , vol.10 , pp. 3175-3189
    • Xu, R.1    Ma, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.