Evolutionary Dynamics of Tumorigenesis: An Application of Dynamical Systems

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Akbari, Mohammad Javad | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 51677 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra; Razvan, Mohammad Reza
Abstract:
Application of optimal control in cancer modeling is studied through both linear and nonlinear modeling of the dynamics in ordinary differential equations. At the outset, a fairly straight-forward analysis of a linear model in presented. Through comparably simple machinery, this seminal work published at early 2000s covers some of most important techniques previously developed. The model here is infinite- dimensional, taking different number of gene amplifications into account. Thereafter by surveying recently published papers, the literature is reviewed and different lines of progress is followed, culminating in detailed study of a specific approach which is theoretically of interest. Combining some elaborate ideas of modern mathematics, such as differential geometry and smooth manifolds, with optimal control machinery this study analyzes dynamics of tumor micro-environment through a 5-dimensional non-linear model controlled by a 2-dimensional combination of chemotherapy and immunotherapy. The result is a bang-bang solution for one, and a continuous one for another
Keywords:
Biomathematics ; Dynamical Systems ; Optimal Feedback Control Theory ; Tumor Growth ; Cancer

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