請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4803
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳秀熙 | |
dc.contributor.author | Chao-Chih Lai | en |
dc.contributor.author | 賴昭智 | zh_TW |
dc.date.accessioned | 2021-05-14T17:47:35Z | - |
dc.date.available | 2016-03-12 | |
dc.date.available | 2021-05-14T17:47:35Z | - |
dc.date.copyright | 2015-03-12 | |
dc.date.issued | 2015 | |
dc.date.submitted | 2015-02-12 | |
dc.identifier.citation | 1. Bacaër, N., Daniel Bernoulli, d’Alembert and the inoculation of smallpox (1760), in A Short History of Mathematical Population Dynamics. 2011, Springer. p. 21-30.
2. Anderson, R. and R. May, Infectious disease of humans: dynamics and control. 1991: Oxford University Press. 3. Lai, C.-C. and H.-H. Chen, Dynamic Infection model Associated with Herd Immunity - Illustrations of Poliomyelitis and Hand-Foot-Mouth Disease in Graduate Institute of Preventive Medicine,College of Public Health. 2007, National Taiwan University. 4. Lai, C.-C., et al., A Dynamic Model of Enterovirus Outbreaks: Hand Foot and Mouth Disease in Taiwan. BMC infectious disease, 2014. 5. Bartlett, M.S., Deterministic and stochastic models for recurrent epidemics. Proc. of the Third Berkeley Symp. on Mathematical Stats. and Probability, 1956. 4: p. 81-108. 6. Bailey, N.J.T., On estimating the latent and infectious periods of measles. 1. Families with two susceptibles Biometrika, 1956. 43: p. 15-22. 7. Bartlett, M.S., Measles periodicity and community size. J. R. Statist. Soc., 1957. A120: p. 48-70. 8. Cox, D. and H. Miller, The theory of stochastic processes. 1965: Chapman and Hall/CRC. 9. WH, H., Epidemic disease in England - the evidence of variability and of persistency of type. Lancet, 1906. 1: p. 733-9. 10. K., D., Transmission and control of arbovirus disease. Society for Industrial and Applied Mathematics, 1975: p. 104-21. 11. RM, A. and M. RM., Immunisation and herd immunity. Lancet, 1990. 335(8690): p. 641-5. 12. Farrington, C.P., M.N. Kanaan, and N.J. Gay, Estimation of the basic reproduction number for infectious diseases from age-stratified serological survey data. Journal of the Royal Statistical Society Series C-Applied Statistics, 2001. 50: p. 251-283. 13. RM, A. and M. RM., Age-related changes in the rate of disease transmission: implications for the design of vaccination programmes. J Hyg. , 1985. 94: p. 365-436. 14. Heffernan, J., R. Smith, and L. Wahl, Perspectives on the basic reproductive ratio. J R Soc Interface, 2005. 2(4): p. 281-93. 15. JM, H., S. RJ, and W. LM, Perspectives on the basic reproductive ratio. J R Soc Interface, 2005. 2(4): p. 281-93. 16. G, S., et al., Key transmission parameters of an institutional outbreak during the 1918 influenza pandemic estimated by mathematical modelling. Theor Biol Med Model, 2006. 3(38): p. 1-7. 17. Lai, C.-C., et al., A Dynamic Model of Hand Foot and Mouth Disease Outbreaks: Hand Foot and Mouth Disease in Taiwan. under submitted, 2015. 18. Becker, N.G., Analysis of Infectious Disease Data. 1989: Chapman & Hall/CRC 19. Greenwood, M., On the Statistical Measure of Infectiousness. J Hyg (Lond), 1931. 31(3): p. 336-51. 20. Thomas, J.C. and D.J. Weber, Epidemiologic methods for the study of infectious disease. the first ed. 2001, United States: Oxford University Press. 21. WH, F., Some conceptions on epidemics in general. Am J Epidemiol, 1976. 103: p. 141-51. 22. T, S., B. BP, and A. GL, Quantifying the impact of hepatitis A immunization in the United States, 1995-2001. Vaccine, 2004. 22(31-32): p. 4342-50. 23. Akhtar, S., T. Carpenter, and S. Rathi, A chain-binomial model for intra-household spread of Mycobacterium tuberculosis in a low socio-economic setting in Pakistan. Epidemiology and infection, 2007. 135(01): p. 27-33. 24. Brooks-Pollock, E., et al., Epidemiologic inference from the distribution of tuberculosis cases in households in Lima, Peru. Journal of Infectious Diseases, 2011. 203(11): p. 1582-1589. 25. Ng, J. and E.J. Orav, A generalized chain binomial model with application to HIV infection. Mathematical biosciences, 1990. 101(1): p. 99-119. 26. Hsu, C.-Y., et al., Surveillance of influenza from household to community in Taiwan. Transactions of The Royal Society of Tropical Medicine and Hygiene, 2014. 108(4): p. 213-220. 27. Nishiura, H. and G. Chowell, Household and community transmission of the Asian influenza A (H2N2) and influenza B viruses in 1957 and 1961. 2007. 28. Azman, A.S., et al., Household transmission of influenza A and B in a school-based study of non-pharmaceutical interventions. Epidemics, 2013. 5(4): p. 181-186. 29. 許辰陽, 應用感染鍊二項模式及隨機概念分析流行性感冒家戶資料 - 運用貝式統計, in Application of Chain Binomial Model with Stochastic Concept to Influenza Household Data - A Bayesian Approach. 2009, 臺灣大學. 30. Hsu, C.-Y., Generalized Linear Stochastic Process with Applications to Infectious Diseases, in Graduate Institute of Epidemiology and Preventive Medicine, College of Public Health. 2014, National Taiwan University: Taiwan. 31. Bailey, N.T., The mathematical theory of infectious diseases and its applications. 