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Volumn 348, Issue 1, 2008, Pages 433-443

Backward bifurcation of an epidemic model with saturated treatment function

Author keywords

Backward bifurcation; Global behavior; Saturated treatment function; SIR

Indexed keywords


EID: 50249102874     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.07.042     Document Type: Article
Times cited : (276)

References (18)
  • 1
    • 0003611945 scopus 로고
    • Anderson R.M., and May R.M. (Eds), Springer-Verlag, Berlin
    • In: Anderson R.M., and May R.M. (Eds). Population Biology of Infectious Diseases (1982), Springer-Verlag, Berlin
    • (1982) Population Biology of Infectious Diseases
  • 2
    • 1042298863 scopus 로고    scopus 로고
    • Global results for an epidemic model with vaccination that exhibits backward bifurcation
    • Arino J., McCluskey C.C., and van den Driessche P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 64 (2003) 260-276
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 260-276
    • Arino, J.1    McCluskey, C.C.2    van den Driessche, P.3
  • 3
    • 0018041874 scopus 로고
    • A generalization of the Kermack-Mckendrick deterministic epidemic model
    • Capasso V., and Serio G. 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
  • 4
    • 0003426971 scopus 로고    scopus 로고
    • Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation
    • John Wiley and Sons, Chichester
    • Diekmann O., and Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation. Wiley Ser. Math. Comput. Biol. (2000), John Wiley and Sons, Chichester
    • (2000) Wiley Ser. Math. Comput. Biol.
    • Diekmann, O.1    Heesterbeek, J.A.P.2
  • 5
    • 0031992574 scopus 로고    scopus 로고
    • Backwards bifurcations and catastrophe in simple models of fatal diseases
    • Dushoff J., Huang W., and Castillo-Chavez C. Backwards bifurcations and catastrophe in simple models of fatal diseases. J. Math. Biol. 36 (1998) 227-248
    • (1998) J. Math. Biol. , vol.36 , pp. 227-248
    • Dushoff, J.1    Huang, W.2    Castillo-Chavez, C.3
  • 6
    • 0030882301 scopus 로고    scopus 로고
    • Backward bifurcation in epidemic control
    • Hadeler K.P., and van den Driessche P. Backward bifurcation in epidemic control. Math. Biosci. 146 (1997) 15-35
    • (1997) Math. Biosci. , vol.146 , pp. 15-35
    • Hadeler, K.P.1    van den Driessche, P.2
  • 7
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • Liu W.M., Levin S.A., and Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23 (1986) 187-204
    • (1986) J. Math. Biol. , vol.23 , pp. 187-204
    • Liu, W.M.1    Levin, S.A.2    Iwasa, Y.3
  • 8
    • 0030277612 scopus 로고    scopus 로고
    • Multiparametric bifurcations for a model in epidemiology
    • Lizana M., and Rivero J. Multiparametric bifurcations for a model in epidemiology. J. Math. Biol. 35 (1996) 21-36
    • (1996) J. Math. Biol. , vol.35 , pp. 21-36
    • Lizana, M.1    Rivero, J.2
  • 9
    • 1642284439 scopus 로고    scopus 로고
    • Progression age enhanced backward bifurcation in an epidemic model with superinfection
    • Martcheva M., and Thieme H.R. Progression age enhanced backward bifurcation in an epidemic model with superinfection. J. Math. Biol. 46 (2003) 385-424
    • (2003) J. Math. Biol. , vol.46 , pp. 385-424
    • Martcheva, M.1    Thieme, H.R.2
  • 10
    • 0037429355 scopus 로고    scopus 로고
    • Dynamical behavior of an epidemic model with a nonlinear incidence rate
    • Ruan S., and Wang W. Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differential Equations 188 (2003) 135-163
    • (2003) J. Differential Equations , vol.188 , pp. 135-163
    • Ruan, S.1    Wang, W.2
  • 11
    • 33846578358 scopus 로고    scopus 로고
    • Global dynamics of SIS models with transport-related infection
    • Takeuchi Y., Liu X., and Cui J. Global dynamics of SIS models with transport-related infection. J. Math. Anal. Appl. 329 (2007) 1460-1471
    • (2007) J. Math. Anal. Appl. , vol.329 , pp. 1460-1471
    • Takeuchi, Y.1    Liu, X.2    Cui, J.3
  • 12
    • 0343442479 scopus 로고    scopus 로고
    • Global asymptotic properties of a delay SIR epidemic model with finite incubation times
    • Takeuchi Y., Ma W., and Beretta E. 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
  • 13
    • 0034198679 scopus 로고    scopus 로고
    • A simple SIS epidemic model with a backward bifurcation
    • van den Driessche P., and Watmough J. A simple SIS epidemic model with a backward bifurcation. J. Math. Biol. 40 (2000) 525-540
    • (2000) J. Math. Biol. , vol.40 , pp. 525-540
    • van den Driessche, P.1    Watmough, J.2
  • 14
    • 33646823979 scopus 로고    scopus 로고
    • Backward bifurcation of an epidemic model with treatment
    • Wang W. Backward bifurcation of an epidemic model with treatment. Math. Biosci. 201 (2006) 58-71
    • (2006) Math. Biosci. , vol.201 , pp. 58-71
    • Wang, W.1
  • 15
    • 0036130937 scopus 로고    scopus 로고
    • Global dynamics of an epidemic model with time delay
    • Wang W., and Ma Z. Global dynamics of an epidemic model with time delay. Nonlinear Anal. Real World Appl. 3 (2002) 365-373
    • (2002) Nonlinear Anal. Real World Appl. , vol.3 , pp. 365-373
    • Wang, W.1    Ma, Z.2
  • 16
    • 1542406443 scopus 로고    scopus 로고
    • Bifurcation in an epidemic model with constant removal rate of the infectives
    • Wang W., and Ruan S. Bifurcation in an epidemic model with constant removal rate of the infectives. J. Math. Anal. Appl. 291 (2004) 775-793
    • (2004) J. Math. Anal. Appl. , vol.291 , pp. 775-793
    • Wang, W.1    Ruan, S.2
  • 17
    • 34547134261 scopus 로고    scopus 로고
    • Global analysis of an epidemic model with nonmonotone incidence rate
    • Xiao D., and Ruan S. Global analysis of an epidemic model with nonmonotone incidence rate. Math. Biosci. 208 (2007) 419-429
    • (2007) Math. Biosci. , vol.208 , pp. 419-429
    • Xiao, D.1    Ruan, S.2
  • 18
    • 56549115873 scopus 로고    scopus 로고
    • X. Zhang, X. Liu, Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment, Nonlinear Anal. Real World Appl. (2008), doi:10.1016/j.nonrwa.2007.10.011, in press
    • X. Zhang, X. Liu, Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment, Nonlinear Anal. Real World Appl. (2008), doi:10.1016/j.nonrwa.2007.10.011, in press


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.