메뉴 건너뛰기




Volumn 9, Issue 73, 2012, Pages 1983-1997

A nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model

Author keywords

Gauss Lobatto collocation; Infectious diseases; Mathematical programming; Measles; Nonlinear optimization

Indexed keywords

COMPUTATIONAL EFFICIENCY; CONTINUOUS TIME SYSTEMS; DIFFERENTIAL EQUATIONS; DISEASES; EFFICIENCY; MATHEMATICAL PROGRAMMING; NONLINEAR EQUATIONS; NONLINEAR PROGRAMMING; TRANSMISSIONS;

EID: 84865063522     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2011.0829     Document Type: Article
Times cited : (10)

References (42)
  • 1
    • 0033671548 scopus 로고    scopus 로고
    • Reconstructing susceptible and recruitment dynamics from measles epidemic data
    • doi:10.1080/08898480009525471
    • Bobashev, G. V., Ellner, S. P., Nychka, D. W. & Grenfell, B. T. 2008 Reconstructing susceptible and recruitment dynamics from measles epidemic data. Math. Popul. Stud. 8, 1-29. (doi:10.1080/08898480009525471)
    • (2008) Math. Popul. Stud. , vol.8 , pp. 1-29
    • Bobashev, G.V.1    Ellner, S.P.2    Nychka, D.W.3    Grenfell, B.T.4
  • 2
    • 74049096785 scopus 로고    scopus 로고
    • Plug-and-play inference for disease dynamics: Measles in large and small populations as a case study
    • doi:10.1098/rsif.2009.0151
    • He, D., Ionides, E. L. & King, A. A. 2010 Plug-and-play inference for disease dynamics: measles in large and small populations as a case study. J. R. Soc. Interface 7, 271-283. (doi:10.1098/rsif.2009.0151)
    • (2010) J. R. Soc. Interface , vol.7 , pp. 271-283
    • He, D.1    Ionides, E.L.2    King, A.A.3
  • 3
    • 79958052495 scopus 로고    scopus 로고
    • Parameterizing state-space models for infectious disease dynamics by generalized profiling: Measles in Ontario
    • doi:10.1098/rsif.2010.0412
    • Hooker, G., Ellner, S. P., Roditi, L. D. V. & Earn, D. J. D. 2011 Parameterizing state-space models for infectious disease dynamics by generalized profiling: measles in Ontario. J. R. Soc. Interface 8, 961-974. (doi:10.1098/rsif.2010.0412)
    • (2011) J. R. Soc. Interface , vol.8 , pp. 961-974
    • Hooker, G.1    Ellner, S.P.2    Roditi, L.D.V.3    Earn, D.J.D.4
  • 5
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • doi:10.1137/S0036144500371907
    • Hethcote, H. W. 2000 The mathematics of infectious diseases. SIAM Rev. 42, 599-653. (doi:10.1137/S0036144500371907)
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 6
    • 0002426167 scopus 로고
    • The interpretation of periodicity in disease prevalence
    • doi:10.2307/2341437
    • Soper, H. E. 1929 The interpretation of periodicity in disease prevalence. J. R. Stat. Soc. 92, 34-73. (doi:10.2307/2341437)
    • (1929) J. R. Stat. Soc. , vol.92 , pp. 34-73
    • Soper, H.E.1
  • 7
    • 0020072418 scopus 로고
    • Measles in England and Wales I: An analysis of factors underlying seasonal patterns
    • doi:10.1093/ije/11.1.5
    • Fine, P. E. & Clarkson, J. A. 1982 Measles in England and Wales I: an analysis of factors underlying seasonal patterns. Int. J. Epidemiol. 11, 5-14. (doi:10.1093/ije/11.1.5)
    • (1982) Int. J. Epidemiol. , vol.11 , pp. 5-14
    • Fine, P.E.1    Clarkson, J.A.2
  • 8
    • 0034360414 scopus 로고    scopus 로고
    • Time series modelling of childhood diseases: A dynamical systems approach
    • doi:10.1111/1467-9876.00187
    • Finkenstädt, B. F. & Grenfell, B. T. 2000 Time series modelling of childhood diseases: a dynamical systems approach. J. R. Stat. Soc. C 49, 187-205. (doi:10.1111/1467-9876.00187)