1975: Charles Griffin & Company Ltd, 5a Crendon Street, High Wycombe, Bucks HP13 6LE. 32. Becker, N.G., Analysis of Infectious Disease Data. 1989, London, New York: Chapman and Hall. 33. Daley, D.J., J. Gani, and J.M. Gani, Epidemic modelling: an introduction. Vol. 15. 2001: Cambridge University Press. 34. O'Neill, P.D., et al., Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000. 49(4): p. 517-542. 35. Hsu, C., et al., Analysis of household data on influenza epidemic with Bayesian hierarchical model. Mathematical biosciences, 2015. 261: p. 13-26. 36. Becker, N., On Parametric Estimation for Mortal Branching Processes. Biometrika, 1974. 61(3): p. 393-399. 37. Becker, N., Estimation for an epidemic model. Biometrics, 1976. 32(4): p. 769-77. 38. Farrington, C.P., M.N. Kanaan, and N.J. Gay, Branching process models for surveillance of infectious diseases controlled by mass vaccination. Biostatistics, 2003. 4(2): p. 279-295. 39. Angelov, A.G. and M. Slavtchova-Bojkova, Bayesian estimation of the offspring mean in branching processes: Application to infectious disease data. Computers and Mathematics with Applications, 2012. 64: p. 229-235. 40. Kretzschmar, M., A renewal equation with a birth-death process as a model for parasitic infections. J Math Biol, 1989. 27(2): p. 191-221. 41. Wood, R.M., J.R. Egan, and I.M. Hall, A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis. J R Soc Interface, 2014. 11(95): p. 20140119. 42. Diekmann, O. and J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. 2000, New York: Wiley. 43. Chiang, C.L., An Introduction to Strochastic Processes and Their Application. 1980: Robert E. Krieger Publishing Company. 44. Blower, S.M., et al., The intrinsic transmission dynamics of tuberculosis epidemics. Nat Med, 1995. 1(8): p. 815-21. 45. Hsu, C.-Y., Generalized linear stochastic process with applications to infectious diseases in Graduate Institute of Epidemiology and Preventive Medicine, College of Public Health. 2014, National Taiwan University: Taiwan. 46. Chen, T.H., et al., Estimation of sojourn time in chronic disease screening without data on interval cases. Biometrics, 2000. 56(1): p. 167-72. 47. Chen, C.D., et al., A case-cohort study for the disease natural history of adenoma-carcinoma and de novo carcinoma and surveillance of colon and rectum after polypectomy: implication for efficacy of colonoscopy. Br J Cancer, 2003. 88(12): p. 1866-73. 48. Hsiu-Hsi Chen, T., et al., Stochastic model for non-standard case-cohort design. Stat Med, 2004. 23(4): p. 633-47. 49. Becker, N., Estimation for discrete time branching processes with application to epidemics. Biometrics, 1977. 33(3): p. 515-22. 50. Farrington, C.P. and A.D. Grant, The distribution of time to extinction in subcritical branching processes: Applications to outbreaks of infectious disease. Journal of Applied Probability, 1999. 36(3): p. 771-779. 51. Diekmann, O. and J. Heesterbeek, Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. 2000, New York: Wiley. 52. Noack, A., On a class of discrete random variables. Annals of Mathematical Statistics, 1950. 21: p. 127-132. 53. Perlman, M.D. Stochastic comparisons among conditional processes derived from a semicritical Galton-Watson branching process. Technical Report No. 594 2012; Available from: http://www.stat.washington.edu/research/reports. 54. Guttorp, P. and M.D. Perlman. Extinction or Explosion in a Galton-Watson Branching Process: Testing or Prediction? Technical Report no. 602 2012; Available from: http://www.stat.washington.edu/research/reports. 55. Haight, F.A. and M.A. Breuer, The Borel-Tanner Distribution. Biometrika, 1960. 47(1/2): p. 143-150. 56. David L. Heymann, M., Control of communicable disease manual. 18th ed. 2004: American Public Health Association. 57. Centers for Disease Control, D.o.H., R.O.C.(Taiwan), TB Control Manual. 2nd ed. 2009: Centers for Disease Control, Department of Health, R.O.C.(Taiwan). 58. van Embden, J.D., et al., Strain identification of Mycobacterium tuberculosis by DNA fingerprinting: recommendations for a standardized methodology. J Clin Microbiol, 1993. 31(2): p. 406-9. 59. Cave, M.D., et al., Stability of DNA fingerprint pattern produced with IS6110 in strains of Mycobacterium tuberculosis. J Clin Microbiol, 1994. 32(1): p. 262-6. 60. Kamerbeek, J., et al., Simultaneous detection and strain differentiation of Mycobacterium tuberculosis for diagnosis and epidemiology. J Clin Microbiol, 1997. 35(4): p. 907-14. 61. Driver, C.R., et al., Which patients' factors predict the rate of growth of Mycobacterium tuberculosis clusters in an urban community? Am J Epidemiol, 2006. 164(1): p. 21-31. 62. Chan-Yeung, M. and R.H. Xu, SARS: epidemiology. Respirology, 2003. 8 Suppl: p. S9-14. 63. Althomsons, S.P., et al., Using routinely reported tuberculosis genotyping and surveillance data to predict tuberculosis outbreaks. PLoS One, 2012. 7(11): p. e48754. 64. de Vries, G., et al., A Mycobacterium tuberculosis cluster demonstrating the use of genotyping in urban tuberculosis control. BMC Infect Dis, 2009. 9: p. 151. 