메뉴 건너뛰기




Volumn 65, Issue 5, 2005, Pages 1794-1816

Bifurcation analysis of an SIRS epidemic model with generalized incidence

Author keywords

Bogdanov Takens bifurcation; Epidemic models; Hopf bifurcation; Nonlinear incidence; Saddle node bifurcation

Indexed keywords

BIFURCATION (MATHEMATICS); DISEASE CONTROL; EPIDEMIOLOGY; IMMUNIZATION; LYAPUNOV METHODS; THEOREM PROVING;

EID: 27844516471     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040604947     Document Type: Article
Times cited : (95)

References (33)
  • 1
    • 1642341634 scopus 로고    scopus 로고
    • Periodicity in an epidemic model with a generalized nonlinear incidence
    • M. E. ALEXANDER AND S. M. MOGHADAS, Periodicity in an epidemic model with a generalized nonlinear incidence, Math. Biosci., 189 (2004), pp. 75-96.
    • (2004) Math. Biosci. , vol.189 , pp. 75-96
    • Alexander, M.E.1    Moghadas, S.M.2
  • 2
    • 0042947617 scopus 로고    scopus 로고
    • Limit cycles in a disease transmission model
    • M. A. M. ALWASH, Limit cycles in a disease transmission model, Appl. Math. Comput., 86 (1997), pp. 85-92.
    • (1997) Appl. Math. Comput. , vol.86 , pp. 85-92
    • Alwash, M.A.M.1
  • 5
    • 0027465252 scopus 로고
    • Chaosand biological complexity in measles dynamics
    • B. M. BOLKER AND B. T. GRENFELL, Chaos and biological complexity in measles dynamics, Philos. Trans. R. Soc. Lond. B, 251 (1993), pp. 75-81.
    • (1993) Philos. Trans. R. Soc. Lond. B , vol.251 , pp. 75-81
    • Bolker, B.M.1    Grenfell, B.T.2
  • 6
    • 0018041874 scopus 로고
    • A generalization of the Kermack-McKendrick deterministic epidemic model
    • V. CAPASSO AND G. SERIO, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci., 42 (1978), pp. 43-61.
    • (1978) Math. Biosci. , vol.42 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 7
    • 0033539297 scopus 로고    scopus 로고
    • Influenza
    • N. J. COX AND K. SUBBARAO, Influenza, Lancet, 354 (1999), pp. 1277-1282.
    • (1999) Lancet , vol.354 , pp. 1277-1282
    • Cox, N.J.1    Subbarao, K.2
  • 8
    • 0043263962 scopus 로고    scopus 로고
    • Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population
    • W. R. DERRICK AND P. VAN DEN DRIESSCHE, Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population, Discrete Contin. Dyn. Syst. Ser. B, 3 (2003), pp. 299-309.
    • (2003) Discrete Contin. Dyn. Syst. Ser. B , vol.3 , pp. 299-309
    • Derrick, W.R.1    Van Den Driessche, P.2
  • 10
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • D. J. D. EARN, P. ROHANI, B. M. BOLKER, AND B. T. GRENFELL, A simple model for complex dynamical transitions in epidemics, Science, 287 (2000), pp. 667-670.
    • (2000) Science , vol.287 , pp. 667-670
    • Earn, D.J.D.1    Rohani, P.2    Bolker, B.M.3    Grenfell, B.T.4
  • 12
    • 0003478288 scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Springer-Verlag, New York
    • J. GUCKENHEIMER AND P. HOLMES, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Appl. Math. Sci. 42, Springer-Verlag, New York, 1983.
    • (1983) Appl. Math. Sci. , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 13
    • 0038521431 scopus 로고    scopus 로고
    • A qualitative study of a vaccination model with nonlinear incidence
    • A. B. GUMEL AND S. M. MOGHADAS, A qualitative study of a vaccination model with nonlinear incidence, Appl. Math. Comput., 143 (2003), pp. 409-419.
    • (2003) Appl. Math. Comput. , vol.143 , pp. 409-419
    • Gumel, A.B.1    Moghadas, S.M.2
  • 14
    • 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 (1994), pp. 41-55.
    • (1994) Math. Biosci. , vol.128 , pp. 41-55
    • Hadeler, K.P.1    Castillo-Chavez, C.2
  • 15
    • 0030882301 scopus 로고    scopus 로고
    • Backward bifurcation in epidemic control
    • K. P. HADELER AND P. VAN DEN DRIESSCHE, Backward bifurcation in epidemic control, Math. Biosci., 146 (1997), pp. 15-35.
    • (1997) Math. Biosci. , vol.146 , pp. 15-35
    • Hadeler, K.P.1    Van Den Driessche, P.2
  • 16
    • 0025985745 scopus 로고
    • Some epidemiological models with nonlinear incidence
    • H. W. HETHCOTE AND P. VAN DEN DRIESSCHE, Some epidemiological models with nonlinear incidence, J. Math. Biol., 29 (1991), pp. 271-287.
    • (1991) J. Math. Biol. , vol.29 , pp. 271-287
    • Hethcote, H.W.1    Van Den Driessche, P.2
  • 18
    • 0037449510 scopus 로고    scopus 로고
    • Measles vaccine efficacy during an epidemic in 1998 in the highly vaccinated population of Poland
    • W. JANASZEK, N. J. GAY, AND W. GUT, Measles vaccine efficacy during an epidemic in 1998 in the highly vaccinated population of Poland, Vaccine, 21 (2003), pp. 473-478.