    • (2000) J. R. Stat. Soc. C , vol.49 , pp. 187-205
    • Finkenstädt, B.F.1    Grenfell, B.T.2
  • 9
    • 4143075752 scopus 로고    scopus 로고
    • Measles metapopulation dynamics: A gravity model for epidemiological coupling and dynamics
    • doi:10.1086/422341
    • Xia, Y., Bjornstad, O. N. & Grenfell, B. T. 2004 Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics. Am. Nat. 164, 267-281. (doi:10.1086/422341)
    • (2004) Am. Nat. , vol.164 , pp. 267-281
    • Xia, Y.1    Bjornstad, O.N.2    Grenfell, B.T.3
  • 10
    • 0038485591 scopus 로고    scopus 로고
    • Interpreting time-series analyses for continuous-time biological models-measles as a case study
    • doi:10.1016/S0022-5193(03)00031-6
    • Glass, K., Xia, Y. & Grenfell, B. 2003 Interpreting time-series analyses for continuous-time biological models-measles as a case study. J. Theor. Biol. 223, 19-25. (doi:10.1016/S0022-5193(03)00031-6)
    • (2003) J. Theor. Biol. , vol.223 , pp. 19-25
    • Glass, K.1    Xia, Y.2    Grenfell, B.3
  • 11
    • 45849091048 scopus 로고    scopus 로고
    • Likelihood-based estimation of continuous-time epidemic models from time-series data: Application to measles transmission in London
    • doi:10.1098/rsif.2007.1292
    • Cauchemez, S. & Ferguson, N. M. 2008 Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London. J. R. Soc. Interface 5, 885-897. (doi:10.1098/rsif.2007. 1292)
    • (2008) J. R. Soc. Interface , vol.5 , pp. 885-897
    • Cauchemez, S.1    Ferguson, N.M.2
  • 13
    • 27144554272 scopus 로고    scopus 로고
    • SIRS epidemic model and simulations using different types of seasonal contact rate
    • doi:10.1080/023929021000008813
    • Greenhalgh, D. & Moneim, I. A. 2003 SIRS epidemic model and simulations using different types of seasonal contact rate. Syst. Anal. Modell. Sim. 43, 573-600. (doi:10.1080/023929021000008813)
    • (2003) Syst. Anal. Modell. Sim. , vol.43 , pp. 573-600
    • Greenhalgh, D.1    Moneim, I.A.2
  • 14
    • 77957185501 scopus 로고
    • An age-structured model of pre and post-vaccination measles transmission
    • doi:10.1093/imammb/1.2.169
    • Schenzle, D. 1984 An age-structured model of pre and post-vaccination measles transmission. Math. Med. Biol. 1, 169-191. (doi:10.1093/imammb/1.2.169)
    • (1984) Math. Med. Biol. , vol.1 , pp. 169-191
    • Schenzle, D.1
  • 15
    • 85014607009 scopus 로고    scopus 로고
    • A sensitivity matrix based methodology for inverse problem formulation
    • doi:10.1515/JIIP.2009.034
    • Cintrón-Arias, A., Banks, H., Capaldi, A. & Lloyd, A. L. 2009 A sensitivity matrix based methodology for inverse problem formulation. J. Inverse Ill-posed Problems 15, 545-564. (doi:10.1515/JIIP.2009.034)
    • (2009) J. Inverse Ill-posed Problems , vol.15 , pp. 545-564
    • Cintrón-Arias, A.1    Banks, H.2    Capaldi, A.3    Lloyd, A.L.4
  • 16
    • 0031447158 scopus 로고    scopus 로고
    • Modelling the persistence of measles
    • doi:10.1016/S0966-842X(97)01147-5
    • Keeling, M. J. 1997 Modelling the persistence of measles. Trends Microbiol. 5, 513-518. (doi:10.1016/S0966-842X(97)01147-5)
    • (1997) Trends Microbiol. , vol.5 , pp. 513-518
    • Keeling, M.J.1
  • 17
    • 0003188315 scopus 로고
    • Measles periodicity and community size
    • doi:10.2307/2342553
    • Bartlett, M. S. 1957 Measles periodicity and community size. J. R. Stat. Soc. A (General ) 120, 48-70. (doi:10.2307/2342553)
    • (1957) J. R. Stat. Soc. A (General ) , vol.120 , pp. 48-70
    • Bartlett, M.S.1
  • 18
    • 0003220545 scopus 로고    scopus 로고