65. Moonan, P.K., et al., What is the outcome of targeted tuberculosis screening based on universal genotyping and location? Am J Respir Crit Care Med, 2006. 174(5): p. 599-604. 66. Kik, S.V., et al., Tuberculosis outbreaks predicted by characteristics of first patients in a DNA fingerprint cluster. Am J Respir Crit Care Med, 2008. 178(1): p. 96-104. 67. Mazurek, G.H., et al., Updated guidelines for using Interferon Gamma Release Assays to detect Mycobacterium tuberculosis infection - United States, 2010. MMWR Recomm Rep, 2010. 59(RR-5): p. 1-25. 68. Lalvani, A., et al., Rapid detection of Mycobacterium tuberculosis infection by enumeration of antigen-specific T cells. Am J Respir Crit Care Med, 2001. 163(4): p. 824-8. 69. Brock, I., et al., Comparison of tuberculin skin test and new specific blood test in tuberculosis contacts. Am J Respir Crit Care Med, 2004. 170(1): p. 65-9. 70. Hsieh, M.-C., A community-based study for latent TB infection in a country with an intermediate TB burden, using QuantiFERON-TB Gold In-Tube and tuberculin skin test, in Graduate Institute of Epidemiology and Preventative Medicine College of Public Health. 2013, National Taiwan University: Taiwan. 71. Wallinga, J. and P. Teunis, Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J Epidemiol, 2004. 160(6): p. 509-16. 72. Choi BC, P.A., A simple approximate mathematical model to predict the number of severe acute respiratory syndrome cases and deaths. J Epidemiol Community Health, 2003. 57(10): p. 831-5. 73. Chowell, G., et al., SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. J Theor Biol, 2003. 224(1): p. 1-8. 74. Yeh, Y.P., et al., Tuberculin reactivity in adults after 50 years of universal bacille Calmette-Guerin vaccination in Taiwan. Trans R Soc Trop Med Hyg, 2005. 99(7): p. 509-16. 75. Chan, P.C., L.M. Huang, and J. Suo, It is time to deal with latent tuberculosis infection in Taiwan. J Formos Med Assoc, 2009. 108(12): p. 901-3. 76. Bowerman, R.J., Community-wide INH treatment of latent TB infection in a BCG-vaccinated population: experience in rural Taiwan. Int J Tuberc Lung Dis, 2007. 11(4): p. 470-2. 77. Marciniuk, D.D., et al., Detection of pulmonary tuberculosis in patients with a normal chest radiograph. Chest, 1999. 115(2): p. 445-52. 78. Harris, T.G., J. Sullivan Meissner, and D. Proops, Delay in diagnosis leading to nosocomial transmission of tuberculosis at a New York City health care facility. Am J Infect Control, 2013. 41(2): p. 155-60. 79. Stead, W.W., Tuberculosis among elderly persons: an outbreak in a nursing home. Ann Intern Med, 1981. 94(5): p. 606-10. 80. Centers for Disease, C., Tuberculosis in a nursing care facility--Washington. MMWR Morb Mortal Wkly Rep, 1983. 32(9): p. 121-2, 128. 81. Ijaz, K., et al., Unrecognized tuberculosis in a nursing home causing death with spread of tuberculosis to the community. J Am Geriatr Soc, 2002. 50(7): p. 1213-8. 82. Malone, J.L., et al., Investigation of healthcare-associated transmission of Mycobacterium tuberculosis among patients with malignancies at three hospitals and at a residential facility. Cancer, 2004. 101(12): p. 2713-21. 83. National Tuberculosis Controllers, A., C. Centers for Disease, and Prevention, Guidelines for the investigation of contacts of persons with infectious tuberculosis. Recommendations from the National Tuberculosis Controllers Association and CDC. MMWR Recomm Rep, 2005. 54(RR-15): p. 1-47. 84. Borgdorff, M.W., et al., The incubation period distribution of tuberculosis estimated with a molecular epidemiological approach. Int J Epidemiol, 2011. 40(4): p. 964-70. 85. MA, S. and B. SM, Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. Am J Epidemiol, 1997. 145(12): p. 1127-37. 86. Thrupp, L., et al., Tuberculosis prevention and control in long-term-care facilities for older adults. Infect Control Hosp Epidemiol, 2004. 25(12): p. 1097-108. 87. The role of BCG vaccine in the prevention and control of tuberculosis in the United States. A joint statement by the Advisory Council for the Elimination of Tuberculosis and the Advisory Committee on Immunization Practices. MMWR Recomm Rep, 1996. 45(RR-4): p. 1-18. 88. Campbell, J.R., et al., A Systematic Review on TST and IGRA Tests Used for Diagnosis of LTBI in Immigrants. Mol Diagn Ther, 2015. 89. Zwerling, A., et al., Interferon-gamma release assays for tuberculosis screening of healthcare workers: a systematic review. Thorax, 2012. 67(1): p. 62-70. 90. Pai, M., et al., T-cell assays for the diagnosis of latent tuberculosis infection: moving the research agenda forward. Lancet Infect Dis, 2007. 7(6): p. 428-38. 91. Dheda, K., et al., T-cell interferon-gamma release assays for the rapid immunodiagnosis of tuberculosis: clinical utility in high-burden vs. low-burden settings. Curr Opin Pulm Med, 2009. 15(3): p. 188-200. 92. Diel, R., R. Loddenkemper, and A. Nienhaus, Evidence-based comparison of commercial interferon-gamma release assays for detecting active TB: a metaanalysis. Chest, 2010. 137(4): p. 952-68. 93. Pai, M. and R. O'Brien, Serial testing for tuberculosis: can we make sense of T cell assay conversions and reversions? PLoS Med, 2007. 4(6): p. e208. 