Saudi Cultural Missions Theses & Dissertations
Permanent URI for this communityhttps://drepo.sdl.edu.sa/handle/20.500.14154/10
Browse
2 results
Search Results
Item Restricted A CLASS OF GAME-THEORETIC AND FOKKER-PLANCK OPTIMAL CONTROL FRAMEWORKS IN COLON AND ESOPHAGEAL CANCER(The University of Texas at Arlington, 2024-05-15) Alajmi, Mesfer; Roy, SouvikIn this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the parameters that require control, thereby revealing the types of drugs suitable for treatment. Afterward, we introduce a differential game framework for assessing the protocols used in the administration of these drugs in colon cancer. In this specific setting, we discuss a new framework for a non-cooperative evolutionary game involving colon cancer and the oncologist. A novel mathematical model considering the dynamical progression of colon cancer, including resistance mechanisms and the various therapies delivered, forms the basis of this framework. To determine the optimal course of action for the patient, this model is used to formulate and compute two equilibrium game theoretic strategies: Stackelberg and Nash's equilibria. Our study concludes with a model of esophageal cancer signaling pathways and monoclonal antibodies engaged in a game of evolutionary competition. This structure illustrates the extent to which evolutionary game theory may provide novel, efficient methods for cancer therapy assessment. Within this framework, we analyze and calculate two game-theoretic techniques, Stackelberg and Nash's equilibria, to find the best possible result for the patient. Numerous numerical experiments are presented to prove the efficacy of the theoretical investigations.37 0Item Restricted Optimal control frameworks for a class of epidemiological and oncological models(University of Texas at Arlington, 2024-05) Alghamdi, Asma; Roy, SouvikIn this thesis, we employ optimal control frameworks in two distinct contexts: Human immunodeficiency virus (HIV) and esophageal cancer. For HIV, we introduce a comprehensive data-driven nonlinear optimization framework designed for personalized therapies. This framework utilizes a deterministic in-host nonlinear ordinary differential equation (ODE) model and formulates two optimization problems using individual patient data. The first problem focuses on estimating patient-specific parameters through constrained optimization, while the second problem determines optimal combination therapies to reduce viral load to undetectable levels. Several numerical experiments suggest that our framework can provide robust and effective optimal dosages with lower toxicity levels to control HIV. In esophageal cancer, we present an innovative approach to model and control aberrant signaling pathways. This involves leveraging an It\^o stochastic process to capture signaling pathway dynamics governed by a degenerate Fokker-Planck partial differential equation. Our study proposes a refined treatment strategy targeting aberrant signaling pathways, specifically focusing on epidermal growth factor (EGF) pathways. This strategy includes developing a pharmacokinetic model considering pathway heterogeneities, preceded by constrained optimization to obtain model parameters from patient data. Subsequently, we propose a personalized optimal treatment strategy targeting aberrant EGF using a non-smooth open-loop control for a stochastic process modeled by the Fokker-Planck equation. The solution to these problems is characterized within the framework of Pontryagin's minimum principle (PMP), and the optimization problem is solved using a sequential quadratic Hamiltonian (SQH) method. Experimental results are presented to validate the proposed framework successfully.21 0