    • A stochastic model for extinction and recurrence of epidemics: Estimation and inference for measles outbreaks
    • doi:10.1093/biostatistics/3.4.493
    • Finkenstädt, B. F., Bjornstad, O. N. & Grenfell, B. T. 2002 A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks. Biostatistics 3, 493-510. (doi:10.1093/ biostatistics/3.4.493)
    • (2002) Biostatistics , vol.3 , pp. 493-510
    • Finkenstädt, B.F.1    Bjornstad, O.N.2    Grenfell, B.T.3
  • 19
    • 35648981518 scopus 로고    scopus 로고
    • Parameter estimation for differential equations: A generalized smoothing approach
    • doi:10.1111/j.1467-9868.2007.00610.x
    • Ramsay, J. O., Hooker, G., Campbell, D. & Cao, J. 2007 Parameter estimation for differential equations: a generalized smoothing approach. J. R. Stat. Soc. B (Stat. Methodol.) 69, 741-796. (doi:10.1111/j.1467-9868.2007.00610. x)
    • (2007) J. R. Stat. Soc. B (Stat. Methodol.) , vol.69 , pp. 741-796
    • Ramsay, J.O.1    Hooker, G.2    Campbell, D.3    Cao, J.4
  • 21
    • 0036590892 scopus 로고    scopus 로고
    • Dynamics of measles epidemics: Estimating scaling of transmission rates using a time series SIR model
    • doi:10.1890/0012-9615(2002)072[0169:DOMEES]2.0.CO;2
    • Bjornstad, O. N., Finkenstädt, B. & Grenfell, B. T. 2002 Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model. Ecol. Monogr. 72, 169-184. (doi:10.1890/0012-9615(2002) 072[0169:DOMEES]2.0.CO;2)
    • (2002) Ecol. Monogr. , vol.72 , pp. 169-184
    • Bjornstad, O.N.1    Finkenstädt, B.2    Grenfell, B.T.3
  • 22
    • 79953138480 scopus 로고    scopus 로고
    • Practical methods for optimal control using nonlinear programming
    • doi:10.1115/1.1483351
    • Betts, J. T. & Kolmanovsky, I. 2002 Practical methods for optimal control using nonlinear programming. Appl. Mech. Rev. 55, B68. (doi:10.1115/1.1483351)
    • (2002) Appl. Mech. Rev. , vol.55
    • Betts, J.T.1    Kolmanovsky, I.2
  • 24
    • 37849187939 scopus 로고    scopus 로고
    • Large-scale parameter estimation in low-density polyethylene tubular reactors
    • doi:10.1021/ie060338n
    • Zavala, V. M. & Biegler, L. T. 2006 Large-scale parameter estimation in low-density polyethylene tubular reactors. Ind. Eng. Chem. Res. 45, 7867-7881. (doi:10.1021/ie060338n)
    • (2006) Ind. Eng. Chem. Res. , vol.45 , pp. 7867-7881
    • Zavala, V.M.1    Biegler, L.T.2
  • 25
    • 52149112337 scopus 로고    scopus 로고
    • Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems
    • doi:10.1016/j.ces.2007.05.022
    • Zavala, V. M., Laird, C. D. & Biegler, L. T. 2008 Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems. Chem. Eng. Sci. 63, 4834-4845. (doi:10.1016/j.ces.2007.05.022)
    • (2008) Chem. Eng. Sci. , vol.63 , pp. 4834-4845
    • Zavala, V.M.1    Laird, C.D.2    Biegler, L.T.3
  • 29
    • 0030151161 scopus 로고    scopus 로고
    • Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules
    • doi:10.2514/3.21662
    • Herman, A. L. & Conway, B. A. 1996 Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules. J. Guid. Control Dynam. 19, 592-599. (doi:10.2514/3.21662)
    • (1996) J. Guid. Control Dynam. , vol.19 , pp. 592-599
    • Herman, A.L.1    Conway, B.A.2
  • 30
    • 52949087564 scopus 로고    scopus 로고
    • Selecting optimal weighting factors in iPDA for parameter estimation in continuous-time dynamic models
    • doi:10.1016/j.compchemeng.2008.04.005
