Modeling stochastic hybrid systems with memory with an application to immune response of cancer dynamics

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2014

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Gökgöz, Nurgül

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Dynamics of cancer involve some complex interactions like immune system responses. Many different models of immune response to tumor growth exist in the literature. Most of the available models are first principles models which have problems in determining the model parameters. For potential use in treatment planning, a model should be able to adopt to subject by subject variability and unknown factors. However, such an approach for a complicated problem like cancer dynamics has some drawbacks. First of all, there exist some unknown factors. Secondly, models with fixed parameters do not allow considering subject-by-subject variability. An alternative approach to this problem is inferring the parameters and determining system behaviour from empirical observation. In inferential modeling case, we first select a model class and infer the parameters from the observations. For this purpose, we used hybrid systems that are suitable for inferential modeling due to their analytical and computational advances. For many biological and physiological systems, the behaviour of system and its responses depend on whole history rather than a combination of historical events. We utilize and further develop hybrid systems with memory to have a more realistic representation. Finally, we also incorporate stochastic calculus in our model to include uncertainities and random perturbation.

Subject Keywords

Cancer, Tumors, Tumors, Immune system, Hybrid systems

URI

http://etd.lib.metu.edu.tr/upload/12616927/index.pdf
https://hdl.handle.net/11511/23387

Collections

Graduate School of Applied Mathematics, Thesis

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Citation Formats

N. Gökgöz, “Modeling stochastic hybrid systems with memory with an application to immune response of cancer dynamics,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.