메뉴 건너뛰기




Volumn 12, Issue 5, 2011, Pages 2692-2705

Analyzing the dynamics of an SIRS vaccination model with waning natural and vaccine-induced immunity

Author keywords

Backward bifurcation; Equilibria; Immunity; Reproduction number; Stability; Vaccination

Indexed keywords

BACKWARD BIFURCATION; EQUILIBRIA; IMMUNITY; REPRODUCTION NUMBER; VACCINATION;

EID: 79957897316     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.03.015     Document Type: Article
Times cited : (50)

References (31)
  • 1
    • 33846102585 scopus 로고    scopus 로고
    • Model for assessing human papillomavirus vaccination strategies
    • E. Elbasha, E. Dasbach, and R. Insinga Model for assessing human papillomavirus vaccination strategies Emerg. Infect. Dis. 13 2007 28 41 (Pubitemid 46057835)
    • (2007) Emerging Infectious Diseases , vol.13 , Issue.1 , pp. 28-41
    • Elbasha, E.H.1    Dasbach, E.J.2    Insinga, R.P.3
  • 2
    • 23044440494 scopus 로고    scopus 로고
    • Mathematical modeling and public policy: Responding to health crises
    • J. Glasser, M. Meltzer, and B. Levin Mathematical modeling and public policy: responding to health crises Emerg. Infect. Dis. 10 2004 http://www.cdc.gov/ncidod/EID/vol10no11/04-079708.htm (accessed: August 2010)
    • (2004) Emerg. Infect. Dis. , vol.10
    • Glasser, J.1    Meltzer, M.2    Levin, B.3
  • 3
    • 49549088827 scopus 로고    scopus 로고
    • Economic evaluation of human papillomavirus vaccination in the United Kingdom
    • 10.1136/bmj.a769
    • M. Jit, Y.H. Choi, and W.J. Edmunds Economic evaluation of human papillomavirus vaccination in the United Kingdom BMJ 337 2008 a769 10.1136/bmj.a769
    • (2008) BMJ , vol.337 , pp. 769
    • Jit, M.1    Choi, Y.H.2    Edmunds, W.J.3
  • 4
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • DOI 10.1016/S0025-5564(00)00003-1, PII S0025556400000031
    • C. Kribs-Zaleta, and J. Valesco-Hernandez A simple vaccination model with multiple endemic states Math. Biosci. 164 2000 183 201 (Pubitemid 30211016)
    • (2000) Mathematical Biosciences , vol.164 , Issue.2 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernandez, J.X.2
  • 6
    • 0030581592 scopus 로고    scopus 로고
    • Low-efficacy HIV vaccines: Potential for community-based intervention programmes
    • DOI 10.1016/S0140-6736(96)07100-0
    • R.M. Anderson, and G.P. Garnett Low-efficacy HIV vaccines: potential for community-based intervention programmes Lancet 348 1996 1010 1013 (Pubitemid 26340759)
    • (1996) Lancet , vol.348 , Issue.9033 , pp. 1010-1013
    • Anderson, R.M.1    Garnett, G.P.2
  • 7
    • 18744407870 scopus 로고    scopus 로고
    • Duration of immunity against pertussis after natural infection or vaccination
    • A.M. Wendelboe, A. Van Rie, S. Salmaso, and J.A. Englund Duration of immunity against pertussis after natural infection or vaccination Pediatr. Infect. Dis. J. 24 5 Suppl. 2005 58 61
    • (2005) Pediatr. Infect. Dis. J. , vol.24 , Issue.5 SUPPL. , pp. 58-61
    • Wendelboe, A.M.1    Van Rie, A.2    Salmaso, S.3    Englund, J.A.4
  • 9
    • 33746597887 scopus 로고    scopus 로고
    • Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits
    • DOI 10.1007/s11538-005-9057-5
    • E.H. Elbasha, and A.B. Gumel Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits Bull. Math. Biol. 68 2006 577 614 (Pubitemid 44195562)
    • (2006) Bulletin of Mathematical Biology , vol.68 , Issue.3 , pp. 577-614