94. Diel, R., et al., Negative and positive predictive value of a whole-blood interferon-gamma release assay for developing active tuberculosis: an update. Am J Respir Crit Care Med, 2011. 183(1): p. 88-95. 95. Haldar, P., et al., Single-step QuantiFERON screening of adult contacts: a prospective cohort study of tuberculosis risk. Thorax, 2013. 68(3): p. 240-6. 96. Raviglione, M.C., D.E. Snider, Jr., and A. Kochi, Global epidemiology of tuberculosis. Morbidity and mortality of a worldwide epidemic. JAMA, 1995. 273(3): p. 220-6. 97. Kang, Y.A., et al., Discrepancy between the tuberculin skin test and the whole-blood interferon gamma assay for the diagnosis of latent tuberculosis infection in an intermediate tuberculosis-burden country. JAMA, 2005. 293(22): p. 2756-61. 98. Bartu, V., M. Havelkova, and E. Kopecka, QuantiFERON-TB Gold in the diagnosis of active tuberculosis. J Int Med Res, 2008. 36(3): p. 434-7. 99. Chee, C.B., et al., Comparison of sensitivities of two commercial gamma interferon release assays for pulmonary tuberculosis. J Clin Microbiol, 2008. 46(6): p. 1935-40. 100. Metcalfe, J.Z., et al., Interferon-gamma release assays for active pulmonary tuberculosis diagnosis in adults in low- and middle-income countries: systematic review and meta-analysis. J Infect Dis, 2011. 204 Suppl 4: p. S1120-9. 101. Sester, M., et al., Interferon-gamma release assays for the diagnosis of active tuberculosis: a systematic review and meta-analysis. Eur Respir J, 2011. 37(1): p. 100-11. 102. Prabhavathi, M., et al., Role of QuantiFERON-TB Gold antigen-specific IL-1beta in diagnosis of active tuberculosis. Med Microbiol Immunol, 2014. 103. Dosanjh, D.P., et al., Improved diagnostic evaluation of suspected tuberculosis. Ann Intern Med, 2008. 148(5): p. 325-36. 104. Bauch, C.T., et al., Dynamically modeling SARS and other newly emerging respiratory illnesses: past, present, and future. Epidemiology, 2005. 16(6): p. 791-801. 105. Choi, B.C. and A.W. Pak, A simple approximate mathematical model to predict the number of severe acute respiratory syndrome cases and deaths. J Epidemiol Community Health, 2003. 57(10): p. 831-5. 106. Chowell, G., et al., Model parameters and outbreak control for SARS. Emerg Infect Dis, 2004. 10(7): p. 1258-63. 107. Breban, R., J. Riou, and A. Fontanet, Interhuman transmissibility of Middle East respiratory syndrome coronavirus: estimation of pandemic risk. Lancet, 2013. 382(9893): p. 694-9. 108. Reichler, M.R., et al., Outbreak of paralytic poliomyelitis in a highly immunized population in Jordan. J Infect Dis, 1997. 175 Suppl 1: p. S62-70. 109. Sanchez, M.A. and S.M. Blower, Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. Am J Epidemiol, 1997. 145(12): p. 1127-37. 110. WJ, E., et al., The pre-vaccination epidemiology of measles, mumps and rubella in Europe: implications for modelling studies. Epidemiol Infect, 2000. 125(3): p. 635-50. 111. P., M., et al., The pre-vaccination regional epidemiological landscape of measles in Italy: contact patterns, effort needed for eradication, and comparison with other regions of Europe. Popul Health Metr., 2005. 3(1): p. 1. 112. Ma, E., et al., Estimation of the basic reproduction number of enterovirus 71 and coxsackievirus A16 in hand, foot, and mouth disease outbreaks. Pediatr Infect Dis J, 2011. 30(8): p. 675-9. 113. G, C., et al., Estimation of the reproductive number of the Spanish flu epidemic in Geneva, Switzerland. Vaccine, 2006. 24: p. 6747-50. 114. Mills, C.E., J.M. Robins, and M. Lipsitch, Transmissibility of 1918 pandemic influenza. Nature, 2004. 432: p. 904–906. 115. E, M., et al., The 1918 influenza A epidemic in the city of Sao Paulo, Brazil. Med Hypotheses, 2007. 68(2): p. 442-5. 116. Hsu, C.Y., et al., Surveillance of influenza from household to community in Taiwan. Trans R Soc Trop Med Hyg, 2014. 108(4): p. 213-20. 117. PD, G., M. A, and E. VC, Encouraging prospects for immunization against primary cytomegalovirus infection. Vaccine, 2001. 19(11-12): p. 1356-62. 118. PG, C., et al., Mathematical models of Haemophilus influenzae type b. Epidemiol Infect., 1998. 120(3): p. 281-95. 119. MN., K. and F. CP., Matrix models for childhood infections: a Bayesian approach with applications to rubella and mumps. Epidemiol Infect., 2005. 133(6): p. 1009-21. 120. E, M., et al., Dengue and the risk of urban yellow fever reintroduction in Sao Paulo State, Brazil. Rev Saude Publica, 2003. 37(4): p. 477-84. 121. G, C., et al., The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. J Theor Biol., 2004. 229(1): p. 119-26. 122. DL, S., et al., Revisiting the Basic Reproductive Number for Malaria and Its Implications for Malaria Control. PLoS Biol, 2007. 5(3): p. e42. 123. G, D., Further studies of the basic factors concerned in the transmission of malaria. Trans R Soc Trop Med Hyg., 1955. 49(4): p. 339-50. 124. G, D. and D. CC, Field studies on some of the basic factors concerned in the transmission of malaria. Trans R Soc Trop Med Hyg., 1953. 47: p. 522–535. 125. TR, B., et al., Human malaria transmission studies in the Anopheles punctulatus complex in Papua New Guinea: sporozoite rates, inoculation rates, and sporozoite densities. Am J Trop Med Hyg, 1988. 