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Volumn 67, Issue 3, 2005, Pages 203-216

A new look at the critical community size for childhood infections

Author keywords

Asymptotic approximation; Demographic stochasticity; Quasi stationary distribution; Time to extinction; Transition region

Indexed keywords

INFECTIOUS DISEASE;

EID: 16244363078     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tpb.2005.01.002     Document Type: Article
Times cited : (48)

References (36)
  • 1
    • 0034572046 scopus 로고    scopus 로고
    • Stochastic epidemics in dynamic populations: Quasi-stationarity and extinction
    • H. Andersson, and T. Britton Stochastic epidemics in dynamic populations: quasi-stationarity and extinction J. Math. Biol. 41 2000 559 580
    • (2000) J. Math. Biol. , vol.41 , pp. 559-580
    • Andersson, H.1    Britton, T.2
  • 4
    • 0003188315 scopus 로고
    • Measles periodicity and community size
    • M.S. Bartlett Measles periodicity and community size J. R. Statist. Soc. Ser. A 1957 1957 48 60
    • (1957) J. R. Statist. Soc. Ser. a , vol.1957 , pp. 48-60
    • Bartlett, M.S.1
  • 5
    • 0003188313 scopus 로고
    • The critical community size for measles in the United States
    • M.S. Bartlett The critical community size for measles in the United States J. R. Statist. Soc. Ser. A 123 1960 37 44
    • (1960) J. R. Statist. Soc. Ser. a , vol.123 , pp. 37-44
    • Bartlett, M.S.1
  • 6
    • 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. Prob. 3 2001 75 95
    • (2001) Methodol. Comput. Appl. Prob. , vol.3 , pp. 75-95
    • Clancy, D.1    O'Neill, P.D.2    Pollett, P.K.3
  • 7
    • 0003063241 scopus 로고
    • On quasi-stationary distributions in absorbing discrete-time finite Markov chains
    • J.N. Darroch, and E. Seneta On quasi-stationary distributions in absorbing discrete-time finite Markov chains J. Appl. Prob. 2 1965 88 100
    • (1965) J. Appl. Prob. , vol.2 , pp. 88-100
    • Darroch, J.N.1    Seneta, E.2
  • 8
    • 0001383449 scopus 로고
    • On quasi-stationary distributions in absorbing continuous-time finite Markov chains
    • J.N. Darroch, and E. Seneta On quasi-stationary distributions in absorbing continuous-time finite Markov chains J. Appl. Prob. 4 1967 192 196
    • (1967) J. Appl. Prob. , vol.4 , pp. 192-196
    • Darroch, J.N.1    Seneta, E.2
  • 10
    • 0003066251 scopus 로고
    • Epidemiology, Society for Industrial and Applied Mathematics, Philadelphia
    • Dietz, K., 1975. Transmission and Control of Arbovirus Diseases. Epidemiology, Society for Industrial and Applied Mathematics, Philadelphia, pp. 104-121.
    • (1975) Transmission and Control of Arbovirus Diseases , pp. 104-121
    • Dietz, K.1
  • 11
    • 0029014859 scopus 로고
    • Recurrent outbreaks of childhood disease revisited: The impact of isolation
    • Z. Feng, and H.R. Thieme Recurrent outbreaks of childhood disease revisited: the impact of isolation Math. Biosci. 128 1995 93 130
    • (1995) Math. Biosci. , vol.128 , pp. 93-130
    • Feng, Z.1    Thieme, H.R.2
  • 13
    • 0001861946 scopus 로고    scopus 로고
    • The expected extinction time of a population within a system of interacting biological populations
    • J. Grasman The expected extinction time of a population within a system of interacting biological populations Bull. Math. Biol. 58 3 1996 555 568
    • (1996) Bull. Math. Biol. , vol.58 , Issue.3 , pp. 555-568
    • Grasman, J.1
  • 14
    • 0001787366 scopus 로고
    • Seasonaliaty, demography and the dynamics of measles in developed countries
