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Volumn 11, Issue 5, 2010, Pages 4154-4163

Dynamics of infection with nonlinear incidence in a simple vaccination model

Author keywords

Backward bifurcation; Multistability; Nonlinear incidence; Vaccination

Indexed keywords

BACKWARD BIFURCATION; DISEASE SPREAD; EPIDEMIC MODELS; MULTISTABILITY; NONLINEAR INCIDENCE; NONLINEAR INCIDENCE RATES;

EID: 77955515975     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.05.002     Document Type: Article
Times cited : (62)

References (30)
  • 1
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • C.M. Kribs-Zaleta, and J.X. Velasco-Hernndez A simple vaccination model with multiple endemic states Math. Biosci. 164 2000 183 201
    • (2000) Math. Biosci. , vol.164 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernndez, J.X.2
  • 2
    • 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 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
    • 0036234426 scopus 로고    scopus 로고
    • Vaccination strategies and backward bifurcation in an age-since-infection structured model
    • C.M. Kribs-Zaleta, and M. Martcheva Vaccination strategies and backward bifurcation in an age-since-infection structured model Math. Biosci. 177&178 2002 317 332
    • (2002) Math. Biosci. , vol.177 , pp. 317-332
    • Kribs-Zaleta, C.M.1    Martcheva, M.2
  • 4
    • 1642341634 scopus 로고    scopus 로고
    • Periodicity in an epidemic model with a generalized non-linear incidence
    • M.E. Alexander, and S.M. Moghadas Periodicity in an epidemic model with a generalized non-linear incidence Math. Biosci. 189 2004 75 96
    • (2004) Math. Biosci. , vol.189 , pp. 75-96
    • Alexander, M.E.1    Moghadas, S.M.2
  • 5
    • 34047187628 scopus 로고    scopus 로고
    • Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases
    • A. d'Onofrio, P. Manfredi, and E. Salinelli Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases Theor. Popul. Biol. 71 2007 301 317
    • (2007) Theor. Popul. Biol. , vol.71 , pp. 301-317
    • D'Onofrio, A.1    Manfredi, P.2    Salinelli, E.3
  • 6
    • 44849133934 scopus 로고    scopus 로고
    • SVIR epidemic models with vaccination strategies
    • X. Liu, Y. Takeuchib, and S. Iwami SVIR epidemic models with vaccination strategies J. Theoret. Biol. 253 2008 1 11
    • (2008) J. Theoret. Biol. , vol.253 , pp. 1-11
    • Liu, X.1    Takeuchib, Y.2    Iwami, S.3
  • 7
    • 70350731589 scopus 로고    scopus 로고
    • A delay SIR epidemic model with pulse vaccination and incubation times
    • X. Meng, L. Chen, and B. Wu A delay SIR epidemic model with pulse vaccination and incubation times Nonlinear Anal. RWA 11 2010 88 98
    • (2010) Nonlinear Anal. RWA , vol.11 , pp. 88-98
    • Meng, X.1    Chen, L.2    Wu, B.3
  • 8
    • 33746833233 scopus 로고    scopus 로고
    • Analysis of a delayed epidemic model with pulse vaccination and saturation incidence
    • S. Gao, L. Chen, J.J. Nieto, and A. Torres Analysis of a delayed epidemic model with pulse vaccination and saturation incidence Vaccine 24 2006 6037 6045
    • (2006) Vaccine , vol.24 , pp. 6037-6045
    • Gao, S.1    Chen, L.2    Nieto, J.J.3    Torres, A.4
  • 9
    • 36248929333 scopus 로고    scopus 로고
    • Analysis of an SIR epidemic model with pulse vaccination and distributed time delay
    • S. Gao, L. Chen, J.J. Nieto, and A. Torres Analysis of an SIR epidemic model with pulse vaccination and distributed time delay J. Biomed. Biotechnol. 2007 10.1155/2007/64870
    • (2007) J. Biomed. Biotechnol.
    • Gao, S.1    Chen, L.2    Nieto, J.J.3    Torres, A.4
  • 10
    • 0003318955 scopus 로고
    • Mathematical Structure of Epidemic Systems
    • Springer Berlin
    • V. Capasso Mathematical Structure of Epidemic Systems Lecture Notes in Biomathematics vol. 97 1993 Springer Berlin
    • (1993) Lecture Notes in Biomathematics , vol.97
    • Capasso, V.1
  • 12
    • 0018041874 scopus 로고
    • A generalization of the KermackCMcKendrick deterministic epidemic model
    • V. Capasso, and G. Serio A generalization of the KermackCMcKendrick deterministic epidemic model Math. Biosci. 42 1978 43 61
    • (1978) Math. Biosci. , vol.42 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 13
    • 0023070210 scopus 로고
    • Dynamical behavior of epidemiological models with nonlinear incidence rates
    • W.M. Liu, H.W. Hethcote, and S.A. Levin Dynamical behavior of epidemiological models with nonlinear incidence rates J. Math. Biol. 25 1987 359 380
    • (1987) J. Math. Biol. , vol.25 , pp. 359-380
    • Liu, W.M.1    Hethcote, H.W.2    Levin, S.A.3
  • 14
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • W.M. Liu, S.A. Levin, and Y. Iwasa 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
  • 15
    • 0004839333 scopus 로고    scopus 로고
