메뉴 건너뛰기




Volumn 138, Issue 2, 1996, Pages 101-130

Dynamical complexity in age-structured models of the transmission of the measles virus: Epidemiological implications at high levels of vaccine uptake

Author keywords

[No Author keywords available]

Indexed keywords

MEASLES VACCINE;

EID: 0030561585     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(96)00127-7     Document Type: Article
Times cited : (38)

References (52)
  • 2
    • 50249220129 scopus 로고
    • Epidemic disease in England - The evidence of variability and of persistency of type
    • 2 W. H. Hamer, Epidemic disease in England - The evidence of variability and of persistency of type, Lancet 1:733-739 (1906).
    • (1906) Lancet , vol.1 , pp. 733-739
    • Hamer, W.H.1
  • 3
    • 0002426167 scopus 로고
    • The interpretation of periodicity in disease prevalence
    • 3 M. A. Soper, The interpretation of periodicity in disease prevalence. J. Roy. Stat. Soc. A 92:34-61 (1929).
    • (1929) J. Roy. Stat. Soc. A , vol.92 , pp. 34-61
    • Soper, M.A.1
  • 4
    • 0000998185 scopus 로고
    • A contribution to the mathematical theory of epidemics
    • 4 W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. London A 115:700-721 (1927).
    • (1927) Proc. Roy. Soc. London A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 5
    • 0003188315 scopus 로고
    • Measles periodicity and community size
    • 5 M. S. Barlett, Measles periodicity and community size. J. Roy. Stat. Soc. A 120:48-70 (1957).
    • (1957) J. Roy. Stat. Soc. A , vol.120 , pp. 48-70
    • Barlett, M.S.1
  • 6
    • 0002454064 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations
    • 6 K. Dietz, The incidence of infectious diseases under the influence of seasonal fluctuations. Lect. Note Biomath. 11:1-15 (1976).
    • (1976) Lect. Note Biomath. , vol.11 , pp. 1-15
    • Dietz, K.1
  • 7
    • 0020072418 scopus 로고
    • Measles in England and Wales. I. An analysis of factors underlying seasonal patterns
    • 7 P. E. M. Fine and J. A. Clarkson, Measles in England and Wales. I. An analysis of factors underlying seasonal patterns. Int. J. Epidemiol 11:5-15 (1982).
    • (1982) Int. J. Epidemiol , vol.11 , pp. 5-15
    • Fine, P.E.M.1    Clarkson, J.A.2
  • 8
    • 0020004047 scopus 로고
    • Directly transmitted infectious diseases: Control by vaccination
    • 8 R. M. Anderson and R. M. May, Directly transmitted infectious diseases: Control by vaccination. Science 215:1053-1060 (1982).
    • (1982) Science , vol.215 , pp. 1053-1060
    • Anderson, R.M.1    May, R.M.2
  • 9
    • 0002836854 scopus 로고
    • Mathematical models for infectious disease statistics
    • A. C. Atkinson and S. E. Feinberg, Eds., Springer, New York
    • 9 K. Dietz and D. Schenzle, Mathematical models for infectious disease statistics, in A Celebration of Statistics, A. C. Atkinson and S. E. Feinberg, Eds., Springer, New York, 1985 pp. 167-204.
    • (1985) A Celebration of Statistics , pp. 167-204
    • Dietz, K.1    Schenzle, D.2
  • 10
    • 77957185501 scopus 로고
    • An age-structured model of pre- and post-vaccination measles transmission
    • 10 D. Schenzle, An age-structured model of pre- and post-vaccination measles transmission. IMA J. Math. Appl. Med. Biol. 1:169-191 (1984).
    • (1984) Ima J. Math. Appl. Med. Biol. , vol.1 , pp. 169-191
    • Schenzle, D.1
  • 11
    • 0021823575 scopus 로고
    • Proportionate mixing models for age-dependent infection transmission
    • 11 K. Dietz and D. Schenzle, Proportionate mixing models for age-dependent infection transmission. J. Math. Biol. 22:117-120 (1985).
    • (1985) J. Math. Biol. , vol.22 , pp. 117-120
    • Dietz, K.1    Schenzle, D.2
  • 12
    • 0022262704 scopus 로고
    • Age-related changes in the rate of disease transmission: Implications for the design of vaccination programmes
    • 12 R. M. Anderson and R. M. May, Age-related changes in the rate of disease transmission: Implications for the design of vaccination programmes. J. Hyg. Cambridge 94:365-436 (1985).
