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Full-Text Articles in Control Theory
Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi
Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi
Mathematics Dissertations - Archive
In 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 a robust and effective optimal dosages with lower toxicity levels to …
A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd
A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd
Mathematics Dissertations - Archive
In 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 …