메뉴 건너뛰기




Volumn 46, Issue 2, 2004, Pages 202-229

In the garden of branching processes

Author keywords

Birth death process; Branching process; Haplotype; HIV; Immigration; Kronecker product; Matrix exponential; Mutation; Poisson process; Progeny generating function; Vaccination; X linked

Indexed keywords

BIRTH-DEATH PROCESS; BRANCHING PROCESS; HAPLOTYPE; IMMIGRATION; KRONECKER PRODUCT; MATRIX EXPONENTIAL; MUTATIONS; POISSON PROCESS; PROGENY GENERATING FUNCTION; X-LINKED;

EID: 3142663437     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144502417843     Document Type: Review
Times cited : (49)

References (42)
  • 4
    • 0001205620 scopus 로고
    • On a certain model of an epidemic
    • R. BARTOSZYNSKI, On a certain model of an epidemic, Zastos. Mat., 13 (1972), pp. 139-151.
    • (1972) Zastos. Mat. , vol.13 , pp. 139-151
    • Bartoszynski, R.1
  • 6
    • 0000224842 scopus 로고    scopus 로고
    • Reproduction numbers and critical immunity levels for epidemics in a community of households
    • C. C. Heyde, Y. V. Prohorov, R. Pyke, and S. T. Rachev, eds., Springer-Verlag, New York
    • N. G. BECKER AND K. DIETZ, Reproduction numbers and critical immunity levels for epidemics in a community of households, in Athens Conference on Applied Probability and Time Series Analysis, Volume I: Applied Probability, C. C. Heyde, Y. V. Prohorov, R. Pyke, and S. T. Rachev, eds., Springer-Verlag, New York, 1996, pp. 267-276.
    • (1996) Athens Conference on Applied Probability and Time Series Analysis, Volume I: Applied Probability , vol.1 , pp. 267-276
    • Becker, N.G.1    Dietz, K.2
  • 7
    • 0020576962 scopus 로고
    • Assessing the heterogeneity of disease spread through a community
    • N. G. BECKER AND J. L. HOPPER, Assessing the heterogeneity of disease spread through a community, Amer. J. Epidemiol., 117 (1983), pp. 362-374.
    • (1983) Amer. J. Epidemiol. , vol.117 , pp. 362-374
    • Becker, N.G.1    Hopper, J.L.2
  • 8
    • 0032100266 scopus 로고    scopus 로고
    • Models for haplotype evolution in a nonstationary population
    • R. FAN AND K. LANGE, Models for haplotype evolution in a nonstationary population, Theor. Popul. Biol., 53 (1998), pp. 184-198.
    • (1998) Theor. Popul. Biol. , vol.53 , pp. 184-198
    • Fan, R.1    Lange, K.2
  • 10
    • 49949126877 scopus 로고
    • A general age-dependent branching process
    • K. S. CRUMP AND C. J. MODE, A general age-dependent branching process, J. Math. Anal. Appl., 24 (1968), pp. 494-508.
    • (1968) J. Math. Anal. Appl. , vol.24 , pp. 494-508
    • Crump, K.S.1    Mode, C.J.2
  • 12
    • 0018029894 scopus 로고
    • Equilibrium distributions for deleterious genes in large stationary populations
    • K. GLADSTIEN AND K. LANGE, Equilibrium distributions for deleterious genes in large stationary populations, Theor. Popul. Biol., 14 (1978), pp. 322-328.
    • (1978) Theor. Popul. Biol. , vol.14 , pp. 322-328
    • Gladstien, K.1    Lange, K.2
  • 13
    • 0018029473 scopus 로고
    • Number of people and number of generations affected by a single deleterious mutation
    • K. GLADSTIEN AND K. LANGE, Number of people and number of generations affected by a single deleterious mutation, Theor. Popul. Biol., 14 (1978), pp. 313-321.
    • (1978) Theor. Popul. Biol. , vol.14 , pp. 313-321
    • Gladstien, K.1    Lange, K.2
  • 15
    • 0026949420 scopus 로고
    • Linkage disequilibrium mapping in isolated founder populations: Diastrophic dysplasia in Finland
    • J. HÄSTBACKA, A. DE LA CHAPELLE, I. KAITILA, P. SISTONEN, A. WEAVER, AND E. LANDER, Linkage disequilibrium mapping in isolated founder populations: Diastrophic dysplasia in Finland, Nat. Genet., 2 (1992), pp. 204-211.
    • (1992) Nat. Genet. , vol.2 , pp. 204-211
    • Hästbacka, J.1    De La Chapelle, A.2    Kaitila, I.3    Sistonen, P.4    Weaver, A.5    Lander, E.6
  • 16
    • 0001351728 scopus 로고
    • Fast fourier methods in computational complex analysis
    • P. HENRICI, Fast Fourier methods in computational complex analysis, SIAM Rev., 21 (1979), pp. 481-527.
    • (1979) SIAM Rev. , vol.21 , pp. 481-527
    • Henrici, P.1
  • 19
    • 0000145168 scopus 로고
    • The reproduction number in deterministic models of contagious diseases
    • J. A. JACQUEZ, C. P. SIMON, AND J. S. KOOPMAN, The reproduction number in deterministic models of contagious diseases, Comments Theor. Biol., 2 (1991), pp. 159-209.
    • (1991) Comments Theor. Biol. , vol.2 , pp. 159-209
    • Jacquez, J.A.1    Simon, C.P.2    Koopman, J.S.3
  • 24
    • 0020336319 scopus 로고
    • Calculation of the equilibrium distribution for a deleterious gene by the finite fourier transform
