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Volumn 16, Issue 1, 2011, Pages 30-46

On the backward bifurcation of a vaccination model with nonlinear incidence

Author keywords

Backward bifurcation; Disease control; Epidemic models; Nonlinear incidence; Vaccination

Indexed keywords


EID: 79952355338     PISSN: 13925113     EISSN: 23358963     Source Type: Journal    
DOI: 10.15388/na.16.1.14113     Document Type: Article
Times cited : (89)

References (25)
  • 1
    • 0038521431 scopus 로고    scopus 로고
    • A qualitative study of a vaccination model with non-linear incidence
    • A.B. Gumel, S.M. Moghadas, A qualitative study of a vaccination model with non-linear incidence, App. Math. Comput., 143, pp. 409-419, 2003.
    • (2003) App. Math. Comput , vol.143 , pp. 409-419
    • Gumel, A.B.1    Moghadas, S.M.2
  • 2
    • 33748307685 scopus 로고    scopus 로고
    • Dynamical models of tubercolosis and their applications
    • C. Castillo-Chavez, B. Song, Dynamical models of tubercolosis and their applications, Math. Biosci. Eng., 1, pp. 361-404, 2004.
    • (2004) Math. Biosci. Eng , vol.1 , pp. 361-404
    • Castillo-Chavez, C.1    Song, B.2
  • 4
    • 42249093128 scopus 로고    scopus 로고
    • F. Brauer, P. van den Driessche, J. Wu (Eds.), Lecture Notes in Mathematics, Mathematical Biosciences Subseries, Springer, Berlin, Heidelberg
    • F. Brauer, P. van den Driessche, J. Wu (Eds.), Mathematical Epidemiology, Lecture Notes in Mathematics, Mathematical Biosciences Subseries, Vol. 1945, Springer, Berlin, Heidelberg, 2008.
    • (2008) Mathematical Epidemiology , vol.1945
  • 6
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42, pp. 599-653, 2000.
    • (2000) SIAM Rev , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 7
    • 0010647130 scopus 로고
    • Global solution for a diffusive nonlinear deterministic epidemic model
    • V. Capasso, Global solution for a diffusive nonlinear deterministic epidemic model, SIAM J. Appl. Math., 35, pp. 274-284, 1978.
    • (1978) SIAM J. Appl. Math , vol.35 , pp. 274-284
    • Capasso, V.1
  • 8
    • 0017464754 scopus 로고
    • I modelli matematici nella indagine epidemiologica. Applicazione all'epidemia di colera verificatasi in Bari nel 1973
    • V. Capasso, E. Grosso, G. Serio, I modelli matematici nella indagine epidemiologica. Applicazione all'epidemia di colera verificatasi in Bari nel 1973, Annali Sclavo, 19, pp. 193-208, 1977.
    • (1977) Annali Sclavo , vol.19 , pp. 193-208
    • Capasso, V.1    Grosso, E.2    Serio, G.3
  • 9
    • 0018041874 scopus 로고
    • A generalization of the Kermack-Mc Kendrick deterministic epidemic model
    • V. Capasso, G. Serio, A generalization of the Kermack-Mc Kendrick deterministic epidemic model, Math. Biosci., 42, pp. 41-61, 1978.
    • (1978) Math. Biosci , vol.42 , pp. 41-61
    • Capasso, V.1    Serio, G.2
  • 10
    • 25644447966 scopus 로고    scopus 로고
    • Vaccination policies and nonlinear force of infection: Generalization of an observation by Alexander and Moghadas (2004)
    • A. d'Onofrio, Vaccination policies and nonlinear force of infection: generalization of an observation by Alexander and Moghadas (2004), Appl. Math. Comput., 168, pp. 613-622, 2005.
    • (2005) Appl. Math. Comput , vol.168 , pp. 613-622
    • D'onofrio, A.1
  • 11
    • 34547134261 scopus 로고    scopus 로고
    • Global analysis of an epidemic model with nonmonotone incidence rate
    • D. Xiao, S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208, pp. 419-429, 2007.
    • (2007) Math. Biosci , vol.208 , pp. 419-429
    • Xiao, D.1    Ruan, S.2
  • 12