    • (2003) Vaccine , vol.21 , pp. 473-478
    • Janaszek, W.1    Gay, N.J.2    Gut, W.3
  • 19
    • 1642309943 scopus 로고    scopus 로고
    • Center manifolds and normal forms in epidemic models
    • Mathematical Approaches for Emerging and Reemerging Infectious Diseases, Springer-Verlag, New York
    • C. M. KRIBS-ZALETA, Center manifolds and normal forms in epidemic models, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases, Inst. Math. Appl. 125, Springer-Verlag, New York, 2002, pp. 269-286.
    • (2002) Inst. Math. Appl. , vol.125 , pp. 269-286
    • Kribs-Zaleta, C.M.1
  • 20
    • 0347663530 scopus 로고    scopus 로고
    • Seasonally forced disease dynamics explored as switching between attractors
    • M. J. KEELING, P. ROHANI, AND B. T. GRENFELL, Seasonally forced disease dynamics explored as switching between attractors, Phys. D, 148 (2001), pp. 317-335.
    • (2001) Phys. D , vol.148 , pp. 317-335
    • Keeling, M.J.1    Rohani, P.2    Grenfell, B.T.3
  • 21
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • C. M. KRIBS-ZALETA AND J. X. VELASCO-HERNÁNDEZ, A simple vaccination model with multiple endemic states, Math. Biosci., 164 (2000), pp. 183-201.
    • (2000) Math. Biosci. , vol.164 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernández, J.X.2
  • 22
    • 0003687338 scopus 로고
    • Elements of applied bifurcation theory
    • Springer-Verlag, New York
    • Y. A. KUZNETSOV, Elements of Applied Bifurcation Theory, Appl. Math. Sci. 112, Springer-Verlag, New York, 1995.
    • (1995) Appl. Math. Sci. , vol.112
    • Kuznetsov, Y.A.1
  • 24
    • 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), pp. 359-380.
    • (1987) J. Math. Biol. , vol.25 , pp. 359-380
    • Liu, W.M.1    Hethcote, H.W.2    Levin, S.A.3
  • 25
    • 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), pp. 187-204.
    • (1986) J. Math. Biol. , vol.23 , pp. 187-204
    • Liu, W.M.1    Levin, S.A.2    Iwasa, Y.3
  • 26
    • 4944233809 scopus 로고    scopus 로고
    • Modelling the effect of imperfect vaccines on disease epidemiology
    • S. M. MOGHADAS, Modelling the effect of imperfect vaccines on disease epidemiology, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), pp. 999-1012.
    • (2004) Discrete Contin. Dyn. Syst. Ser. B , vol.4 , pp. 999-1012
    • Moghadas, S.M.1
  • 27
    • 0031234909 scopus 로고    scopus 로고
    • Global stability in an S → I → R → I model
    • H. N. MOREIRA AND W. YUQUAN, Global stability in an S → I → R → I model, SIAM Rev., 39 (1997), pp. 496-502.
    • (1997) SIAM Rev. , vol.39 , pp. 496-502
    • Moreira, H.N.1    Yuquan, W.2
  • 28
    • 0019164741 scopus 로고
    • Heterogeneity in disease-transmission modeling
    • A. NOLD, Heterogeneity in disease-transmission modeling, Math. Biosci., 52 (1980), pp. 227-240.
    • (1980) Math. Biosci. , vol.52 , pp. 227-240
    • Nold, A.1
  • 29
    • 0036229603 scopus 로고    scopus 로고
    • The interplay between determinism and stochasticity in childhood diseases
    • P. ROHANI, M. J. KEELING, AND B. T. GRENFELL, The interplay between determinism and stochasticity in childhood diseases, Amer. Naturalist, 159 (2002), pp. 469-481.
    • (2002) Amer. Naturalist , vol.159 , pp. 469-481
    • Rohani, P.1    Keeling, M.J.2    Grenfell, B.T.3
  • 30
    • 0037429355 scopus 로고    scopus 로고
    • Dynamical behavior of an epidemic model with a nonlinear incidence rate
    • S. RUAN AND W. WANG, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations, 188 (2003), pp. 135-163.
    • (2003) J. Differential Equations , vol.188 , pp. 135-163
    • Ruan, S.1    Wang, W.2
  • 31
    • 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), pp. 525-540.
    • (2000) J. Math. Biol. , vol.40 , pp. 525-540
    • Van Den Driessche, P.1    Watmough, J.2
  • 32
    • 0033537354 scopus 로고    scopus 로고
    • Effect of subclinical infection on maintaining immunity against measles in vaccinated children in West Africa
    • H. C. WHITTLE, P. AABY, B. SAMB, H. JENSEN, J. BENNET, AND F. SIMONDON, Effect of subclinical infection on maintaining immunity against measles in vaccinated children in West Africa, Lancet, 353 (1999), pp. 98-102.
    • (1999) Lancet , vol.353 , pp. 98-102
    • Whittle, H.C.1    Aaby, P.2    Samb, B.3    Jensen, H.4    Bennet, J.5    Simondon, F.6
  • 33
    • 0015711463 scopus 로고
    • Recurrent outbreaks of measles, chickenpox and mumps II
    • J. A. YORKE AND W. P. LONDON, Recurrent outbreaks of measles, chickenpox and mumps II, Amer. J. Epidemiol., 98 (1973), pp. 469-482.
    • (1973) Amer. J. Epidemiol. , vol.98 , pp. 469-482
    • Yorke, J.A.1    London, W.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.