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Volumn 32, Issue 3, 2012, Pages 851-865

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

Author keywords

Distributed delays; Global asymptotic stability; Lyapunov functional; Nonlinear incidence rate; SIRS epidemic model

Indexed keywords


EID: 84860842742     PISSN: 02529602     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0252-9602(12)60066-6     Document Type: Article
Times cited : (32)

References (19)
  • 1
    • 0031167217 scopus 로고    scopus 로고
    • Convergence results in SIR epidemic models with varying population size
    • Beretta E, Takeuchi Y Convergence results in SIR epidemic models with varying population size. Nonlinear Anal 1997, 28:1909-1921.
    • (1997) Nonlinear Anal , vol.28 , pp. 1909-1921
    • Beretta, E.1    Takeuchi, Y.2
  • 2
    • 0018041874 scopus 로고
    • A generalization of the Kermack-McKendrick deterministic epidemic model
    • Capasso V, Serio G A generalization of the Kermack-McKendrick deterministic epidemic model. Math Biosci 1978, 42:43-61.
    • (1978) Math Biosci , vol.42 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 3
    • 78651244615 scopus 로고    scopus 로고
    • Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
    • Enatsu Y, Nakata Y, Muroya Y Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays. Discrete and Continuous Dynamical Systems 2011, 15B:61-74.
    • (2011) Discrete and Continuous Dynamical Systems , vol.15 B , pp. 61-74
    • Enatsu, Y.1    Nakata, Y.2    Muroya, Y.3
  • 4
    • 0038485591 scopus 로고    scopus 로고
    • Interpreting time-series analyses for continuous-time biological models-measles as a case study
    • Glass K, Xia Y, Grenfell BT Interpreting time-series analyses for continuous-time biological models-measles as a case study. J Theor Biol 2003, 2:19-25.
    • (2003) J Theor Biol , vol.2 , pp. 19-25
    • Glass, K.1    Xia, Y.2    Grenfell, B.T.3
  • 6
    • 77954623221 scopus 로고    scopus 로고
    • Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate
    • Huang G, Takeuchi Y, Ma W, Wei D Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate. Bull Math Biol 2010, 72:1192-1207.
    • (2010) Bull Math Biol , vol.72 , pp. 1192-1207
    • Huang, G.1    Takeuchi, Y.2    Ma, W.3    Wei, D.4
  • 7
    • 69049101951 scopus 로고    scopus 로고
    • Dynamics of a delayed epidemic model with non-monotonic incidence rate
    • Huo HF, Ma ZP Dynamics of a delayed epidemic model with non-monotonic incidence rate. Commun Nonlinear Sci Numer Simulat 2010, 15:459-468.
    • (2010) Commun Nonlinear Sci Numer Simulat , vol.15 , pp. 459-468
    • Huo, H.F.1    Ma, Z.P.2
  • 8
    • 34250220630 scopus 로고    scopus 로고
    • An SIRS model with a nonlinear incidence rate
    • Jin Y, Wang W, Xiao S An SIRS model with a nonlinear incidence rate. Chaos, Solitons and Fractals 2007, 34:1482-1497.
    • (2007) Chaos, Solitons and Fractals , vol.34 , pp. 1482-1497
    • Jin, Y.1    Wang, W.2    Xiao, S.3
  • 9
    • 25144476559 scopus 로고    scopus 로고
    • Nonlinear incidence and stability of infectious disease models
    • Korobeinikov A, Maini PK Nonlinear incidence and stability of infectious disease models. Math Med Biol 2005, 22:113-128.
    • (2005) Math Med Biol , vol.22 , pp. 113-128
    • Korobeinikov, A.1    Maini, P.K.2
  • 10
    • 33746594608 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
    • Korobeinikov A Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission. Bull Math Biol 2006, 68:615-626.
    • (2006) Bull Math Biol , vol.68 , pp. 615-626
    • Korobeinikov, A.1
  • 11
    • 34547655762 scopus 로고    scopus 로고
    • Global Properties of Infectious Disease Models with Nonlinear Incidence
    • Korobeinikov A Global Properties of Infectious Disease Models with Nonlinear Incidence. Bull Math Biol 2007, 69:1871-1886.
    • (2007) Bull Math Biol , vol.69 , pp. 1871-1886
    • Korobeinikov, A.1
  • 12
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • Liu WM, Levin SA, Iwasa Y Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J Math Biol 1986, 23:187-204.
    • (1986) J Math Biol , vol.23 , pp. 187-204
    • Liu, W.M.1    Levin, S.A.2    Iwasa, Y.3
  • 13
    • 70350722240 scopus 로고    scopus 로고
    • Complete global stability for an SIR epidemic model with delay-Distributed or discrete
    • McCluskey CC Complete global stability for an SIR epidemic model with delay-Distributed or discrete. Nonl Anal RWA 2010, 11:55-59.
    • (2010) Nonl Anal RWA , vol.11 , pp. 55-59
    • McCluskey, C.C.1
  • 14
    • 77958068384 scopus 로고    scopus 로고
    • Global stability of an SIR epidemic model with delay and general nonlinear incidence
    • McCluskey CC Global stability of an SIR epidemic model with delay and general nonlinear incidence. Math Biosci Engi 2010, 7:837-850.
    • (2010) Math Biosci Engi , vol.7 , pp. 837-850
    • McCluskey, C.C.1
  • 15
    • 0026491804 scopus 로고
    • Dynamic models of infectious diseases as regulators of population size
    • Mena-Lorca J, Hethcote HW Dynamic models of infectious diseases as regulators of population size. J Math Biol 1992, 30:693-716.
    • (1992) J Math Biol , vol.30 , pp. 693-716
    • Mena-Lorca, J.1    Hethcote, H.W.2
  • 16
    • 78651240621 scopus 로고    scopus 로고
    • Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate
    • Muroya Y, Enatsu Y, Nakata Y Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate. J Math Anal Appl 2011, 377:1-14.
    • (2011) J Math Anal Appl , vol.377 , pp. 1-14
    • Muroya, Y.1    Enatsu, Y.2    Nakata, Y.3
  • 17
    • 79955524982 scopus 로고    scopus 로고
    • Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays
    • Muroya Y, Enatsu Y, Nakata Y Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays. Nonl Anal RWA 2011, 12:1897-1910.
    • (2011) Nonl Anal RWA , vol.12 , pp. 1897-1910
    • Muroya, Y.1    Enatsu, Y.2    Nakata, Y.3
  • 18
    • 67649304819 scopus 로고    scopus 로고
    • Stability of a delayed SIRS epidemic model with a nonlinear incidence rate
    • Xu R, Ma Z Stability of a delayed SIRS epidemic model with a nonlinear incidence rate. Chaos, Solitons and Fractals 2009, 41:2319-2325.
    • (2009) Chaos, Solitons and Fractals , vol.41 , pp. 2319-2325
    • Xu, R.1    Ma, Z.2
  • 19
    • 76549112764 scopus 로고    scopus 로고
    • Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models
    • Yang Y, Xiao D Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models. Discrete and Continuous Dynamical Systems 2010, 13B:195-211.
    • (2010) Discrete and Continuous Dynamical Systems , vol.13 B , pp. 195-211
    • Yang, Y.1    Xiao, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.