    • D. Mollison Cambridge University Press, Publications of the Newton Institute Cambridge
    • B.T. Grenfell, B. Bolker, and A. Kleczkowski Seasonaliaty, demography and the dynamics of measles in developed countries D. Mollison Epidemic Models: Their Structure and Relation to Data 1995 Cambridge University Press, Publications of the Newton Institute Cambridge 248 268
    • (1995) Epidemic Models: Their Structure and Relation to Data , pp. 248-268
    • Grenfell, B.T.1    Bolker, B.2    Kleczkowski, A.3
  • 15
    • 50249220129 scopus 로고
    • Epidemic disease in England - The evidence of variability and of persistence of types
    • W.H. Hamer Epidemic disease in England - the evidence of variability and of persistence of types Lancet 1 1906 733 739
    • (1906) Lancet , vol.1 , pp. 733-739
    • Hamer, W.H.1
  • 16
    • 0017228276 scopus 로고
    • Qualitative analyses of communicable disease models
    • H. Hethcote Qualitative analyses of communicable disease models Math. Biosci. 28 1976 335 356
    • (1976) Math. Biosci. , vol.28 , pp. 335-356
    • Hethcote, H.1
  • 17
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H. Hethcote The mathematics of infectious diseases SIAM Rev. 42 4 2000 599 653
    • (2000) SIAM Rev. , vol.42 , Issue.4 , pp. 599-653
    • Hethcote, H.1
  • 18
    • 0036846383 scopus 로고    scopus 로고
    • Effects of quarantine in six models for infectious diseases
    • H. Hethcote, M. Zhien, and L. Shengbing Effects of quarantine in six models for infectious diseases Math. Biosci. 180 2002 141 160
    • (2002) Math. Biosci. , vol.180 , pp. 141-160
    • Hethcote, H.1    Zhien, M.2    Shengbing, L.3
  • 19
    • 0000236256 scopus 로고
    • Periodicity in epidemiological models
    • L. Gross T.G. Hallam S.A. Levin Springer Berlin
    • H.W. Hethcote, and S.A. Levin Periodicity in epidemiological models L. Gross T.G. Hallam S.A. Levin Applied Mathematical Ecology vol.18 1989 Springer Berlin
    • (1989) Applied Mathematical Ecology , vol.18
    • Hethcote, H.W.1    Levin, S.A.2
  • 20
    • 0031015249 scopus 로고    scopus 로고
    • Disease extinction and community size: Modelling the persistence of measles
    • M.J. Keeling, and B.T. Grenfell Disease extinction and community size: modelling the persistence of measles Science 275 1997 65 67
    • (1997) Science , vol.275 , pp. 65-67
    • Keeling, M.J.1    Grenfell, B.T.2
  • 22
    • 0347063875 scopus 로고    scopus 로고
    • Estimating variability in models for recurrent epidemics: Assessing the use of moment closure techniques
    • A.L. Lloyd Estimating variability in models for recurrent epidemics: assessing the use of moment closure techniques Theor. Popul. Biol. 65 2004 49 65
    • (2004) Theor. Popul. Biol. , vol.65 , pp. 49-65
    • Lloyd, A.L.1
  • 23
    • 0029980587 scopus 로고    scopus 로고
    • Spatial heterogeneity in epidemic models
    • A.L. Lloyd, and R.M. May Spatial heterogeneity in epidemic models J. Theor. Biol. 179 1996 1 11
    • (1996) J. Theor. Biol. , vol.179 , pp. 1-11
    • Lloyd, A.L.1    May, R.M.2
  • 24
    • 0009369775 scopus 로고
    • Martini's equations for the epidemiology of immunising diseases
    • A.J. Lotka Martini's equations for the epidemiology of immunising diseases Nature 111 1923 633 634
    • (1923) Nature , vol.111 , pp. 633-634
    • Lotka, A.J.1
  • 26
    • 0013612207 scopus 로고
    • Hybrid Models of Tropical Infections
    • Springer, Berlin, Heidelberg, New York, Tokyo.
    • Nåsell, I., 1985. Hybrid Models of Tropical Infections. Lecture Notes in Biomathematics, vol. 59. Springer, Berlin, Heidelberg, New York, Tokyo.