    • Immunity boosted by low level of exposure to infetion in an SIRS model
    • A.K. Ghosh, J. Chattopadhyay, and P.K. Tapaswi Immunity boosted by low level of exposure to infetion in an SIRS model Ecol. Model. 78 1996 227 233
    • (1996) Ecol. Model. , vol.78 , pp. 227-233
    • Ghosh, A.K.1    Chattopadhyay, J.2    Tapaswi, P.K.3
  • 17
    • 0041774290 scopus 로고    scopus 로고
    • Approximations for the long-term behaviour of an open-population epidemic model
    • D. Clancy, P.D. O'Neill, and P.K. Pollett Approximations for the long-term behaviour of an open-population epidemic model Methodol. Comput. Appl. Probab. 3 2001 75 95
    • (2001) Methodol. Comput. Appl. Probab. , vol.3 , pp. 75-95
    • Clancy, D.1    O'Neill, P.D.2    Pollett, P.K.3
  • 18
    • 0028063956 scopus 로고
    • Exposure efficacy and change in contact rates in evaluating prophylactic HIV vaccines in the field
    • M.E. Halloran, I.M. Longini Jr., M.J. Haber, C.J. Struchiner, and R.C. Brunet Exposure efficacy and change in contact rates in evaluating prophylactic HIV vaccines in the field Stat. Med. 13 1994 357 377
    • (1994) Stat. Med. , vol.13 , pp. 357-377
    • Halloran, M.E.1    Longini Jr., I.M.2    Haber, M.J.3    Struchiner, C.J.4    Brunet, R.C.5
  • 19
    • 0014693081 scopus 로고
    • Complications to smallpox vaccination, 1968: National Surveillance in the United States
    • J.M. Lane, F.L. Ruben, J.M. Neff, and J.D. Millar Complications to smallpox vaccination, 1968: National Surveillance in the United States New Engl. J. Med. 281 1969 1201 1207
    • (1969) New Engl. J. Med. , vol.281 , pp. 1201-1207
    • Lane, J.M.1    Ruben, F.L.2    Neff, J.M.3    Millar, J.D.4
  • 20
    • 0028145367 scopus 로고
    • Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco
    • S.M. Blower, and A.R. McLean Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco Science 265 1994 1451 1454
    • (1994) Science , vol.265 , pp. 1451-1454
    • Blower, S.M.1    McLean, A.R.2
  • 21
    • 0037462713 scopus 로고    scopus 로고
    • Candidate HIV/AIDS vaccines: Lessons learned from the worlds first phase III efficacy trials
    • D.P. Francis, W.L. Heyward, and V. Popovic Candidate HIV/AIDS vaccines: lessons learned from the worlds first phase III efficacy trials AIDS 17 2003 147 156
    • (2003) AIDS , vol.17 , pp. 147-156
    • Francis, D.P.1    Heyward, W.L.2    Popovic, V.3
  • 22
    • 12444285808 scopus 로고    scopus 로고
    • Potential public health impact of imperfect HIV type 1 vaccines
    • R. Anderson, and M. Hanson Potential public health impact of imperfect HIV type 1 vaccines J. Infect. Dis. 191 2005 585 596
    • (2005) J. Infect. Dis. , vol.191 , pp. 585-596
    • Anderson, R.1    Hanson, M.2
  • 24
    • 0029055539 scopus 로고
    • A core group model for disease transmission
    • K.P. Hadeler, and C. Castillo-Chavez A core group model for disease transmission Math. Biosci. 128 1995 41 55
    • (1995) Math. Biosci. , vol.128 , pp. 41-55
    • Hadeler, K.P.1    Castillo-Chavez, C.2
  • 25
    • 0028968938 scopus 로고
    • Community treatment of HIV-1: Initial stage and asymptotic dynamics
    • Y.H. Hsieh, and J.X. Velasco-Hernndez Community treatment of HIV-1: initial stage and asymptotic dynamics BioSystems 35 1995 75 81
    • (1995) BioSystems , vol.35 , pp. 75-81
    • Hsieh, Y.H.1    Velasco-Hernndez, J.X.2
  • 26
    • 0028309908 scopus 로고
    • Modeling the e.ect of treatment and behavioral change in HIV transmission dynamics
    • J.X. Velasco-Hernndez, and Y.H. Hsieh Modeling the e.ect of treatment and behavioral change in HIV transmission dynamics J. Math. Biol. 32 1994 233 249
    • (1994) J. Math. Biol. , vol.32 , pp. 233-249
    • Velasco-Hernndez, J.X.1    Hsieh, Y.H.2
  • 27
  • 28
    • 36148968419 scopus 로고    scopus 로고
    • Role of incidence function in vaccine-induced backward bifurcation in some HIV models
    • O. Sharomi, C.N. Podder, A.B. Gumel, E.H. Elbasha, and James Watmough Role of incidence function in vaccine-induced backward bifurcation in some HIV models Math. Biosci. 210 2007 436 463
    • (2007) Math. Biosci. , vol.210 , pp. 436-463
    • Sharomi, O.1    Podder, C.N.2    Gumel, A.B.3    Elbasha, E.H.4    Watmough, J.5
  • 29
    • 0034198679 scopus 로고    scopus 로고
    • A simple SIS epidemic model with a backward bifurcation
    • P. van den Driessche, and J. Watmough 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
  • 30
    • 0142243570 scopus 로고    scopus 로고
    • Dynamical behavior for a stage structure SIR infectious disease model
    • Y. Xiao, L. Chen, and F. Van den Bosch Dynamical behavior for a stage structure SIR infectious disease model Nonlinear Anal. RWA 3 2002 175 190
    • (2002) Nonlinear Anal. RWA , vol.3 , pp. 175-190
    • Xiao, Y.1    Chen, L.2    Van Den Bosch, F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.