    • Elbasha, E.H.1    Gumel, A.B.2
  • 10
    • 3142598855 scopus 로고    scopus 로고
    • Breaking new ground - Are changes in immunization services needed for the introduction of future HIV/AIDS vaccines and other new vaccines targeted at adolescents?
    • DOI 10.1016/j.vaccine.2004.01.002, PII S0264410X04000295
    • C.J. Clements, Q. Abdool-Karim, M.L. Chang, B. Nkowane, and J. Esparza Breaking new groundare changes in immunization services needed for the introduction of future HIV/AIDS vaccines and other new vaccines targeted at adolescents? Vaccine 22 2004 2822 2826 (Pubitemid 38900660)
    • (2004) Vaccine , vol.22 , Issue.21-22 , pp. 2822-2826
    • Clements, C.J.1    Abdool-Karim, Q.2    Chang, M.-L.3    Nkowane, B.4    Esparza, J.5
  • 11
    • 77955137093 scopus 로고    scopus 로고
    • Qualitative dynamics of a vaccination model for HSV-2
    • C.N. Podder, and A.B. Gumel Qualitative dynamics of a vaccination model for HSV-2 IMA J. Appl. Math. 75 1 2010 75 107
    • (2010) IMA J. Appl. Math. , vol.75 , Issue.1 , pp. 75-107
    • Podder, C.N.1    Gumel, A.B.2
  • 12
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • DOI 10.1016/S0025-5564(02)00108-6, PII S0025556402001086
    • P. van den Driessche, and J. Watmough Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 180 2002 29 48 (Pubitemid 35304346)
    • (2002) Mathematical Biosciences , vol.180 , pp. 29-48
    • Van Den Driessche, P.1    Watmough, J.2
  • 14
    • 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
  • 15
    • 10144259346 scopus 로고    scopus 로고
    • Backward bifurcations in simple vaccination models
    • DOI 10.1016/j.jmaa.2004.05.045, PII S0022247X04004378
    • F. Brauer Backward bifurcations in simple vaccination models J. Math. Anal. Appl. 298 2 2004 418 431 (Pubitemid 39615063)
    • (2004) Journal of Mathematical Analysis and Applications , vol.298 , Issue.2 , pp. 418-431
    • Brauer, F.1
  • 16
    • 36148968419 scopus 로고    scopus 로고
    • Role of incidence function in vaccine-induced backward bifurcation in some HIV models
    • DOI 10.1016/j.mbs.2007.05.012, PII S0025556407001071
    • O. Sharomi, C.N. Podder, A.B. Gumel, E.H. Elbasha, and J. Watmough Role of incidence function in vaccine-induced backward bifurcation in some HIV models Bull. Math. Biol. 210 2007 436 463 (Pubitemid 350116899)
    • (2007) Mathematical Biosciences , vol.210 , Issue.2 , pp. 436-463
    • Sharomi, O.1    Podder, C.N.2    Gumel, A.B.3    Elbasha, E.H.4    Watmough, J.5
  • 18
    • 0030128038 scopus 로고    scopus 로고
    • Competitive exclusion in gonorrhea models and other sexually transmitted diseases
    • C. Castillo-Chavez, W. Huang, and J. Li Competitive exclusion in gonorrhea models and other sexually transmitted diseases SIAM J. Appl. Math. 56 1996 494 508 (Pubitemid 126554149)
    • (1996) SIAM Journal on Applied Mathematics , vol.56 , Issue.2 , pp. 494-508
    • Castillo-Chavez, C.1    Huang, W.2    Li, J.3
  • 19
    • 0033356422 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence of multiple strains in an SIS STD model
    • C. Castillo-Chavez, W. Huang, and J. Li Competitive exclusion and coexistence of multiple strains in an SIS STD models SIAM J. Appl. Math. 59 1999 1790 1811 (Pubitemid 30505689)
    • (1999) SIAM Journal on Applied Mathematics , vol.59 , Issue.5 , pp. 1790-1811