39(2): p. 135-44. 126. R, H., et al., Malaria and its possible control on the island of Principe. Malar J, 2003. 2: p. 15. 127. ME, W., et al., Heterogeneities in the transmission of infectious agents: implications for the design of control programs. Proc Natl Acad Sci U S A, 1997. 94(1): p. 338-42. 128. JJ, P., et al., Chlamydia transmission: concurrency, reproduction number, and the epidemic trajectory. Am J Epidemiol, 1999. 150(12): p. 1331-9. 129. RH, G., et al., Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV transmission; Rakai, Uganda. AIDS, 2003. 17(13): p. 1941–1951. 130. N, B., A. X, and Y. J, Modeling the HIV/AIDS epidemic among injecting drug users and sex workers in Kunming, China. Bull Math Biol, 2006. 68(3): p. 525-50. 131. F, F., Nature, nurture and my experience with smallpox eradication. The Medical Journal of Australia, 1999. 171: p. 638-41. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4803 | - |
dc.description.abstract | 研究背景
決定論模型(deterministic model)有助於推導非常重要的傳染病指標,用以評估傳染病的散播,如大規模的流行,地方性的流行等,此指標就是傳染病的閾值-基礎再生數(R0)。然而,決定論模型在面對中小型人口及傳播傳染病滅絕(extinction)機率的估計是有疑問的,此時使用決定論模型是不適當。此外,當基礎再生數小於1,卻仍發生小規模群突發時,使用決定論模型也是不適合的。此時,應用隨機模型便是其替代的方法。 在這些隨機模型中,分支過程(branching process) 是其中被考慮的隨機模型之一。因為它對於傳染病滅絕(extinction)的機率及基礎再生數(R0)進行評估是較容易的。儘管有上述的優點,但因為我們常常得到的資料是在一段期間中,受到感染的人數及受感染的各不同子代間,時常相互重疊,以至於造成使用分支過程估計基礎再生數的困難。因此,連續時間馬可夫過程(continue time Markov process)中的生死過程(birth-death process)會是適合的方法。 研究目的 本論文的研究目標是在發展一系列隨機模型,利用嚴重急性呼吸道症候群及結核病兩個應用實例,估計基礎再生數及傳染病的滅絶機率。具體研究目的為: (1)應用決定性間隔模型,估計嚴重急性呼吸道症候群之基礎再生數。 (2)以分支過程及生死過程,估計嚴重急性呼吸道症候群之基礎再生數及滅絶機率,並進一步擴展分支過程至mortal 分支過程。 (3)應用Becker的SIR模型,估計無法觀察之結核病從感染至發生症狀之潛伏期(incubation)及從感染至可傳染期之潛伏期(latent)。 (4)發展三階段馬可夫模型結合生死過程,並以貝氏蒙地卡羅-馬可夫鏈(MCMC; Markov chain Monte Carlo)方法,了解IGRA(Interferon-γ release assays)於潛伏結核病感染率及結核病轉移率在不同疾病進程上所扮演的角色,且進一步運用生死過程計算潛伏結核病感染數及滅絶機率。 研究材料及方法 模擬資料 本論文以分支過程給定2, 1.5, 1.1, 0.9等不同基礎再生數下,模擬9代的資料且計算滅絶機率。給定出生率、死亡率及不同初始感染個案數以生死過程模擬資料,且計算從初始個案到達最後狀態的平均時間及其變異數。 臨床及社區資料 嚴重急性呼吸道症候群 本研究利用台灣地區2002年11月至2003年7月期間,罹患嚴重急性呼吸道症候群共346位確定個案,以及新加坡2003年3月26日至4月15日共56位在醫院感染嚴重急性呼吸道症候群之個案資料進行研究。 結核菌 長期照護機構結核病群突發流行資料 利用長期照護機構之結核病群突發資料,進行結核菌從受感染至發生症狀之潛伏期(incubation)及受感染至發生可傳染之潛伏期(latent)之估計。 結核病自然病史估計資料 利用彰化縣結核病2009至2011年監視系統共2,420位30歲以上結核病個案資料,與2005至2011年接觸者登記個案系統共22,510位30歲以上結核病接觸個案資料,以及2012至2014年結核病危險因子病例對照配對研究,加上2011至2013年一般族群IGRA調查資料進行分析。 模式發展及統計分析 本論文提出三種隨機過程,首先以分支過程及生死過程估計嚴重急性呼吸道症候群之基礎再生數、滅絶機率與擴散至最終感染數的時間。應用Becker的SIR模型估計無法觀察之結核菌從受感染至發生症狀之潛伏期(incubation)及受感染至發生可傳染之潛伏期(latent),再以貝氏蒙地卡羅-馬可夫鏈方法,導入三階段馬可夫模型並結合生死過程,估計IGRA於潛伏結核病感染率及結核病轉移率在不同疾病進程之影響。 研究結果 1.模擬 分支過程 由假定布瓦松、二項及負二項等不同子代分佈,透過分支過程模擬6代的資料來估計基礎再生數。在不同分佈條件下,基礎再生數分別以無母數及母數方法進行估計,不同方法所估計之基礎再生數結果一致。然而不同方法下其變異數是具異質性。 純出生過程 在λ=0.5的假設下,經1000次的純出生過程(pure birth process)模擬並與精確公式所得之估計結果進行比較。經模擬的曲線與得自精確公式之結果曲線相異。然而當初始數越大,則經模擬的曲線就越接近精確公式所得結果曲線。而當λ大到3時,結果並没有改變太多。 2. 嚴重急性呼吸道症候群流行之基礎再生數估計 利用分支過程,在16-22代及5-7天的感染潛伏期假設下,基礎再生數為0.9971 (0.5090~1.4852),在布瓦松分佈的假設下,滅絶機率為0.9912。在Borel-Tanner分佈且基礎再生數小於1的條件下,基礎再生數介於0.9790 (0.8437 ~ 1.1143)與 1.0134 (0.8535 ~ 1.1733)之間,滅絶機率為0.9709 ~ 0.9989。 由於線性生死過程無法最適配觀測資料,我們採以一般生死過程對觀察到的累積性個案資料進行配適。出生率觀察為0.57 (於流行期小於55天),11.45 (於流行期介於55天至80天),以及1.413(於流行期超過80天)。預期達到最終感染數a的時間(Ta)為:在T32、T300以及T346分別為54.97(10.09)天、80.00 (10.41)天以及112.01 (11.47)天。 3. 結核病自然病史 結核病群突發 結核病受感染至發生可傳染之潛伏期(latent)經估計為223.6天[λ=0.0045 (2.17*10-6) ],而症狀發生前之感染期經估計為55.9天[ β=0.0179 (3.47*10-5)]。因此從受感染至發生症狀之潛伏期(incubation)約為279.6天。而依據潛伏期的估計,感染至少2代至多3代。基礎再生數的範圍介於0.9739 及 0.9796間。 IGRA對結核病發生的危險性 利用病例對照配對研究,在調整TST後,QFT-GIT陽性對結核病發生的危險性為2.47 (95% CI: 1.72-3.54),若廻歸模式考量交互作用, TST陽性者,QFT-GIT陽性對結核病發生的危險性為4.28 (95% CI: 1.16-15.76), TST陰性者,QFT-GIT陽性對結核病發生的危險性為1.15 (95% CI: 0.66-2.00)。 IGRA在潛伏結核病感染率及結核病轉移率不同疾病進程之影響 整體結核病感染率(每人年)及轉移率(每人年自潛伏結核病感染轉移至結核病)經估計分別為0.0168 (95% CI: 0.0157-0.0180)及 0.0113 (95% CI: 0.0098-0.0129)。感染率表現在年輕族群(30-44歲)及男性都較高。那些陽性IGRA檢測值者,相較於陰性IGRA者,有1.6倍 (RR=1.59, 95% CI:1.39-1.84)的危險性,較易成為潛伏結核病感染個案。相對地,年老族群有較高轉移率,但男性轉移率仍較女性為高。陽性IGRA檢測者,相較於陰性IGRA檢測者有約2倍 (RR=2.12, 95% CI:1.57-2.85)的危險性較易轉移至結核病。經年齡及性別的調整後,QFT-GIT陽性者在結核病感染及轉移率之危險比分別為1.71 (95% CI: 1.49-2.00) 及 1.58 (95% CI: 1.15-2.17)。 應用三階段馬可夫模式估計所得到參數於生死過程發現,在不考量共變數因子下,一個初始個案要擴散到10個個案約花61天,而要擴散到30個個案約花87天。年輕族群、男性及QFT-GIT陽性擴散愈迅速。年齡小於45歲且QFT-GIT陽性的男性,若在初始個案為5位的狀況下,擴散到最終為10位個案約需1週的時間。值得注意的是,若增加初始個案,則要達到預期的擴散個案數,所花費時間會越短。而初始個案若超過5位,則結核病滅絕的機率則幾乎不可能。 結論 本論文在結果的發現上可歸納出5個主要結論如下: 1.當評估新加坡及台灣兩個地區嚴重急性呼吸道症候群的基礎再生數時,在新加坡發生的嚴重急性呼吸道症候群3至8代的感染資料,經評估發現基礎再生數介於1至1.5之間,利用分支過程可幾乎確定必定滅絶。而透過分支過程剖析台灣地區嚴重急性呼吸道症候群流行,其基礎再生數為0.99,滅絶機率為0.99。Borel-Tanner分佈之分支過程也有相同的發現。 2.估計結核菌從感染到發生症狀之潛伏期約9個月,其中從感染至可傳染之潛伏期約7個月,在症狀發生前之可傳染期約2個月。結核病群突發時,進行TST篩檢監視,追蹤TST陰性個案後來也發生結核病。所以針對長照機構的TST陰性年老族群,仍需進行監視,以期在結核病群突發時能獲得控制。 3.本論文是在考量人口學特性及TST檢測結果下,針對IGRA對結核病發生之影響所進行的第一個病例對照研究。 4.本論文也是第一個針對評估年齡、性別及IGRA在潛伏結核病感染(LTBI)及結核病轉移不同疾病進程影響之結核病自然病史研究。年輕族群有較高潛伏結核病感染率,而年老族群有較高轉移率,男性在潛伏結核病感染率及轉移率均較女性高。考量年齡及性別因素後,IGRA在潛伏結核病感染率及轉移率上均扮演重要角色。 5.運用生死過程,在不同年齡、性別、IGRA狀態下,可在給定潛伏結核病感染率(出生率)及轉移率(死亡率)下,計算到達潛伏結核病感染數目之預期時間及滅絶機率。 本論文在傳染病相關的方法學發展有三項貢獻綜述如下: 1.提出多項統計模擬方法包含以分支過程模擬基礎再生數,或以生死過程估計滅絶機率及傳染病擴散時間。 2.示範如何應用Becker的SIR模型結合分支過程估計潛伏期及感染潛伏期以監視結核病。 3.以嶄新病例世代設計加上連續時間馬可夫模型,並結合生死過程以了解IGRA在潛伏結核病感染率及結核病轉移率之不同疾病進程上所扮演的角色。更進一步運用生死過程模擬SARS,以計算其滅絶機率及到達最後感染人數之預期時間。兩種方法對於在傳染病之防治政策問題上,能提供相當助益。 | zh_TW |