    • K. LANGE, Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform, Biometrics, 38 (1982), pp. 79-86.
    • (1982) Biometrics , vol.38 , pp. 79-86
    • Lange, K.1
  • 25
    • 0342998934 scopus 로고
    • Moment computations for subcritical branching processes
    • K. LANGE, M. BOEHNKE, AND R. CARSON, Moment computations for subcritical branching processes, J. Appl. Probab., 18 (1981), pp. 52-64.
    • (1981) J. Appl. Probab. , vol.18 , pp. 52-64
    • Lange, K.1    Boehnke, M.2    Carson, R.3
  • 26
    • 0342894769 scopus 로고    scopus 로고
    • Branching process models for mutant genes in nonstationary populations
    • K. LANGE AND R. FAN, Branching process models for mutant genes in nonstationary populations, Theor. Popul. Biol., 51 (1997), pp. 118-133.
    • (1997) Theor. Popul. Biol. , vol.51 , pp. 118-133
    • Lange, K.1    Fan, R.2
  • 27
    • 0019052397 scopus 로고
    • Further characterization of the long-run population distribution of a deleterious gene
    • K. LANGE AND K. GLADSTIEN, Further characterization of the long-run population distribution of a deleterious gene, Theor. Popul. Biol., 18 (1980), pp. 31-43.
    • (1980) Theor. Popul. Biol. , vol.18 , pp. 31-43
    • Lange, K.1    Gladstien, K.2
  • 28
    • 0005479341 scopus 로고
    • Branching processes applied to cell surface aggregation phenomena
    • Springer-Verlag, New York
    • C. A. MACKEN AND A. S. PERELSON, Branching Processes Applied to Cell Surface Aggregation Phenomena, Lecture Notes in Biomath. 58, Springer-Verlag, New York, 1985.
    • (1985) Lecture Notes in Biomath. , vol.58
    • Macken, C.A.1    Perelson, A.S.2
  • 30
    • 0033863985 scopus 로고    scopus 로고
    • Retracing the evolutionary pathways of human immunodeficiency virus type 1 resistance to protease inhibitors: Virus fitness in the absence and in the presence of drug
    • F. MAMMANO, V. TROUPLIN, V. ZENNOU, AND F. CLAVEL, Retracing the evolutionary pathways of human immunodeficiency virus type 1 resistance to protease inhibitors: Virus fitness in the absence and in the presence of drug, J. Virol., 74 (2000), pp. 8524-8531.
    • (2000) J. Virol. , vol.74 , pp. 8524-8531
    • Mammano, F.1    Trouplin, V.2    Zennou, V.3    Clavel, F.4
  • 31
    • 0030060447 scopus 로고    scopus 로고
    • Forward mutation rate of human immunodeficiency virus type l in a T lymphoid cell line
    • L. M. MANSKY, Forward mutation rate of human immunodeficiency virus type l in a T lymphoid cell line, AIDS Res. Hum. Retroviruses, 12 (1996), pp. 307-314.
    • (1996) AIDS Res. Hum. Retroviruses , vol.12 , pp. 307-314
    • Mansky, L.M.1
  • 35
    • 0001918317 scopus 로고    scopus 로고
    • Mathematical analysis of HIV-l dynamics in vivo
    • A. S. PERELSON AND P. W. NELSON, Mathematical analysis of HIV-l dynamics in vivo, SIAM Rev., 41 (1999), pp. 3-44.
    • (1999) SIAM Rev. , vol.41 , pp. 3-44
    • Perelson, A.S.1    Nelson, P.W.2
  • 36
    • 0035941395 scopus 로고    scopus 로고
    • Use of a stochastic model to develop understanding of the impact of different patterns of antiretroviral drug use on resistance development
    • A. N. PHILLIPS, N. YOULE, M. JOHNSON, AND C. LOVEDAY, Use of a stochastic model to develop understanding of the impact of different patterns of antiretroviral drug use on resistance development, AIDS, 15 (2001), pp. 2211-2220.
    • (2001) AIDS , vol.15 , pp. 2211-2220
    • Phillips, A.N.1    Youle, N.2    Johnson, M.3    Loveday, C.4
  • 39
    • 0032568196 scopus 로고    scopus 로고
    • The frequency of resistant mutant virus before antiretroviral therapy
    • R. M. RIBEIRO, S. BONHOEFFER, AND M. A. NOWAK, The frequency of resistant mutant virus before antiretroviral therapy, AIDS, 12 (1998), pp. 461-465.
    • (1998) AIDS , vol.12 , pp. 461-465
    • Ribeiro, R.M.1    Bonhoeffer, S.2    Nowak, M.A.3
  • 40
    • 0034608864 scopus 로고    scopus 로고
    • Production of resistant HIV mutants during antiretroviral therapy
    • R. M. RIBEIRO AND S. BONHOEFFER, Production of resistant HIV mutants during antiretroviral therapy, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 7681-7686.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 7681-7686
    • Ribeiro, R.M.1    Bonhoeffer, S.2
  • 42
    • 0010246118 scopus 로고
    • Branching process and neutral evolution
    • Springer-Verlag, New York
    • Z. TAÏB, Branching Process and Neutral Evolution, Lecture Notes in Biomath. 93, Springer-Verlag, New York, 1992.
    • (1992) Lecture Notes in Biomath. , vol.93
    • Taïb, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.