臺灣博碩士論文加值系統

傳染病模擬模型在流行病學中被用來探索一些在現實中難以探究的問題。
其中，個體化模擬模型(Agent-based model)利用在電腦中的虛擬個體模擬由複雜行為組成的系統。
近年來，由於電腦運算技術的進步，個體化模擬模型有許多的應用產生，然而對於如何擬合與校正個體化模擬模型的研究甚少。
本研究利用連續時間貝氏網路(Continuous-time Bayesian Networks)發展了一組具有統計界面的傳染病個體化模擬模型，並進一步以過去的擬和架構為基礎，發展出一套擬合程序。
我們成功將遺傳演算法中的數值點突變(Numerical mutation)及參數分組策略(Blocking strategy)應用於序列蒙地卡羅法(Sequential Monte Carlo)中，使擬合程序可以處理大量參數且來源各異的資料。
最後，我們以肺結核的接觸者追蹤政策為例，使用易感受-感染者-復原者模型(Susceptible-Infectious-Recovery model)來演示我們為個體化模擬模型從模型建構、估計到預測所發展的實證架構。

The simulation models in epidemiology were developed to answer the questions which were not easy to solve by observational studies in the real world.
In particular, Agent-based models (ABMs) were usually employed to deal with the complex system of disease transmission by simulating computational agents in the virtual world.
However, the fitting scheme of ABMs is less developed than the applications..
With the aim of investigating disease dynamics and creating an interface for statistical analysis, we proposed a class of ABMs with Continuous-time Bayesian network, a temporal multivariate probability model.
While retaining the strength of existing procedure for simulation model fitting based on sequential Monte Carlo, we set up an improved framework for fitting ABMs.
We further synthesized the numerical mutation in genetic algorithm and the parameters augmentation in blocking Gibbs sampling in order to overcome the challenges of multidimensional parameters and multi-sources data.
Using an example of Susceptible-Infectious-Recovery model for contact tracing in tuberculosis control, we briefly presented the properties of our proposed model and demonstrated its potential applications in the future.
By including model construction, fitting, and forecasting, we formalized an empirical scheme for individual based models in simulating disease dynamics.

致謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vii
List of Tables viii
1 Introduction 1
1.1 Modern challenge of infectious disease control . . . . . . . . . . . . . . 1
1.2 Why simulation model? . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Agent-based models (ABMs) . . . . . . . . . . . . . . . . . . . 2
1.3 Challenges in ABMs construction for epidemiologist . . . . . . . . . . . 3
1.4 Fitting scheme and research gap . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Example: Tuberculosis control in Taiwan . . . . . . . . . . . . . . . . . 5
1.6 Objective and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Model Construction 7
2.1 An Agent-Based Model with Bayesian networks for modelling infectious diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Conceptual model: Disease Triangle Model . . . . . . . . . . . . 7
2.2 Dynamic Bayesian Networks (DBNs) . . . . . . . . . . . . . . . . . . . 8
2.2.1 Dynamic model for infectious diseases . . . . . . . . . . . . . . 9
2.3 An illustrative example: SIR model . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Collect information . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 Identify nodes and form the agent . . . . . . . . . . . . . . . . . 12
2.3.3 Set the interaction between nodes . . . . . . . . . . . . . . . . . 12
2.3.4 Set the initial states . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.6 Sub-model inference: basic reproductive numbers (R 0 ) . . . . . . 13
3 Fitting Scheme 22
3.1 General fitting scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.1 Bayesian approach: Sequential Monte Carlo . . . . . . . . . . . . 22
3.1.2 Frequentist approach: Genetic algorithm . . . . . . . . . . . . . 23
3.2 Fitting scheme for single dataset . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Numerical mutation . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Fitting scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Fitting for multiple datasets . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Blocking strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.2 Reducing problem of spurious correlation . . . . . . . . . . . . . 28
3.3.3 Identifying the order of processes . . . . . . . . . . . . . . . . . 28
3.3.4 Fitting scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Tuberculosis Dynamic Model 33
4.1 Tuberculosis control model . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 Environments agents . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.2 Human agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.3 Tuberculosis agents . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.4 Health care seeking . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.5 Intervention model . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Model fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Forecasting: Policy analysis . . . . . . . . . . . . . . . . . . . . . . . . 36
5 Results for TB Model 40
5.1 Population-level inference . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Individual-level inference . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Discussion 46
6.1 Connection of the proposed agent-based model with epidemiological studies 46
6.2 Advantage of using continuous-time sampling . . . . . . . . . . . . . . . 47
6.3 Computation time saving . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.4 Numerical mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.5 Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.6 Tuberculosis control policy . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Armbruster, B. and Brandeau, M. L. (2007a). Contact tracing to control infectious disease:when enough is enough. Health care management science, 10(4):341–355.
Armbruster, B. and Brandeau, M. L. (2007b). Who do you know? a simulation study of infectious disease control through contact tracing. In Proceedings of the 2007 Western Multiconference on Computer Simulation, pages 79–85. Citeseer.