    • 78649989180 scopus 로고    scopus 로고
    • On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate
    • B. Buonomo, S. Rionero, On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate, Appl. Math. Comput., 217(8), pp. 4010-4016, 2010.
    • (2010) Appl. Math. Comput , vol.217 , Issue.8 , pp. 4010-4016
    • Buonomo, B.1    Rionero, S.2
  • 13
    • 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, pp. 1871-1886, 2007.
    • (2007) Bull. Math. Biol , vol.69 , pp. 1871-1886
    • Korobeinikov, A.1
  • 15
    • 1042298863 scopus 로고    scopus 로고
    • Global results for an epidemic model with vaccination that exhibits backward bifurcation
    • J. Arino, C.C. McCluskey, P. van den Driessche, Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64, pp. 260-276, 2003.
    • (2003) SIAM J. Appl. Math , vol.64 , pp. 260-276
    • Arino, J.1    McCluskey, C.C.2    van den Driessche, P.3
  • 16
    • 0036234426 scopus 로고    scopus 로고
    • Vaccination strategies and backward bifurcation in an agesince-infection structured model
    • C.M. Kribs-Zaleta, M. Martcheva, Vaccination strategies and backward bifurcation in an agesince- infection structured model, Math. Biosci., 177/178, pp. 317-332, 2002.
    • (2002) Math. Biosci , vol.177-178 , pp. 317-332
    • Kribs-Zaleta, C.M.1    Martcheva, M.2
  • 17
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • C.M. Kribs-Zaleta, J.X. Velasco-Hernandez, A simple vaccination model with multiple endemic states, Math. Biosci., 164, pp. 183-201, 2000.
    • (2000) Math. Biosci , vol.164 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernandez, J.X.2
  • 18
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, pp. 29-48, 2002.
    • (2002) Math. Biosci , vol.180 , pp. 29-48
    • van den Driessche, P.1    Watmough, J.2
  • 19
    • 0034198679 scopus 로고    scopus 로고
    • A simple SIS epidemic model with a backward bifurcation
    • P. van den Driessche, J. Watmough, A simple SIS epidemic model with a backward bifurcation, J. Math. Biol., 40, pp. 525-540, 2000.
    • (2000) J. Math. Biol , vol.40 , pp. 525-540
    • van den Driessche, P.1    Watmough, J.2
  • 20
    • 33646823979 scopus 로고    scopus 로고
    • Backward bifurcation of an epidemic model with treatment
    • W. Wang, Backward bifurcation of an epidemic model with treatment, Math. Biosci., 201, pp. 58-71, 2006.
    • (2006) Math. Biosci , vol.201 , pp. 58-71
    • Wang, W.1
  • 21
    • 77952674174 scopus 로고    scopus 로고
    • Backward bifurcation and optimal control in transmission dynamics of West Nile Virus
    • K.W. Blayneh, A.B. Gumel, S. Lenhart, T. Clayton, Backward bifurcation and optimal control in transmission dynamics of West Nile Virus, Bull. Math. Biol., 72, pp. 1006-1028, 2010.
    • (2010) Bull. Math. Biol , vol.72 , pp. 1006-1028
    • Blayneh, K.W.1    Gumel, A.B.2    Lenhart, S.3    Clayton, T.4
  • 22
    • 58549084832 scopus 로고    scopus 로고
    • On the dynamics of an SEIR epidemic model with a convex incidence rate
    • B. Buonomo, D. Lacitignola, On the dynamics of an SEIR epidemic model with a convex incidence rate, Ric. Mat., 57, pp. 261-281, 2008.
    • (2008) Ric. Mat , vol.57 , pp. 261-281
    • Buonomo, B.1    Lacitignola, D.2
  • 23
    • 79952356210 scopus 로고    scopus 로고
    • Analysis of a tuberculosis model with a case study in Uganda
    • B. Buonomo, D. Lacitignola, Analysis of a tuberculosis model with a case study in Uganda, J. Biol. Dyn., 4(6), pp. 571-593, 2010.
    • (2010) J. Biol. Dyn , vol.4 , Issue.6 , pp. 571-593
    • Buonomo, B.1    Lacitignola, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.