    • (1985) J. Hyg. Cambridge , vol.94 , pp. 365-436
    • Anderson, R.M.1    May, R.M.2
  • 13
    • 0025196595 scopus 로고
    • Chaos versus noisy periodicity: Alternative hypotheses for childhood epidemics
    • 13 L. F. Olsen and W. M. Schaffer, Chaos versus noisy periodicity: Alternative hypotheses for childhood epidemics. Science 249:499-504 (1990).
    • (1990) Science , vol.249 , pp. 499-504
    • Olsen, L.F.1    Schaffer, W.M.2
  • 14
    • 0027465252 scopus 로고
    • Chaos and biological complexity in measles dynamics
    • 14 B. M. Bolker and B. T. Grenfell, Chaos and biological complexity in measles dynamics. Proc. Roy. Soc. London B 251:75-81 (1993).
    • (1993) Proc. Roy. Soc. London B , vol.251 , pp. 75-81
    • Bolker, B.M.1    Grenfell, B.T.2
  • 15
    • 0028937480 scopus 로고
    • Predicting the impact of measles vaccination in England and Wales: Model validation and analysis of policy options
    • 15 H. R. Babad, D. J. Nokes, N. J. Gay, E. Miller, P. Morgan-Caper, and R. M. Anderson, Predicting the impact of measles vaccination in England and Wales: Model validation and analysis of policy options. Epidemiol. Inf. 114:319-344 (1995).
    • (1995) Epidemiol. Inf. , vol.114 , pp. 319-344
    • Babad, H.R.1    Nokes, D.J.2    Gay, N.J.3    Miller, E.4    Morgan-Caper, P.5    Anderson, R.M.6
  • 16
    • 0001093949 scopus 로고
    • Space, persistence and dynamics of measles epidemics
    • 16 B. M. Bolker and B. T. Grenfell, Space, persistence and dynamics of measles epidemics. Proc. Roy. Soc. London B 348:308-320 (1995).
    • (1995) Proc. Roy. Soc. London B , vol.348 , pp. 308-320
    • Bolker, B.M.1    Grenfell, B.T.2
  • 17
    • 0019567714 scopus 로고
    • On estimating the contagiousness of a disease transmitted from person to person
    • 17 N. G. Becker and J. Angulo, On estimating the contagiousness of a disease transmitted from person to person. Math. Biosci. 54:137-154 (1981).
    • (1981) Math. Biosci. , vol.54 , pp. 137-154
    • Becker, N.G.1    Angulo, J.2
  • 18
    • 0021678935 scopus 로고
    • Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: Time series analysis
    • 18 R. M. Anderson, B. T. Grenfell, and R. M. May, Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: Time series analysis. J. Hyg. Cambridge 93:587-608 (1984).
    • (1984) J. Hyg. Cambridge , vol.93 , pp. 587-608
    • Anderson, R.M.1    Grenfell, B.T.2    May, R.M.3
  • 19
    • 0011985411 scopus 로고
    • Office of Population, Census and Surveys, H. M. S. O., London
    • 19 O. P. C. S., Registrar General's weekly reports, England and Wales, Office of Population, Census and Surveys, H. M. S. O., London, 1948-1968.
    • (1948) Registrar General's Weekly Reports, England and Wales
  • 20
    • 0011916579 scopus 로고
    • H. M. S. O., London
    • 20 O. P. C. S., OPCS Monitor, H. M. S. O., London, 1968-1995.
    • (1968) Opcs Monitor
  • 21
    • 0028782308 scopus 로고
    • Populations, infectious disease and immunity: A very nonlinear world
    • 21 R. M. Anderson, Populations, infectious disease and immunity: A very nonlinear world. Proc. Roy. Soc. London B 346:457-505 (1994).
    • (1994) Proc. Roy. Soc. London B , vol.346 , pp. 457-505
    • Anderson, R.M.1
  • 22
    • 0020519519 scopus 로고
    • Vaccination against rubella and measles: Quantitative investigations of different policies
    • 22 R. M. Anderson and R. M. May, Vaccination against rubella and measles: Quantitative investigations of different policies. J. Hyg. Cambridge 90:259-325 (1983).
    • (1983) J. Hyg. Cambridge , vol.90 , pp. 259-325
    • Anderson, R.M.1    May, R.M.2
  • 23
    • 77957182038 scopus 로고
    • Spatial, temporal and genetic heterogeneity in host populations and the design of immunization programmes
    • 23 R. M. Anderson and R. M. May, Spatial, temporal and genetic heterogeneity in host populations and the design of immunization programmes. IMA J. Math. Appl. Med. Biol. 1:233-266 (1984).
    • (1984) Ima J. Math. Appl. Med. Biol. , vol.1 , pp. 233-266
