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Volumn 7, Issue 3, 2010, Pages 1186-1204

Branching processes: Their role in epidemiology

Author keywords

Age dependence; Branching process; Epidemic size; Extinction time; Population dependence

Indexed keywords

ARTICLE; BIOSTATISTICS; EPIDEMIC; POPULATION DYNAMICS; POPULATION RESEARCH; POPULATION SIZE; PROBABILITY; PROGENY; RISK ASSESSMENT; STATISTICAL ANALYSIS; STATISTICAL MODEL; EPIDEMIOLOGY; HUMAN; STATISTICS;

EID: 77950903646     PISSN: None     EISSN: 16604601     Source Type: Journal    
DOI: 10.3390/ijerph7031204     Document Type: Article
Times cited : (25)

References (40)
  • 2
    • 0016326272 scopus 로고
    • On parametric estimation for mortal branching processes
    • Becker, N.G. On parametric estimation for mortal branching processes. Biometrika 1974, 61, 393-399.
    • (1974) Biometrika , vol.61 , pp. 393-399
    • Becker, N.G.1
  • 3
    • 0017051552 scopus 로고
    • Estimation for an epidemic model
    • Becker, N.G. Estimation for an epidemic model. Biometrics 1976, 32, 769-777.
    • (1976) Biometrics , vol.32 , pp. 769-777
    • Becker, N.G.1
  • 4
    • 0017692317 scopus 로고
    • Estimation for discrete time branching processes with applications to epidemics
    • Becker, N.G. Estimation for discrete time branching processes with applications to epidemics. Biometrics 1977, 33, 515-522.
    • (1977) Biometrics , vol.33 , pp. 515-522
    • Becker, N.G.1
  • 5
    • 0019577882 scopus 로고
    • A general chain binomial model for infectious diseases
    • Becker, N.G. A general chain binomial model for infectious diseases. Biometrics 1981, 37, 251-258.
    • (1981) Biometrics , vol.37 , pp. 251-258
    • Becker, N.G.1
  • 7
    • 0039836567 scopus 로고
    • The branching process method in Lagrange random variate generation
    • Devroye, L. The branching process method in Lagrange random variate generation. Commun. Statistics-Simulat. Comput. 1992, 21, 1-14.
    • (1992) Commun. Statistics-Simulat. Comput , vol.21 , pp. 1-14
    • Devroye, L.1
  • 9
    • 0003504382 scopus 로고    scopus 로고
    • 3rd ed.; Undergraduate Texts in Mathematics. Springer: New York, NY, USA
    • Elaydi, S. An Introduction to Difference Equations, 3rd ed.; Undergraduate Texts in Mathematics. Springer: New York, NY, USA, 2005.
    • (2005) An Introduction to Difference Equations
    • Elaydi, S.1
  • 10
    • 0033236715 scopus 로고    scopus 로고
    • The distribution of time to extinction in subcritical branching processes: Applications to outbreaks of infectious disease
    • Farrington, C.P.; Grant, A.D. The distribution of time to extinction in subcritical branching processes: Applications to outbreaks of infectious disease. J. Appl. Probab. 1999,36,771-779.
    • (1999) J. Appl. Probab , vol.36 , pp. 771-779
    • Farrington, C.P.1    Grant, A.D.2
  • 11
    • 0142089895 scopus 로고    scopus 로고
    • Branching process models for surveillance of infectious diseases controlled by mass vaccination
    • Farrington, C.P.; Kanaan, M.N.; Gay, N.J. Branching process models for surveillance of infectious diseases controlled by mass vaccination. Biostatistics 2003, 4, 279-295.
    • (2003) Biostatistics , vol.4 , pp. 279-295
    • Farrington, C.P.1    Kanaan, M.N.2    Gay, N.J.3
  • 12
    • 0016484764 scopus 로고
    • The Lagrange distributions and branching processes
    • Good, I.J. The Lagrange distributions and branching processes. SIAM J. Appl. Math. 1975, 28, 270-275.
    • (1975) SIAM J. Appl. Math , vol.28 , pp. 270-275
    • Good, I.J.1
  • 16
    • 0004010598 scopus 로고
    • Die Grundlehren der Mathematischen Wissenschaften, Bd. 119 Springer-Verlag, Berlin, Germany; Prentice-Hall, Inc., Englewood Cliffs, N.J., USA
    • Harris, T.E. The Theory of Branching Processes; Die Grundlehren der Mathematischen Wissenschaften, Bd. 119 Springer-Verlag, Berlin, Germany; Prentice-Hall, Inc., Englewood Cliffs, N.J., USA, 1963.