Auchincloss, A. H. and Roux, A. V. D. (2008). A new tool for epidemiology: the usefulness of dynamic-agent models in understanding place effects on health. American journal of epidemiology, 168(1):1–8.
Beaumont, M. A., Zhang, W., and Balding, D. J. (2002). Approximate bayesian computation in population genetics. Genetics, 162(4):2025–2035.
Begun, M., Newall, A. T., Marks, G. B., and Wood, J. G. (2013). Contact tracing of tuberculosis: a systematic review of transmission modelling studies. PloS one, 8(9):e72470.
Blower, S. and Go, M.-H. (2011). The importance of including dynamic social networks when modeling epidemics of airborne infections: does increasing complexity increase accuracy? BMC medicine, 9(1):88.
Boudali, H. and Bechta Dugan, J. (2006). A continuous-time bayesian network reliability modeling, and analysis framework. Reliability, IEEE Transactions on, 55(1):86–97.
Box, G. E., Jenkins, G. M., and Reinsel, G. C. (1976). Time series analysis: forecasting and control. John Wiley &; Sons.
Casella, G. and George, E. I. (1992). Explaining the gibbs sampler. The American Statistician, 46(3):167–174.
Charniak, E. (1991). Bayesian networks without tears. AI magazine, 12(4):50.
Cohen, T., Colijn, C., Finklea, B., and Murray, M. (2007). Exogenous re-infection and the dynamics of tuberculosis epidemics: local effects in a network model of transmission. Journal of The Royal Society Interface, 4(14):523–531.
Darwin, C. (1859). ON THE ORIGIN OF SPECIES-6TH. John Murray, London.
Dean, T. and Kanazawa, K. (1989). A model for reasoning about persistence and causation. Computational intelligence, 5(2):142–150.
Deisboeck, T. S., Wang, Z., Macklin, P., and Cristini, V. (2011). Multiscale cancer modeling. Annual review of biomedical engineering, 13.
Doran, J. (2001). Agent-based modelling of ecosystems for sustainable resource management. In Multi-Agent Systems and Applications, pages 383–403. Springer.
Doucet, A., De Freitas, N., and Gordon, N. (2001). Sequential Monte Carlo methods in practice. Springer.
Duboz, R., Versmisse, D., Travers, M., Ramat, E., and Shin, Y.-J. (2010). Application of an evolutionary algorithm to the inverse parameter estimation of an individual-based model. Ecological modelling, 221(5):840–849.
Engel, Y. and Etzion, O. (2011). Towards proactive event-driven computing. In Proceedings of the 5th ACM international conference on Distributed event-based system, pages 125–136. ACM.
Epstein, J. M. (1999). Agent-based computational models and generative social science.
Generative Social Science: Studies in Agent-Based Computational Modeling, 4(5):4–46.
Farmer, J. D. and Foley, D. (2009). The economy needs agent-based modelling. Nature,460(7256):685–686.
Fogel, D. B. (1994). An introduction to simulated evolutionary optimization. Neural Networks, IEEE Transactions on, 5(1):3–14.
Fraser, A. S. (1960). Simulation of genetic systems by automatic digital computers vi. epistasis. Australian Journal of Biological Sciences, 13(2):150–162.
Galea, S., Riddle, M., and Kaplan, G. A. (2010). Causal thinking and complex system approaches in epidemiology. International Journal of Epidemiology, 39(1):97–106.
Gatti, E., Luciani, D., and Stella, F. (2012). A continuous time bayesian network model for cardiogenic heart failure. Flexible Services and Manufacturing Journal, 24(4):496–515.
Gopalratnam, K., Kautz, H., and Weld, D. S. (2005). Extending continuous time bayesian networks. In Proceedings of the National Conference on Artificial Intelligence, volume 20, page 981. Menlo Park, CA; Cambridge, MA; London; AAAI Press; MIT Press;1999.
Gordon, N. J., Salmond, D. J., and Smith, A. F. (1993). Novel approach to nonlinear/non-gaussian bayesian state estimation. In IEE Proceedings F (Radar and Signal Processing), volume 140, pages 107–113. IET.
Grassly, N. C. and Fraser, C. (2008). Mathematical models of infectious disease transmis-
sion. Nature Reviews Microbiology, 6(6):477–487.
Greenland, S., Pearl, J., and Robins, J. M. (1999). Causal diagrams for epidemiologic
research. Epidemiology, pages 37–48.
Grimm, V. and Railsback, S. F. (2013). Individual-based modeling and ecology. Princeton
university press.
Grimm, V., Revilla, E., Berger, U., Jeltsch, F., Mooij, W. M., Railsback, S. F., Thulke, H.H., Weiner, J., Wiegand, T., and DeAngelis, D. L. (2005). Pattern-oriented modeling of agent-based complex systems: lessons from ecology. science, 310(5750):987–991.
Guzzetta, G., Ajelli, M., Yang, Z., Merler, S., Furlanello, C., and Kirschner, D. (2011).
Modeling socio-demography to capture tuberculosis transmission dynamics in a low burden setting. Journal of theoretical biology, 289:197–205.
