Mathematical analysis and optimal control of the cauchy problem for cancer chemotherapy
In this research the technique of mathematical modeling and non-linear analysis is used in the study of the patho-physiology of human cancers. Using the state-of-the-art clinical data from the medical literature, the physiodynamics of human solid tumors is reformulated into a system of nonlinear deterministic Nani-Freedman type ordinary differential equations. The cancer chemotherapy models analyzed in this thesis were formulated by Frank Nani. These equations depict the time evolution of the disease with and without chemotherapy. The clinically applicable mathematical model incorporates the stoichiometric interaction between noncancerous cells, cancer cells, metastatic cancer cells, and molecules of an anti-neoplastic cancer drug. Using the principles of Dynamical Systems Theory and Linearized Stability Theory, a collection of therapeutic criteria are derived depicting the pathological scenarios of annihilation, cancer recurrence, cancer remission, and patient incapacitation or death due to therapeutic failure. In particular, Optimal Control Theory is used in the determination of cancer treatment protocols under which the patient encounters less drug toxicity but maximum tumor cell-kill. The Pontryagin's Minimum Principle and Pontryagin's Hamiltonian are used in the formulation and computation of the admissible optimal control. The admissible control is explicitly analyzed for its therapeutic efficacy.
Carter, Phylisicia Nicole, "Mathematical analysis and optimal control of the cauchy problem for cancer chemotherapy" (2013). ETD Collection for Fayetteville State University. AAI1524765.