Murray State Theses and Dissertations


Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost of the chemotherapy and the number of cancer cells. Numerical methods, such as a forward-backward sweep method and adjusted methods to evaluate delays, are used to show qualitative treatment options.

Year manuscript completed


Year degree awarded


Author's Keywords

optimal control, numerical, delay differential equation

Thesis Advisor

Craig D Collins

Committee Member

Renee K Fister

Committee Member

David Roach

Document Type