dc.description.abstract | Background
Deterministic models are conducive to estimate a very important indicator for assessing the spread of infectious disease such as epidemic, endemic, and extinction, namely, the basic reproductive number (R0). However, when small or moderate population size and the question of the probability of the extinction of infectious disease in question are involved the deterministic model is therefore not adequate. Furthermore, it may not be adequate when minor outbreak occurred if the R0 is less than 1. The alternative is the application of stochastic model. Of these stochastic models, the branching process is one of considerations because it can be easily applied to estimating both the extinction probability and R0. In spite of these two advantages, because we often have the total number of infected individuals for a given period of time and generations usually overlap each other in reality that enables the branching processes difficult to estimate R0. The continuous-time Markov process embodied with birth-death process may be more appropriate. Objectives The objectives of my thesis are to develop various types of stochastic models for estimating R0 and the extinct probability of infectious disease by demonstrating the two examples of SARS and pulmonary TB. Specific aims are to (1)apply the deterministic compartmental model to data on SARS poliomyelitis for estimating R0; (2)develop branching process and birth-death process to SARS dataset to estimate both R0 and the extinct probability and also extend the simple branching process to mortal branching process for measles; (3)apply the Becker’s SIR model to the data of TB for estimating latent period and incubation period; (4)develop a novel three-state Markov model embodied with birth-death process to assess the effect of covariates (such as IGRA) on infection rate and conversion rate using Bayesian MCMC method and to further apply birth-death process to estimate extinct probability and the expected time to reach final size. Materials and Methods Generating Data by simulations We simulated a branching process with 9 generations of data for a given offspring distribution under various values of R0=2, 1.5, 1.1 and 0.9 for calculating the extinction probability. We simulated a birth-death process with given birth rate, death rate and different initial infected cases. We calculate the mean and variance of arrival time from the initial state. Empirical Data . SARS The thesis used 346 confirmed cases with SRAS from November 2002 to July 2003 in Taiwan obtained from Taiwan CDC and also 22,520,776 population of Taiwan at the beginning of 2003. This thesis also made use of total 56 infected with SARS in a hospital in Singapore from Mar. 26 to Apr. 15, 2003. Only 3 generation of offspring was noted after outbreak investigation. Mycobacterium tuberculosis The outbreaks of TB in the Long-term Care Facility The data on outbreak of TB in the LTCF provide empirical data for estimating the unobserved incubation period and latent period before onset of symptoms. Data for estimating parameters of TB natural course Various datasets were used including a total of 2,420 TB cases with age ≥ 30 enrolled in our cohort study from 2009 to 2011 (surveillance system for TB from 2009 to 2011 in Changhua County), a total of 22,510 TB contacts with age ≥ 30 enrolled in our cohort study from 2005 to 2011 (B contact registry database from 2005 to 2011 in Changhua County), a matched case-control study for risk factors of TB from 2012 to 2014 in Changhua County, and a IGRA survey for general population from 2011 to 2013 in Changhua County Model Specification and Statistical Analysis Three types of stochastic processes were applied and proposed. We first applied branching process and birth-death process to estimate R0, extinct probability and the expected time to reach final size for SARS epidemics. We then applied the Becker’s SIR model to estimate unobserved incubation period (including latent period) to the outbreak of TB to estimate its R0 and extinct probability. The novel three-state Markov process embodied with birth-death process was develop to assess the effect of IGRA on the transition from susceptible to LTBI and the conversion from LTBI to TB with Bayesian MCMC method. Results Part I Simulation Branching Process The results of estimating R0 on the generating data of a branching process with six generations for a given offspring distribution (such as Poisson, Binomial, and Negative Binomial distributions) are presented. The estimated R0 were consistent with the nonparametric or parametric method with different distributions. However, the variances were heterogeneous by different methods. Pure birth process The simulated results of 1000 simulations for pure birth process assuming λ=0.5 compared with the true results estimated the exact equation for E(Ta). It is very interesting to note that the simulated curve with mean value was still deviant from the curve obtained from the exact