    • (1985) Lecture Notes in Biomathematics , vol.59
    • Nåsell, I.1
  • 27
    • 0000635179 scopus 로고    scopus 로고
    • On the quasi-stationary distribution of the closed endemic SIS model
    • I. Nåsell On the quasi-stationary distribution of the closed endemic SIS model Adv. Appl. Prob. 28 1996 895 932
    • (1996) Adv. Appl. Prob. , vol.28 , pp. 895-932
    • Nåsell, I.1
  • 28
    • 0033475339 scopus 로고    scopus 로고
    • On the time to extinction in recurrent epidemics
    • I. Nåsell On the time to extinction in recurrent epidemics J. R. Stat. Soc. Ser. B 61 1999 309 330
    • (1999) J. R. Stat. Soc. Ser. B , vol.61 , pp. 309-330
    • Nåsell, I.1
  • 29
    • 0035822368 scopus 로고    scopus 로고
    • Extinction and quasi-stationarity in the Verhulst logistic model
    • I. Nåsell Extinction and quasi-stationarity in the Verhulst logistic model J. Theor. Biol. 211 2001 11 27
    • (2001) J. Theor. Biol. , vol.211 , pp. 11-27
    • Nåsell, I.1
  • 30
    • 24544434555 scopus 로고    scopus 로고
    • Endemicity persistence and quasi-stationarity
    • C. Castillo-Chavez S. Blower P. van den Driessche D. Kirschner A.-A. Yakubu Springer New York, Berlin, Heidelberg, Barcelona, Hong Kong, London, Milan, Paris, Singapore, Tokyo
    • I. Nåsell Endemicity persistence and quasi-stationarity C. Castillo-Chavez S. Blower P. van den Driessche D. Kirschner A.-A. Yakubu Mathematical Approaches for Emerging and Reemerging Infectious Diseases. An Introduction, The IMA Volumes in Mathematics and its Applications vol. 125 2002 Springer New York, Berlin, Heidelberg, Barcelona, Hong Kong, London, Milan, Paris, Singapore, Tokyo 199 227
    • (2002) Mathematical Approaches for Emerging and Reemerging Infectious Diseases. An Introduction, the IMA Volumes in Mathematics and Its Applications , vol.125 , pp. 199-227
    • Nåsell, I.1
  • 31
    • 0347506351 scopus 로고    scopus 로고
    • An extension of the moment closure method
    • I. Nåsell An extension of the moment closure method Theor. Popul. Biol. 64 2003 233 239
    • (2003) Theor. Popul. Biol. , vol.64 , pp. 233-239
    • Nåsell, I.1
  • 33
    • 0000830143 scopus 로고
    • An asymptotic solution to a two-dimensional exit problem arising in population dynamics
    • H. Roozen An asymptotic solution to a two-dimensional exit problem arising in population dynamics SIAM J. Appl. Math. 49 1989 1793 1810
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1793-1810
    • Roozen, H.1
  • 34
    • 77957185501 scopus 로고
    • An age-structured model of pre- and post-vaccination measles transmission
    • D. Schenzle An age-structured model of pre- and post-vaccination measles transmission IMA J. Math. Appl. Med. Biol. 1 1984 169 191
    • (1984) IMA J. Math. Appl. Med. Biol. , vol.1 , pp. 169-191
    • Schenzle, D.1
  • 35
    • 0002426167 scopus 로고
    • The interpretation of periodicity in disease prevalence (with discussion)
    • H.E. Soper The interpretation of periodicity in disease prevalence (with discussion) J. R. Stat. Soc. 92 1929 34 73
    • (1929) J. R. Stat. Soc. , vol.92 , pp. 34-73
    • Soper, H.E.1
  • 36
    • 0001637131 scopus 로고
    • On the use of the normal approximation in the treatment of stochastic processes
    • P. Whittle On the use of the normal approximation in the treatment of stochastic processes J. R. Stat. Soc. Ser. B 19 1957 268 281
    • (1957) J. R. Stat. Soc. Ser. B , vol.19 , pp. 268-281
    • Whittle, P.1


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