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Volumn 40, Issue 6, 2000, Pages 525-540

A simple SIS epidemic model with a backward bifurcation

Author keywords

Backward bifurcation; Distributed delay; Multiple equilibria; Nonlinear Volterra integral equation; SIS epidemic model

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; DISEASE TRANSMISSION; EPIDEMIC; GONORRHEA; HUMAN; STATISTICS;

EID: 0034198679     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000032     Document Type: Article
Times cited : (274)

References (20)
  • 2
    • 33747590310 scopus 로고
    • Perturbations of the nonlinear renewal equation
    • Brauer, F.: Perturbations of the nonlinear renewal equation. Advances in Mathematics, 22(1):32-51, (1976)
    • (1976) Advances in Mathematics , vol.22 , Issue.1 , pp. 32-51
    • Brauer, F.1
  • 3
    • 25644446425 scopus 로고
    • Some equations modelling growth processes and gonorrhea epidemics
    • Cooke, K.L., Yorke, J.A.: Some equations modelling growth processes and gonorrhea epidemics. Mathematical Biosciences, 16:75-101, (1973)
    • (1973) Mathematical Biosciences , vol.16 , pp. 75-101
    • Cooke, K.L.1    Yorke, J.A.2
  • 4
    • 0030573518 scopus 로고    scopus 로고
    • Incorporating immunological ideas in epidemiological models
    • Dushoff, J.: Incorporating immunological ideas in epidemiological models. Journal of Theoretical Biology, 180:181-187, (1996)
    • (1996) Journal of Theoretical Biology , vol.180 , pp. 181-187
    • Dushoff, J.1
  • 5
    • 0031992574 scopus 로고    scopus 로고
    • Backwards bifurcations and catastrophe in simple models of fatal diseases
    • Dushoff, J., Huang, W., Castillo-Chavez, C.: Backwards bifurcations and catastrophe in simple models of fatal diseases. Journal of Mathematical Biology, 36:227-248, (1998)
    • (1998) Journal of Mathematical Biology , vol.36 , pp. 227-248
    • Dushoff, J.1    Huang, W.2    Castillo-Chavez, C.3
  • 6
    • 0000572783 scopus 로고
    • On the integral equation of renewal theory
    • Feller, W.: On the integral equation of renewal theory. The Annals of Mathematical Statistics, 12:243-267, (1941)
    • (1941) The Annals of Mathematical Statistics , vol.12 , pp. 243-267
    • Feller, W.1
  • 10
    • 0023177943 scopus 로고
    • Epidemiological models for heterogeneous populations: Propertionate mixing, parameter estimation, and immunization programs
    • Hethcote, H.W., van Ark, J.W.: Epidemiological models for heterogeneous populations: propertionate mixing, parameter estimation, and immunization programs. Mathematical Biosciences, 84:85-118, (1987)
    • (1987) Mathematical Biosciences , vol.84 , pp. 85-118
    • Hethcote, H.W.1    Van Ark, J.W.2
  • 13
    • 0003020529 scopus 로고
    • Gonorrhea Transmission Dynamics and Control
    • Springer-Verlag, Berlin
    • Hethcote, H.W., Yorke, J.A.: Gonorrhea Transmission Dynamics and Control, volume 56 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin, (1984)
    • (1984) Lecture Notes in Biomathematics , vol.56
    • Hethcote, H.W.1    Yorke, J.A.2
  • 14
    • 0000723140 scopus 로고
    • Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission
    • Huang, W., Cooke, K.L., Castillo-Chavez, C.: Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM Journal of Applied Math, 52(3):835-854, (1992)
    • (1992) SIAM Journal of Applied Math , vol.52 , Issue.3 , pp. 835-854
    • Huang, W.1    Cooke, K.L.2    Castillo-Chavez, C.3
  • 16
    • 0023070210 scopus 로고
    • Dynamical behaviour of epidemiological models with nonlinear incidence rates
    • Liu, W., Hethcote, H.W., Levin, S.A.: Dynamical behaviour of epidemiological models with nonlinear incidence rates. Journal of Mathematical Biology, 25(4):359-380, (1987)
    • (1987) Journal of Mathematical Biology , vol.25 , Issue.4 , pp. 359-380
    • Liu, W.1    Hethcote, H.W.2    Levin, S.A.3
  • 17
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behaviourof SIRS epidemiological models
    • Liu, W., Levin, S.A., Iwasa, Y.: Influence of nonlinear incidence rates upon the behaviourof SIRS epidemiological models. Journal of Mathematical Biology, 23(2):187-204, (1986)
    • (1986) Journal of Mathematical Biology , vol.23 , Issue.2 , pp. 187-204
    • Liu, W.1    Levin, S.A.2    Iwasa, Y.3
  • 18
    • 0041887324 scopus 로고
    • On the asymptotic behaviour of the bounded solutions of a non-linear Volterra equation
    • Londen, S.-O.: On the asymptotic behaviour of the bounded solutions of a non-linear Volterra equation. SIAM Journal on Mathematical Analysis, 5(6):849-875, (1974)
    • (1974) SIAM Journal on Mathematical Analysis , vol.5 , Issue.6 , pp. 849-875
    • Londen, S.-O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.