formula. However, when n0 became larger, the simulated curve with mean value was close to the true curve obtained from the formula with larger n0 but deviant from the formula with smaller n0. When λ was enlarged to 3, the results were not changed at all. Part II Estimation of R0 for the outbreak of SARS in Taiwan The estimated R0 was 0.9971 (0.5090~1.4852) by using branching process given 16~22 generations assuming the incubation of 5 or 7 days. The estimated extinction probability was 0.9912 under the assumption of Poisson distribution. Using Borel-Tanner distribution under the assumption of R<1, the stimulated R0 was from 0.9790 (0.8437 ~ 1.1143) to 1.0134 (0.8535 ~ 1.1733). The estimated extinction probability was 0.9709 ~ 0.9989. As linear birth-death process did not fit well with data apply instead general birth death process to fit the observed cumulated SARS data. The estimated birth rates were 0.57 (< 55 day of outbreak), 11.45 (the 55th ~ 80th day of outbreak) and 1.413 (after the 80th day of outbreak). The expected time to reach final size a (Ta) were 54.97(10.09), 80.00 (10.41) and 112.01 (11.47) days for T32 , T300 and T346, respectively. Part III Natural Course of TB Outbreak of TB The latent period was estimated about 223.6 days [λ=0.0045 (2.17*10-6) ] and the infectious period before symptoms onset was estimated about 55.9 days [ β=0.0179 (3.47*10-5)]. Hence, the incubation period was about 279.5 days. According to our estimation of latent period, there were at least two generations and at most 3 generations. R0 was bounded between 0.9739 and 0.9796 in this cluster. The extinction probability was almost certain. The effect of IGRA on the occurrence of TB with a case-control study Using a match-case-control study, the estimated odds ratios in multivariable logistic regression mode for positive QFT-GIT after further adjustment for positive TST was 2.47 (95% CI: 1.72-3.54). After further considering the interaction term in the model, the odds ratio of QFT-GIT for subjects with positive TST was estimated as 4.28 (95% CI: 1.16-15.76) whereas the odds ratio of QFT-GIT for subjects with negative TST was estimated as 1.15 (95% CI: 0.66-2.00). The effect of IGRA on the infection rate and conversion rate with multi-state Markov model The overall estimated infection rate (per person-years) and conversion rate (per year) were 0.0168 (95% CI: 0.0157-0.0180) and 0.0113 (95% CI: 0.0098-0.0129). The infection rate was higher for the young age group (30-44 years old) and male sex. Those with positive IGRA were 1.60 (RR=1.59, 95% CI:1.39-1.84) times likely to be susceptible to LTBI compared with negative IGRA. In contrast to the effect of age on infection rate, the older the subject was, the higher the conversion rate. Males still had higher conversion rate than females. Those with positive IGRA were two times (RR=2.12, 95% CI:1.57-2.85) likely to surface to TB compared with negative IGRA. After taking the effect of age and sex on both infection rate and conversion rate into account, subjects with positive QFT-GIT still had higher risk of being infected and converting to tuberculosis with estimated RR being 1.71 (95% CI: 1.49-2.00) and 1.58 (95% CI: 1.15-2.17), respectively. Application of birth-and-death process with the parameters obtained from three-state Markov model found one initial case may take about 61 days to have 10 of final size and 87 days to have 30 of final size without considering covariates. The young people, male and positive IGRA tended to spread quickly. The male aged less than 45 years with positive results of IGRA took only one week to reach final size given five initial cases. It should be noted that an increase in initial size reduced the time to reach the expected final size. When initial size was larger than five the extinct probability of TB was very unlikely. Conclusion There are five major conclusions on the practical findings reached as follows. 1.While evaluating SARS in the two regions, the estimation of R0 given 3~8 generations was between 1 and 1.5, and the estimated extinct probability was almost certain using branching process in Singarepore. The SAS outbreak yielded 0.99 of R0 using branching process in Taiwan. The estimated extinct probability was 0.99. The similar findings were noted by using the mortal branching process with Borel-Tanner distribution. 2.Estimate unobserved incubation period with approximately 9 months, including seven months of latent period and two months of infectious period before onset of symptoms given data from an outbreak of TB occuring even among subjects with negative TST result after undergoing TB screening. Surveillance of the elderly people even with a negative TST after TB screening is still necessary given a long latent period if the outbreak of TB in a long-term care facility is to be controlled. 