메뉴 건너뛰기




Volumn 2, Issue 4, 2008, Pages 392-414

A stochastic SIR model with contact-tracing: Large population limits and statistical inference

Author keywords

Central limit theorem; Contact tracing; HIV; Large population approximation; Mathematical epidemiology; Maximum likelihood estimation; Measure valued Markov process; Stochastic SIR model

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; COMPUTER SIMULATION; CONTACT EXAMINATION; CUBA; DISEASE PREDISPOSITION; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; POPULATION DYNAMICS; STATISTICAL MODEL; STATISTICS;

EID: 77955097265     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513750801993266     Document Type: Article
Times cited : (43)

References (40)
  • 1
    • 0003362526 scopus 로고
    • Sobolev Spaces
    • New York: Academic Press
    • Adams, R. A., 1975. “ Sobolev Spaces ”. In Pure and Applied Mathematics, Vol. 65, New York:Academic Press.
    • (1975) Pure and Applied Mathematics , vol.65
    • Adams, R.A.1
  • 2
    • 0000044071 scopus 로고
    • Stopping times and tightness
    • Aldous, D., 1978. Stopping times and tightness. Ann. Probab., 6:335–340.
    • (1978) Ann. Probab. , vol.6 , pp. 335-340
    • Aldous, D.1
  • 5
    • 0031089630 scopus 로고    scopus 로고
    • Uses of the EM algorithm in the analysis of data on HIV/AIDS and other infectious diseases
    • Becker, N. G., 1997. Uses of the EM algorithm in the analysis of data on HIV/AIDS and other infectious diseases. Statist. Meth. Med. Res., 6:164–171.
    • (1997) Statist. Meth. Med. Res. , vol.6 , pp. 164-171
    • Becker, N.G.1
  • 6
    • 33646690994 scopus 로고    scopus 로고
    • Exact and computationally efficient likelihood-based inference for discretely observed diffusion processes
    • Series B (Statistical Methodology)
    • Beskos, A., 2006. Exact and computationally efficient likelihood-based inference for discretely observed diffusion processes. J. Roy. Statist. Soc., 68:333–382. Series B (Statistical Methodology)
    • (2006) J. Roy. Statist. Soc. , vol.68 , pp. 333-382
    • Beskos, A.1
  • 11
    • 0036765837 scopus 로고    scopus 로고
    • A nonlinear model for sexually transmitted disease with contact-tracing
    • de Arazoza, H., and Lounes, R., 2002. A nonlinear model for sexually transmitted disease with contact-tracing. J. Math. Appl. Med. Biol., 19:221–234.
    • (2002) J. Math. Appl. Med. Biol. , vol.19 , pp. 221-234
    • de Arazoza, H.1    Lounes, R.2
  • 12
    • 85025308472 scopus 로고
    • Markov Processus, Characterization and Convergence
    • New York
    • Ethier, S. N., and Kurtz, T. G., 1986. “ Markov Processus, Characterization and Convergence ”. In John Wiley & Sons New York
    • (1986) John Wiley & Sons
    • Ethier, S.N.1    Kurtz, T.G.2
  • 13
    • 26844479973 scopus 로고    scopus 로고
    • A microscopic probabilistic description of a locally regulated population and macroscopic approximations
    • Fournier, N., and Méléard, S., 2004. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab., 14 (4):1880–1919.
    • (2004) Ann. Appl. Probab. , vol.14 , Issue.4 , pp. 1880-1919
    • Fournier, N.1    Méléard, S.2
  • 14
    • 0036303842 scopus 로고    scopus 로고
    • Estimating the number of Cubans infected sexually by human immunodeficiency virus using contact tracing data
    • Hsieh, Y. H., 2002. Estimating the number of Cubans infected sexually by human immunodeficiency virus using contact tracing data. Int. J. Epidemiol., 31 (no3):679–83.
    • (2002) Int. J. Epidemiol. , vol.31 , pp. 679-683
    • Hsieh, Y.H.1
  • 15
    • 18744370716 scopus 로고    scopus 로고
    • Modeling the impact of random screening and contact tracing in reducing the spread of HIV
    • Hyman, J. M., Li, J., and Stanley, E. A., 2003. Modeling the impact of random screening and contact tracing in reducing the spread of HIV. Math. Biosc.,:17–54.
    • (2003) Math. Biosc. , pp. 17-54
    • Hyman, J.M.1    Li, J.2    Stanley, E.A.3
  • 17
    • 33845508786 scopus 로고    scopus 로고
    • Inference for nonlinear dynamical systems
    • USA
    • Ionides, E. L., Bretó, C., and King, A. A., 2006. “ Inference for nonlinear dynamical systems ”. In Proc. Nat. Acad. Sci Vol. 103, 18438–18443. USA
    • (2006) Proc. Nat. Acad. Sci , vol.103 , pp. 18438-18443
    • Ionides, E.L.1    Bretó, C.2    King, A.A.3
  • 18
    • 0002305276 scopus 로고
    • Stochastic models for epidemics with special reference to AIDS
    • Isham. 1993. Stochastic models for epidemics with special reference to AIDS. Ann. Appl. Probab., 3 (1):1–27.
    • (1993) Ann. Appl. Probab. , vol.3 , Issue.1 , pp. 1-27
    • Isham1
  • 20
    • 0002639718 scopus 로고
    • Weak Convergence of Sequences of Semimartingales with Applications to Multitype Branching Processes