    • (1963) The Theory of Branching Processes
    • Harris, T.E.1
  • 17
    • 0030535568 scopus 로고    scopus 로고
    • The concept of Ro in epidemic theory
    • Heesterbeek, J.A.P.; Dietz, K. The concept of Ro in epidemic theory. Stat. Neerl. 1996, 50, 89-110.
    • (1996) Stat. Neerl , vol.50 , pp. 89-110
    • Heesterbeek, J.A.P.1    Dietz, K.2
  • 19
    • 0034486891 scopus 로고    scopus 로고
    • The Mathematics of Infectious Diseases
    • Hethcote, H.W. The Mathematics of Infectious Diseases. SIAM Rev. 2000, 42, 599-653.
    • (2000) SIAM Rev , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 20
    • 84990498287 scopus 로고
    • On assessing the potential severity of an outbreak of a rare infectious disease: A Bayesian approach
    • Heyde, C.C. On assessing the potential severity of an outbreak of a rare infectious disease: a Bayesian approach. Austral. J. Statist. 1979, 21, 282-292.
    • (1979) Austral. J. Statist , vol.21 , pp. 282-292
    • Heyde, C.C.1
  • 21
    • 0037368193 scopus 로고    scopus 로고
    • Epidemiological modeling in a branching population. Particular case of a general SIS model with two age classes
    • Jacob, C.; Viet, A.F. Epidemiological modeling in a branching population. Particular case of a general SIS model with two age classes. Math. Biosci. 2003, 182, 93-111.
    • (2003) Math. Biosci , vol.182 , pp. 93-111
    • Jacob, C.1    Viet, A.F.2
  • 22
    • 36849022169 scopus 로고    scopus 로고
    • Influence of the routine slaughtering on the evolution of BSE. Example of the British and French slaughterings
    • Jacob, C.; Magal, P. Influence of the routine slaughtering on the evolution of BSE. Example of the British and French slaughterings. Risk Anal. 2007, 27, 1151-1167.
    • (2007) Risk Anal , vol.27 , pp. 1151-1167
    • Jacob, C.1    Magal, P.2
  • 25
    • 73949089455 scopus 로고    scopus 로고
    • Statistical inference for processes depending on environments and application in regenerative processes
    • Jacob C.; Lalam N.; Yanev N. Statistical inference for processes depending on environments and application in regenerative processes. Pliska Stud. Math. Bulgar. 2005, 17, 109-136.
    • (2005) Pliska Stud. Math. Bulgar , vol.17 , pp. 109-136
    • Jacob, C.1    Lalam, N.2    Yanev, N.3
  • 26
    • 46449104999 scopus 로고    scopus 로고
    • A new class of processes for formalizing and generalizing individual-based models: The semi-semi-Markov processes
    • Jacob, C.; Viet, A.F. A new class of processes for formalizing and generalizing individual-based models: the semi-semi-Markov processes. Pliska Stud. Math. Bulgar. 2007, 121-144.
    • (2007) Pliska Stud. Math. Bulgar , pp. 121-144
    • Jacob, C.1    Viet, A.F.2
  • 27
    • 77950872013 scopus 로고    scopus 로고
    • Saturation Effects in Population Dynamics: Use Branching Processes or Dynamical Systems?
    • In, Deutsch, A., Bravo de la Parra, R., de Boer, R., Dieckmann, O., Jagers, P., Kisdi, E., Kretzschmar, M., Lansky, P., Metz, H., Eds.; Birkhäuser: Boston, MA, USA
    • Jacob C, Saturation Effects in Population Dynamics: Use Branching Processes or Dynamical Systems? In Mathematical Modeling of Biological Systems; Deutsch, A., Bravo de la Parra, R., de Boer, R., Dieckmann, O., Jagers, P., Kisdi, E., Kretzschmar, M., Lansky, P., Metz, H., Eds.; Birkhäuser: Boston, MA, USA, 2008; pp. 339-352.
    • (2008) Mathematical Modeling of Biological Systems , pp. 339-352
    • Jacob, C.1
  • 29
    • 84945631074 scopus 로고
    • A general stochastic model for population development
    • Jagers, P. A general stochastic model for population development. Skan. Aktuarietidskr. 1969, 52, 84-103.
    • (1969) Skan. Aktuarietidskr , vol.52 , pp. 84-103
    • Jagers, P.1
  • 30
    • 0020766915 scopus 로고
    • Population-size-dependent branching process with linear rate of growth
