The development of infectious disease models remains important to provide scientists with tools to better understand disease dynamics and develop more effective control strategies. In this work we focus on the estimation of seasonally varying transmission parameters in infectious disease models from real measles case data. We formulate both discrete-time and continuous-time models and discussed the benefits and shortcomings of both types of models. Additionally, this work demonstrates the flexibility inherent in large-scale nonlinear programming techniques and the ability of these techniques to efficiently estimate transmission parameters even in very large-scale problems. This computational efficiency and flexibility opens the door for investigating many alternative model formulations and encourages use of these techniques for estimation of larger, more complex models like those with age-dependent dynamics, more complex compartment models, and spatially distributed data. How- ever, the size of these problems can become excessively large even for these powerful estimation techniques, and parallel estimation strategies must be explored. Two parallel decomposition approaches are presented that exploited scenario based de- composition and decomposition in time. These approaches show promise for certain types of estimation problems.

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Diffuse liver disease is a growing problem and a major cause of death worldwide. In the final stages the treatment often involves liver resection or transplant and in deciding what course of action is to be taken it is crucial to have a correct assessment of the function of the liver. The current “gold standard” for this assessment is to take a liver biopsy which has a number of disadvantages. As an alternative, a method involving magnetic resonance imaging and mechanistic modeling of the liver has been developed at Linköping University. One of the obstacles for this method to overcome in order to reach clinical implementation is the speed of the parameter estimation. In this project the methodology of metamodeling is tested as a possible solution to this speed problem. Metamodeling involve making models of models using extensive model simulations and mathematical tools. With the use of regression methods, clustering algorithms, and optimization, different methods for parameter estimation have been evaluated. The results show that several, but not all, of the parameters could be accurately estimated using metamodeling and that metamodeling could be a highly useful tool when modeling biological systems. With further development, metamodeling could bring this non-invasive method for estimation of liver function a major step closer to application in the clinic.

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One of heavy oils upgrading processes is hydroconversion. As it is a complex process involving many chemical reactions, the mathematical model of hydroconversion process often has more kinetic parameters than can be estimated from the data. In this thesis, a model for hydroconversion processing of vacuum residue is proposed. It is proved that the model is structurally identifiable, but shown that it is inestimable and good parameter estimates may be impossible to obtain even if the model fit is good. As a proof to the model inestimability, it is shown that literature data can be fitted using a subset of only three (of seven) parameters. To improve parameter estimability, a method is proposed for designing additional experiments. The method is based on designing experiments that provide data that is complementary (in an appropriate sense) to existing data. The approach is illustrated using the hydroconversion model. For the hydroconversion model, using two additional experiments provides a good balance between parameter estimation and experimental effort. / Process Control

Lic.-avh. Uppsala : Univ., 2004.

Thesis (M.App.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 161-165). Also available in electronic format on the Internet.

Thesis (M.S.)--Ohio University, March, 1995. / Title from PDF t.p.