    • Varziri, M. S., Poyton, A. A., McAuley, K. B., McLellan, P. J. & Ramsay, J. O. 2008 Selecting optimal weighting factors in iPDA for parameter estimation in continuous-time dynamic models. Comput. Chem. Eng. 32, 3011-3022. (doi:10.1016/j.compchemeng.2008.04.005)
    • (2008) Comput. Chem. Eng. , vol.32 , pp. 3011-3022
    • Varziri, M.S.1    Poyton, A.A.2    McAuley, K.B.3    McLellan, P.J.4    Ramsay, J.O.5
  • 33
    • 29144523061 scopus 로고    scopus 로고
    • On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
    • doi:10.1007/s10107-004-0559-y
    • Wächter, A. & Biegler, L. T. 2006 On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programm. 106, 25-57. (doi:10.1007/s10107-004-0559-y)
    • (2006) Math. Programm. , vol.106 , pp. 25-57
    • Wächter, A.1    Biegler, L.T.2
  • 34
    • 77954541393 scopus 로고    scopus 로고
    • Optimal design of cryogenic air separation columns under uncertainty
    • Zhu, Y., Legg, S. & Laird, C. D. 2010 Optimal design of cryogenic air separation columns under uncertainty. Comput. Chem. Eng. 34, 1377-1384.
    • (2010) Comput. Chem. Eng. , vol.34 , pp. 1377-1384
    • Zhu, Y.1    Legg, S.2    Laird, C.D.3
  • 35
    • 79961008480 scopus 로고    scopus 로고
    • A multiperiod nonlinear programming approach for operation of air separation plants with variable power pricing
    • doi:10.1002/aic.12464
    • Zhu, Y., Legg, S. & Laird, C. D. 2010 A multiperiod nonlinear programming approach for operation of air separation plants with variable power pricing. AIChE J. 57, 2421-2430. (doi:10.1002/aic.12464)
    • (2010) AIChE J. , vol.57 , pp. 2421-2430
    • Zhu, Y.1    Legg, S.2    Laird, C.D.3
  • 36
    • 78651103847 scopus 로고    scopus 로고
    • Optimal operation of cryogenic air separation systems with demand uncertainty and contractual obligations
    • doi:10.1016/j.ces.2010.11.039
    • Zhu, Y., Legg, S. & Laird, C. D. 2011 Optimal operation of cryogenic air separation systems with demand uncertainty and contractual obligations. Chem. Eng. Sci. 66, 953-963. (doi:10.1016/j.ces.2010.11.039)
    • (2011) Chem. Eng. Sci. , vol.66 , pp. 953-963
    • Zhu, Y.1    Legg, S.2    Laird, C.D.3
  • 37
    • 0015711463 scopus 로고
    • Recurrent outbreaks of measles, chicken pox, and mumps
    • Yorke, J. A. & London, W. P. 1973 Recurrent outbreaks of measles, chicken pox, and mumps. Am. J. Epidemiol. 98, 469-482.
    • (1973) Am. J. Epidemiol. , vol.98 , pp. 469-482
    • Yorke, J.A.1    London, W.P.2
  • 40
    • 0038504773 scopus 로고    scopus 로고
    • Design for model parameter uncertainty using nonlinear confidence regions
    • doi:10.1002/aic.690470811
    • Rooney, W. C. & Biegler, L. T. 2004 Design for model parameter uncertainty using nonlinear confidence regions. AIChE J. 47, 1794-1804. (doi:10.1002/aic.690470811)
    • (2004) AIChE J. , vol.47 , pp. 1794-1804
    • Rooney, W.C.1    Biegler, L.T.2
  • 41
    • 84865085270 scopus 로고
    • The City of New York Department of Health. New York, NY: Bureau of Records and Statistics, USA
    • The City of New York Department of Health. 1964 Vital statistics 1956 to 1963. New York, NY: Bureau of Records and Statistics, USA.
    • (1964) Vital Statistics 1956 to 1963
  • 42
    • 84865082872 scopus 로고
    • Bureau of Epidemiology. Bangkok, Thailand: Department of Disease Control, Ministry of Public Health, Thailand
    • Bureau of Epidemiology. 1983 Annual epidemiological surveillance report: measles. Bangkok, Thailand: Department of Disease Control, Ministry of Public Health, Thailand.
    • (1983) Annual Epidemiological Surveillance Report: Measles


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.