    • Anderson, R.M.1    May, R.M.2
  • 24
    • 0022035886 scopus 로고
    • An age-dependent epidemic model with application to measles
    • 24 D. W. Tudor, An age-dependent epidemic model with application to measles. Math. Biosci. 73:131-147 (1985).
    • (1985) Math. Biosci. , vol.73 , pp. 131-147
    • Tudor, D.W.1
  • 25
    • 0023887538 scopus 로고
    • Optimal ages for vaccination for measles
    • 25 H. W. Hethcote, Optimal ages for vaccination for measles. Math. Biosci. 89:29-52 (1988).
    • (1988) Math. Biosci. , vol.89 , pp. 29-52
    • Hethcote, H.W.1
  • 26
    • 0020956406 scopus 로고
    • Multiple stable subharmonics for a periodic epidemic model
    • 26 H. L. Smith, Multiple stable subharmonics for a periodic epidemic model. J. Math. Biol. 17:179-190 (1983).
    • (1983) J. Math. Biol. , vol.17 , pp. 179-190
    • Smith, H.L.1
  • 27
    • 0021051389 scopus 로고
    • Infinite subharmonic bifurcation in an SEIR epidemic model
    • 27 I. B. Schwartz and H. L. Smith, Infinite subharmonic bifurcation in an SEIR epidemic model. J. Math. Biol. 18:233-253 (1983).
    • (1983) J. Math. Biol. , vol.18 , pp. 233-253
    • Schwartz, I.B.1    Smith, H.L.2
  • 28
    • 0021690803 scopus 로고
    • Seasonality and period-doubling bifurcations in an epidemic model
    • 28 J. L. Aron and I. B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol. 110:665-679 (1984).
    • (1984) J. Theor. Biol. , vol.110 , pp. 665-679
    • Aron, J.L.1    Schwartz, I.B.2
  • 29
    • 0021990877 scopus 로고
    • Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models
    • 29 I. B. Schwartz, Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models. J. Math. Biol. 21:347-61 (1985).
    • (1985) J. Math. Biol. , vol.21 , pp. 347-361
    • Schwartz, I.B.1
  • 30
    • 0021912738 scopus 로고
    • Nearly one dimensional dynamics in an epidemic
    • 30 W. M. Schaffer and M. Kot, Nearly one dimensional dynamics in an epidemic. J. Theor. Biol. 112:403-427 (1985).
    • (1985) J. Theor. Biol. , vol.112 , pp. 403-427
    • Schaffer, W.M.1    Kot, M.2
  • 31
    • 0024029039 scopus 로고
    • Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark
    • 31 L. F. Olsen, G. L. Truty, and W. M. Schaffer, Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark. J. Theor. Pop. Biol 33:344-370 (1988).
    • (1988) J. Theor. Pop. Biol , vol.33 , pp. 344-370
    • Olsen, L.F.1    Truty, G.L.2    Schaffer, W.M.3
  • 32
    • 0000740021 scopus 로고
    • The case for chaos in childhood epidemics
    • S. Krasner, Ed., AAAS, Washington D. C
    • 32 W. M. Schaffer, L. F. Olsen, G. L. Truty, and S. L. Fulmer, The case for chaos in childhood epidemics, in The Ubiquity of Chaos, S. Krasner, Ed., AAAS, Washington D. C, 1990, pp. 136-166.
    • (1990) The Ubiquity of Chaos , pp. 136-166
    • Schaffer, W.M.1    Olsen, L.F.2    Truty, G.L.3    Fulmer, S.L.4
  • 33
    • 0025876128 scopus 로고
    • Chaotic stochasticity: A ubiquitous source of unpredictability in epidemics
    • 33 D. A. Rand and H. B. Wilson, Chaotic stochasticity: A ubiquitous source of unpredictability in epidemics. Proc. Roy. Soc. London B 246:179-184 (1991).
    • (1991) Proc. Roy. Soc. London B , vol.246 , pp. 179-184
    • Rand, D.A.1    Wilson, H.B.2
  • 35
    • 0027422718 scopus 로고
    • Chaos and complexity in measles models: A comparative numerical study
    • 35 B. M. Bolker, Chaos and complexity in measles models: A comparative numerical study. IMA J. Math. Appl. Med. Biol. 10:83-95 (1993).
    • (1993) Ima J. Math. Appl. Med. Biol. , vol.10 , pp. 83-95
    • Bolker, B.M.1
  • 36
    • 0027769668 scopus 로고
    • The case for chaos in childhood epidemics. II. Predicting historical epidemics from mathematical models
    • 36 C. W. Tidd, L. F. Olsen, and W. M. Schaffer, The case for chaos in childhood epidemics. II. Predicting historical epidemics from mathematical models. Proc. Roy. Soc. London B 254:257-273 (1993).
    • (1993) Proc. Roy. Soc. London B , vol.254 , pp. 257-273
    • Tidd, C.W.1    Olsen, L.F.2    Schaffer, W.M.3
