Applications of Stochastic Processes to Cancer Research - Steely, Kristin Michelle (East Carolina University, 2013)
The purpose of this thesis is to implement stochastic models that are currently used to analyze the impact of different drug treatments on cancer and to model drug resistance by cancer cells. Mathematical models are used to compare single-cancer treatment results with those that involve multiple drugs at the same time. Using various parameters for the model, the probability of treatment success was calculated. A comparison was made with a probability theory approach and good agreement was obtained.
Keywords: Mathematics; Applied mathematics; Medicine; Kolmogorov forward equation; Markov processes; Ordinary differential equations; Partial differential equations; Probability generating function; Stochastic processes; Stochastic analysis; Drug resistance in cancer cells