    • Castillo-Chavez, C.1    Huang, W.2    Li, J.3
  • 20
    • 38049037455 scopus 로고    scopus 로고
    • Global stability of the endemic equilibrium of multigroup SIR epidemic models
    • H. Guo, M.Y. Li, and Z. Shaui Global stability of the endemic equilibrium of multigroup SIR epidemic models Can. Appl. Math. Q. 14 3 2006 259 284
    • (2006) Can. Appl. Math. Q. , vol.14 , Issue.3 , pp. 259-284
    • Guo, H.1    Li, M.Y.2    Shaui, Z.3
  • 21
    • 3042703290 scopus 로고    scopus 로고
    • Lyapunov functions and global properties for SEIR and SEIS epidemic models
    • A. Korobeinikov Lyapunov functions and global properties for SEIR and SEIS epidemic models Math. Med. Biol.: J. IMA 21 2004 75 83 (Pubitemid 38867853)
    • (2004) Mathematical Medicine and Biology , vol.21 , Issue.2 , pp. 75-83
    • Korobeinikov, A.1
  • 22
    • 33746594608 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
    • DOI 10.1007/s11538-005-9037-9
    • A. Korobeinikov Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission Bull. Math. Biol. 30 2006 615 626 (Pubitemid 44195563)
    • (2006) Bulletin of Mathematical Biology , vol.68 , Issue.3 , pp. 615-626
    • Korobeinikov, A.1
  • 23
    • 27244439640 scopus 로고    scopus 로고
    • A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence
    • A. Korobeinikov, and P.K. Maini A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence Math. Biosci. Eng. 1 1 2004 57 60
    • (2004) Math. Biosci. Eng. , vol.1 , Issue.1 , pp. 57-60
    • Korobeinikov, A.1    Maini, P.K.2
  • 24
    • 41049114695 scopus 로고    scopus 로고
    • Global stability of equilibria in a two-sex HPV vaccination model
    • E.H. Elbasha Global stability of equilibria in a two-sex HPV vaccination model Bull. Math. Biol. 70 3 2008 894 909
    • (2008) Bull. Math. Biol. , vol.70 , Issue.3 , pp. 894-909
    • Elbasha, E.H.1
  • 27
    • 33748912539 scopus 로고    scopus 로고
    • Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria
    • DOI 10.1016/S0252-9602(06)60029-5, PII S0252960206600295
    • Jianquan Li, Zhien Ma, and Yicang Zhou Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria Acta Math. Sci. Ser. B 26 1 2006 83 93 (Pubitemid 44428293)
    • (2006) Acta Mathematica Scientia , vol.26 , Issue.1 , pp. 83-93
    • Li, J.1    Ma, Z.2    Zhou, Y.3
  • 28
    • 0028046642 scopus 로고
    • Waning immunity and its effects on vaccination schedules
    • R. Rouderfer, N.G. Becker, and H.W. Hethcote Waning immunity and its effects on vaccination schedules Math. Biosci. 124 1994 59 82
    • (1994) Math. Biosci. , vol.124 , pp. 59-82
    • Rouderfer, R.1    Becker, N.G.2    Hethcote, H.W.3
  • 29
    • 0034799244 scopus 로고    scopus 로고
    • Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics
    • DOI 10.1006/tpbi.2001.1525
    • A.L. Lloyd Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics Theor. Popul. Biol 60 2001 59 71 (Pubitemid 32965156)
    • (2001) Theoretical Population Biology , vol.60 , Issue.1 , pp. 59-71
    • Lloyd, A.L.1
  • 31
    • 33748307685 scopus 로고    scopus 로고
    • Dynamical models of tuberculosis and their applications
    • C. Castillo-Chavez, and B. Song Dynamical models of tuberculosis and their applications Math. Biosci. Eng. 1 2 2004 361 404
    • (2004) Math. Biosci. Eng. , vol.1 , Issue.2 , pp. 361-404
    • Castillo-Chavez, C.1    Song, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.