3.This is the first study to assess the effect of IGRA on the occurrence of TB by conducting a case-control study making allowance for demographic characteristics and induration size of TST. 4.This is the first study to assess the effects of age, gender, and IGRA on infection from susceptible to LTBI and also the conversion from LTBI to TB in the natural course of TB. The young age was at increased risk for being LTBI but the old age enhanced the risk of conversion from LTBI to TB. Male had higher risk for being infected as LTBI and also the conversion from LTBI to TB. The elevated IGRA plays a significant role not in the infection rate (from free of LTBI (susceptible) to LTBI) but also in the conversion rate after adjusting for age and gender. 5.The application of infection rate (birth rate) and conversion rate (death rate) gives the time expected to reach number of LTBI of final size and the extinct probability by various combinations of age, gender, and the results of IGRA. Subjects with positive IGRA results had shorter expected time to reach final size than those with negative result. This thesis has also contributed to developing the methodological part related to infectious disease consisting of three summary points: 1.Provide several statistical simulated methods for simulating various R0 with branching process and also birth-and-death process so as to estimate the extinct probability and the expected time to reach final size. 2.Demonstrate how to apply the Becker’s SIR model in conjunction with branching process to estimate incubation period and latent period for the surveillance of TB. 3.Develop a continuous-time Markov process embodied with birth-and-death process in conjunction with a novel case-cohort design data given the known sampling fraction to assess how covariates such as IGRA affect the infection rate and the conversion rate framed with a three-state Markov process. The further application of birth-and-death process used in the simulation of SARS process can compute the extinct probability and the expected time to reach final size, both of which provide a new insight into the golden period for the formulation of policy for the containment of infectious disease in question. | en |
dc.description.provenance | Made available in DSpace on 2021-05-14T17:47:35Z (GMT). No. of bitstreams: 1 ntu-104-D99849014-1.pdf: 9460534 bytes, checksum: 08d0cfc258cb7ff91e0c4130ebaa5282 (MD5) Previous issue date: 2015 | en |
dc.description.tableofcontents | Catalog
誌謝 i 中文摘要 ii Abstract viii Table xviii Figure xx Chapter 1、 Introduction 1 1.1 Basic Reproductive number (R0) and mathematical models 1 1.2 Discrete-time stochastic model for estimating R0 2 1.3 Continuous-time stochastic model for estimating R0 3 1.4 Objectives 3 Chapter 2、Literature Reviews 5 2.1 Epidemic threshold method 5 2.2 Deterministic model 9 2.3 Markov model applied to infectious disease 10 2.4 Branching processes 14 2.5 Birth death process 18 Chapter 3、Methodology 19 3.1 Becker’s SIR model 19 3.2 Various Types of Stochastic Processes for Estimating R0 23 3.2.1 Deterministic model 23 3.2.2 Markov Renewal process 24 3.2.3 Birth-death process 24 (1) Linear birth-death process 25 (2) Generalized birth-death process 28 3.2.4 Multi-state continue time Markov process 32 3.2.5 Branching process 39 3.3 Parameter Estimation 49 3.3.1 Deterministic model 49 3.3.2 Estimation of latent period for TB 49 3.3.3 Three state Continue time Markov process 53 3.3.4 Discrete time Markov process 55 3.4. Simulation 58 3.4.1 Simulation of birth-death process 58 3.4.2 Simulation of a branching process 60 Chapter 4、Data sources 62 4.1 Generating Data by simulations 62 4.2 Empirical Data 62 4.2.1 SARS 62 4.2.2 Mycobacterium tuberculosis 63 Chapter 5、Results 67 5.1 Simulation of R0 with different methods 67 5.1.1. Simulation of R0 using branching process 67 5.1.2 Simulation of R0 using birth-death process 68 5.2 SARS (Severe Acute Respiratory Syndrome) 69 5.2.1 Outbreak of SARS in Singapore 69 5.3.1 Application to TB in the Long-term Care Facility (LTCF) 72 Chapter 6 Discussion 80 6.1 Summary of findings 80 6.1.1 Clinical and epidemiological findings on outbreak of SARS and TB 80 6.1.2 Methodological development 81 6.2 Clinical Usefulness 82 6.2.1 SARS 82 6.2.2 TB 83 6.3 Strength and concerns of methodology 90 6.3.1 The novelty of multi-state Markov model in conjunction with birth-death process 90 6.3.2 Expedient use of non-standard case-cohort design 91 6.3.3 Simulations 91 6.5 Limitation 92 6.6 Conclusion 93 References 94 Appendix 182 Appendix Table 182 IRB 206 | |
dc.language.iso | en | |
dc.title | 隨機過程在肺結核及嚴重急性呼吸道症候群傳染病之運用 | zh_TW |
dc.title | Stochastic Processes for SARS and TB Infectious Diseases | en |
dc.type | Thesis | |
dc.date.schoolyear | 103-1 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 葉彥伯,江大雄,余承平,王振泰,潘信良 | |
dc.subject.keyword | 隨機模型,分支模型,生死過程,肺結核,嚴重呼吸道症候群, | zh_TW |
dc.subject.keyword | stochastic process,branching process,birth-death process,TB,SARS, | en |
dc.relation.page | 207 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2015-02-12 | |
dc.contributor.author-college | 公共衛生學院 | zh_TW |
dc.contributor.author-dept | 流行病學與預防醫學研究所 | zh_TW |
顯示於系所單位: | 流行病學與預防醫學研究所 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-104-1.pdf | 9.24 MB | Adobe PDF | 檢視/開啟 |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。