  • 37
    • 0025470862 scopus 로고
    • Multiple attractors in the response to a vaccination program
    • 37 J. L. Aron, Multiple attractors in the response to a vaccination program. Theor. Pop. Biol. 38:58-67 (1990).
    • (1990) Theor. Pop. Biol. , vol.38 , pp. 58-67
    • Aron, J.L.1
  • 39
    • 77957182377 scopus 로고
    • Analytical results on the stability of age-structured recurrent epidemic models
    • 39 D. Greenhalgh, Analytical results on the stability of age-structured recurrent epidemic models. IMA J. Math. Appl. Med. Biol. 4:109-144 (1987).
    • (1987) Ima J. Math. Appl. Med. Biol. , vol.4 , pp. 109-144
    • Greenhalgh, D.1
  • 40
    • 0022354857 scopus 로고
    • The estimation of age-related rates of infection from case notifications and serological data
    • 40 B. T. Grenfell and R. M. Anderson, The estimation of age-related rates of infection from case notifications and serological data. J. Hyg. Cambridge 95:419-436 (1985).
    • (1985) J. Hyg. Cambridge , vol.95 , pp. 419-436
    • Grenfell, B.T.1    Anderson, R.M.2
  • 41
    • 0002157780 scopus 로고
    • Elimination of fast variables
    • 41 N. G. van Kampen, Elimination of fast variables. Phys. Rep. 124:69-160 (1985).
    • (1985) Phys. Rep. , vol.124 , pp. 69-160
    • Van Kampen, N.G.1
  • 45
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractors, and transient chaos
    • 45 C. Grebogi, E. Ott, and J. E. Yorke, Crises, sudden changes in chaotic attractors, and transient chaos. Phys. D. 7:181-200 (1983).
    • (1983) Phys. D. , vol.7 , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.E.3
  • 46
    • 0020059396 scopus 로고
    • Measles in England and Wales. II. Impact of the measles vaccination programme on the distribution of immunity in the population
    • 46 P. E. M. Fine and J. A. Clarkson, Measles in England and Wales. II. Impact of the measles vaccination programme on the distribution of immunity in the population, Int. J. Epidemiol. 11:15-25 (1982).
    • (1982) Int. J. Epidemiol. , vol.11 , pp. 15-25
    • Fine, P.E.M.1    Clarkson, J.A.2
  • 47
    • 0020956395 scopus 로고
    • Measles in England and Wales. III. Assessing published predictions of the impact of vaccination on incidence
    • 47 P. E. M. Fine and J. A. Clarkson, Measles in England and Wales. III. Assessing published predictions of the impact of vaccination on incidence. Int. J. Epidemiol. 12:332-339 (1982).
    • (1982) Int. J. Epidemiol. , vol.12 , pp. 332-339
    • Fine, P.E.M.1    Clarkson, J.A.2
  • 48
    • 0029987668 scopus 로고    scopus 로고
    • Mass vaccination to control chickenpox: The influence of zoster
    • 48 N. M. Ferguson, R. M. Anderson, and G. P. Garnett, Mass vaccination to control chickenpox: The influence of zoster. Proc. Nat. Acad. Sci. USA, 93:7231-7235 (1996).
    • (1996) Proc. Nat. Acad. Sci. Usa , vol.93 , pp. 7231-7235
    • Ferguson, N.M.1    Anderson, R.M.2    Garnett, G.P.3
  • 49
    • 0029956730 scopus 로고    scopus 로고
    • Impact of vaccination on the spatial correlation and persistence of measles dynamics
    • in press
    • 49 B. M. Bolker and B. T. Grenfell, Impact of vaccination on the spatial correlation and persistence of measles dynamics. Proc. Nat. Acad. Sci. USA, in press (1996).
    • (1996) Proc. Nat. Acad. Sci. Usa
    • Bolker, B.M.1    Grenfell, B.T.2
  • 51
    • 0011984141 scopus 로고
    • Spatial heterogeneity in epidemic models
    • in press
    • 51 A. L. Lloyd and R. M. May, Spatial heterogeneity in epidemic models. J. Theor. Biol., in press (1995).
    • (1995) J. Theor. Biol.
    • Lloyd, A.L.1    May, R.M.2
  • 52
    • 77957177077 scopus 로고
    • The control of childhood viral infections by pulse vaccination
    • 52 D. J. Nokes and J. Swinton, The control of childhood viral infections by pulse vaccination. IMA J. Math. Appl. Med. Biol., 12:29-35 (1995).
    • (1995) Ima J. Math. Appl. Med. Biol. , vol.12 , pp. 29-35
    • Nokes, D.J.1    Swinton, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.