Hartig, F., Calabrese, J. M., Reineking, B., Wiegand, T., and Huth, A. (2011). Statistical inference for stochastic simulation models–theory and application. Ecology Letters, 14(8):816–827.
Hutchins, D. (1999). Just in time. Gower Publishing, Ltd.
Janssen, M. (2002). Complexity and ecosystem management: the theory and practice of multi-agent systems. Edward Elgar Publishing.
Jensen, C. S., Kjarulff, U., and Kong, A. (1995). Blocking gibbs sampling in very large probabilistic expert systems. International Journal of Human-Computer Studies, 42(6): 647–666.
Jewell, C. P., Kypraios, T., Neal, P., Roberts, G. O., et al. (2009). Bayesian analysis for emerging infectious diseases. Bayesian Analysis, 4(3):465–496.
Kasaie, P., Andrews, J. R., Kelton, W. D., and Dowdy, D. W. (2014). Timing of tuberculosis transmission and the impact of household contact tracing. an agent-based simulation model. American journal of respiratory and critical care medicine, 189(7):845–852.
Kranzer, K., Afnan-Holmes, H., Tomlin, K., Golub, J., Shapiro, A., Schaap, A., Corbett, E., Lonnroth, K., and Glynn, J. (2013). The benefits to communities and individuals of screening for active tuberculosis disease: a systematic review. Int J Tuberc Lung Dis, 17(4):432–46.
Liu, J. S., Wong, W. H., and Kong, A. (1994). Covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika, 81(1):27–40.
Macal, C. M. and North, M. J. (2005). Tutorial on agent-based modeling and simulation. In Proceedings of the 37th conference on Winter simulation, pages 2–15. Winter Simulation Conference.
Maglio, P. P. and Mabry, P. L. (2011). Agent-based models and systems science approaches to public health. American journal of preventive medicine, 40(3):392.
Meltzer, M. I., Cox, N. J., Fukuda, K., et al. (1999). The economic impact of pandemic influenza in the united states: priorities for intervention. Emerging infectious diseases, 5:659–671.
Nodelman, U. and Horvitz, E. (2003). Continuous time bayesian networks for inferring users'' presence and activities with extensions for modeling and evaluation. Microsoft Research, July-August.
Nodelman, U., Koller, D., and Shelton, C. R. (2012). Expectation propagation for continuous time bayesian networks. arXiv preprint arXiv:1207.1401.
Nodelman, U., Shelton, C. R., and Koller, D. (2002a). Continuous time bayesian networks. In Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence, pages 378–387. Morgan Kaufmann Publishers Inc.
Nodelman, U., Shelton, C. R., and Koller, D. (2002b). Learning continuous time bayesian networks. In Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence, pages 451–458. Morgan Kaufmann Publishers Inc.
O’cinneide, C. A. (1999). Phase-type distributions: open problems and a few properties. Stochastic Models, 15(4):731–757.
O’Shea, M. K., Koh, G. C., Munang, M., Smith, G., Banerjee, A., and Dedicoat, M. (2014). Time-to-detection in culture predicts risk of mycobacterium tuberculosis transmission: A cohort study. Clinical Infectious Diseases, page ciu244.
Parunak, H. V. D., Savit, R., and Riolo, R. L. (1998). Agent-based modeling vs. equation-based modeling: A case study and users'' guide. In Multi-agent systems and agent-based simulation, pages 10–25. Springer.
Pearl, J. (1988). Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann.
Pearl, J. (2014). Is scientific knowledge useful for policy analysis? a peculiar theorem says: No. Journal of Causal Inference J. Causal Infer., 2(1):109–112.
Pearson, K. (1896). Mathematical contributions to the theory of evolution.–on a form of spurious correlation which may arise when indices are used in the measurement of organs. Proceedings of the royal society of london, 60(359-367):489–498.
Tiemersma, E. W., van der Werf, M. J., Borgdorff, M. W., Williams, B. G., and Nagelkerke, N. J. (2011). Natural history of tuberculosis: duration and fatality of untreated pulmonary tuberculosis in hiv negative patients: a systematic review. PloS one, 6(4):e17601.
Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. P. (2009). Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface, 6(31):187–202.
Tostmann, A., Kik, S. V., Kalisvaart, N. A., Sebek, M. M., Verver, S., Boeree, M. J., and van Soolingen, D. (2008). Tuberculosis transmission by patients with smear-negative pulmonary tuberculosis in a large cohort in the netherlands. Clinical infectious diseases, 47(9):1135–1142.
Uusitalo, L. (2007). Advantages and challenges of bayesian networks in environmental modelling. Ecological modelling, 203(3):312–318.
VanderWeele, T. J. and Robins, J. M. (2007). Directed acyclic graphs, sufficient causes, and the properties of conditioning on a common effect. American journal of epidemiology, 166(9):1096–1104.
Vynnycky, E. and Fine, P. (1997). The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiology and infection, 119(02):183–201.
Vynnycky, E. and Fine, P. (1999). Interpreting the decline in tuberculosis: the role of secular trends in effective contact. International journal of epidemiology, 28(2):327-334.