    • Klebaner, F.C. Population-size-dependent branching process with linear rate of growth. J. Appl. Probab. 1983, 20, 242-250.
    • (1983) J. Appl. Probab , vol.20 , pp. 242-250
    • Klebaner, F.C.1
  • 31
    • 0001814148 scopus 로고
    • On population-size-dependent branching processes
    • Klebaner, F.C. On population-size-dependent branching processes. Adv. Appl. Probab. 1984, 16, 30-55.
    • (1984) Adv. Appl. Probab , vol.16 , pp. 30-55
    • Klebaner, F.C.1
  • 32
    • 0002201705 scopus 로고
    • Linear growth in near-critical population-size-dependent multitype Galton-Watson processes
    • Klebaner, F.C. Linear growth in near-critical population-size-dependent multitype Galton-Watson processes. J. Appl. Probab. 1989, 26, 431-445.
    • (1989) J. Appl. Probab , vol.26 , pp. 431-445
    • Klebaner, F.C.1
  • 33
    • 0002262005 scopus 로고
    • Correction: Linear growth in near-critical population-size-dependent multitype Galton-Watson processes [J. Appl. Probab. 26 (1989), no. 3, 431-445] and Asymptotic behavior of near-critical multitype branching processes [J. Appl. Probab. 28 (1991), no. 3, 512-519]
    • Klebaner, F.C. Correction: Linear growth in near-critical population-size-dependent multitype Galton-Watson processes [J. Appl. Probab. 26 (1989), no. 3, 431-445] and Asymptotic behavior of near-critical multitype branching processes [J. Appl. Probab. 28 (1991), no. 3, 512-519]. J. Appl. Probab. 1992,29,246.
    • (1992) J. Appl. Probab , vol.29 , pp. 246
    • Klebaner, F.C.1
  • 34
    • 38249002245 scopus 로고
    • Population-dependent branching processes with a threshold
    • Klebaner, F.C. Population-dependent branching processes with a threshold. Stochastic Process. Appl. 1993, 46, 115-127.
    • (1993) Stochastic Process. Appl , vol.46 , pp. 115-127
    • Klebaner, F.C.1
  • 35
    • 38149147759 scopus 로고
    • Autoregressive approximation in branching processes with a threshold
    • Klebaner, F.C.; Nerman, O. Autoregressive approximation in branching processes with a threshold. Stochastic Process. Appl. 1994, 51, 1-7.
    • (1994) Stochastic Process. Appl , vol.51 , pp. 1-7
    • Klebaner, F.C.1    Nerman, O.2
  • 36
    • 0001277523 scopus 로고
    • The exit problem for a class of density-dependent branching systems
    • Klebaner, F.C.; Zeitouni, O. The exit problem for a class of density-dependent branching systems. Ann. Appl. Probab. 1994, 4, 1188-1205.
    • (1994) Ann. Appl. Probab , vol.4 , pp. 1188-1205
    • Klebaner, F.C.1    Zeitouni, O.2
  • 37
    • 0042606598 scopus 로고    scopus 로고
    • Population and density dependent branching processes
    • IMA Vol. Math. Appl., 84, Springer: New York, NY, USA
    • Klebaner, F.C. Population and density dependent branching processes. In Classical and Modern Branching Processes; IMA Vol. Math. Appl., 84, Springer: New York, NY, USA, 1997; pp. 165-169.
    • (1997) Classical and Modern Branching Processes , pp. 165-169
    • Klebaner, F.C.1
  • 38
    • 0032398248 scopus 로고    scopus 로고
    • On the quasi-stationary distribution for some randomly perturbed transformations of an interval
    • Klebaner, F.C.; Lazar, J.; Zeitouni, O. On the quasi-stationary distribution for some randomly perturbed transformations of an interval. Ann. Appl. Probab. 1998, 8, 300-315.
    • (1998) Ann. Appl. Probab , vol.8 , pp. 300-315
    • Klebaner, F.C.1    Lazar, J.2    Zeitouni, O.3
  • 39
    • 77950873947 scopus 로고    scopus 로고
    • Regenerative Branching Processes
    • Ahsanullah, M., Yanev, G.P., Eds.; Nova Science Publishers, Inc.: New York, NY, USA, Chapter 3
    • Yanev, N.M.; Mitov, K.V. Regenerative Branching Processes. In Records and Branching processes; Ahsanullah, M., Yanev, G.P., Eds.; Nova Science Publishers, Inc.: New York, NY, USA, 2008, Chapter 3; pp. 37-62.
    • (2008) Records and Branching Processes , pp. 37-62
    • Yanev, N.M.1    Mitov, K.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.