    • Joffe, A., and Métivier, M., 1986. Weak Convergence of Sequences of Semimartingales with Applications to Multitype Branching Processes. Adv. Appl. Probab., 18:20–65.
    • (1986) Adv. Appl. Probab. , vol.18 , pp. 20-65
    • Joffe, A.1    Métivier, M.2
  • 21
    • 0025985176 scopus 로고
    • Contributions to the Mathematical Theory of Epidemics
    • Kermack, W. O., and McKendrick, A. G., 1991. Contributions to the Mathematical Theory of Epidemics. Bull. Math. Biol., 53 (1–2):33–55.
    • (1991) Bull. Math. Biol. , vol.53 , Issue.1-2 , pp. 33-55
    • Kermack, W.O.1    McKendrick, A.G.2
  • 23
    • 52649164300 scopus 로고    scopus 로고
    • American mathematical society ed., Translations of Mathematical Monographs, 196, Providence, Translated from the 1993 Russian original by Victor Kotov
    • Linkov, Y. N., 2001. Asymptotic Statistical Methods for Stochastic Processes. American mathematical society ed., Translations of Mathematical Monographs, 196, Providence, Translated from the 1993 Russian original by Victor Kotov
    • (2001) Asymptotic Statistical Methods for Stochastic Processes
    • Linkov, Y.N.1
  • 24
    • 0009954021 scopus 로고    scopus 로고
    • Convergence of the fluctuations for interacting diffusions with jumps associated with Boltzmann equations
    • Méléard, S., 1998. Convergence of the fluctuations for interacting diffusions with jumps associated with Boltzmann equations. Stoch. Stoch. Rep., 63:195–225.
    • (1998) Stoch. Stoch. Rep. , vol.63 , pp. 195-225
    • Méléard, S.1
  • 25
    • 26844563668 scopus 로고
    • Sur les convergences étroite ou vague de processus à valeurs mesures
    • Méléard, S., and Roelly, S., 1993. Sur les convergences étroite ou vague de processus à valeurs mesures. C.R. Acad. Sci. Paris, Serie I, 317:785–788.
    • (1993) C.R. Acad. Sci. Paris, Serie I , vol.317 , pp. 785-788
    • Méléard, S.1    Roelly, S.2
  • 27
    • 0001340188 scopus 로고
    • Stability of markovian processes III: Foster-Lyapunov criteria for continuous-time processes
    • Meyn, S. P., and Tweedie, R. L., 1993. Stability of markovian processes III:Foster-Lyapunov criteria for continuous-time processes. Adv. Appl. Probab., 25 (3):518–548.
    • (1993) Adv. Appl. Probab. , vol.25 , Issue.3 , pp. 518-548
    • Meyn, S.P.1    Tweedie, R.L.2
  • 28
    • 0037764863 scopus 로고    scopus 로고
    • Contact tracing in stochastic and deterministic epidemic models
    • Müller, J., Kretzschmar, M., and Dietz, K., 2000. Contact tracing in stochastic and deterministic epidemic models. Math. Biosc.,:39–64.
    • (2000) Math. Biosc. , pp. 39-64
    • Müller, J.1    Kretzschmar, M.2    Dietz, K.3
  • 31
    • 33750548006 scopus 로고    scopus 로고
    • Mathematical epidemiology of HIV/AIDS in Cuba during the period 1986–2000
    • Rapatski, B., 2006. Mathematical epidemiology of HIV/AIDS in Cuba during the period 1986–2000. Math. Bios. Engin., 3 (3):545–556.
    • (2006) Math. Bios. Engin. , vol.3 , Issue.3 , pp. 545-556
    • Rapatski, B.1
  • 32
    • 10244252366 scopus 로고    scopus 로고
    • On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm
    • Roberts, G., and Stramer, O., 2001. On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm. Biometrika, 88:603–621.
    • (2001) Biometrika , vol.88 , pp. 603-621
    • Roberts, G.1    Stramer, O.2
  • 33
    • 0002770407 scopus 로고
    • A criterion of convergence of measure-valued processes: Application to measure branching processes
    • Roelly, S., 1986. A criterion of convergence of measure-valued processes:Application to measure branching processes. Stochastics, 17:43–65.
    • (1986) Stochastics , vol.17 , pp. 43-65
    • Roelly, S.1
  • 35
    • 69849104486 scopus 로고    scopus 로고
    • Tran V.C. Large population limit time behaviour of a stochastic particle model describing an age-structured population ESAIM: P&S (2008) to appear DOI:10.1051/ps:2007052
    • Tran V.C. Large population limit time behaviour of a stochastic particle model describing an age-structured population ESAIM:P&S (2008) to appear DOI:10.1051/ps:2007052.
  • 38
    • 0000381122 scopus 로고
    • Quasi-stationary Distributions and Convergence to Quasi-stationarity of Birth-death Processes
    • van Doorn, E., 1991. Quasi-stationary Distributions and Convergence to Quasi-stationarity of Birth-death Processes. Adv. Appl. Probab., 23:683–700.
    • (1991) Adv. Appl. Probab. , vol.23 , pp. 683-700
    • van Doorn, E.1
  • 40
    • 85025352215 scopus 로고    scopus 로고
    • World Health Organization, Web site and related documents,
    • World Health Organization, Web site and related documents, http://www.who.int/countries/cub/en/, http://dataunaids.org/pub/EpiReport/2006/20061121_EPI_FS_C_en.pdf.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.