Mathematical Approach to Predict the Drug Effects on Cancer Stem Cell Models

The mechanism behind the growth and development of tumors is intensively studied using several mathematical approaches that rely on linear and non-linear techniques to model the cell population dynamics to better understand the development and progression of cancer. In this paper, we study the progression of a type of malignant tumors characterized by the stem-differentiation hierarchy. Two main issues are modeled and investigated: the differentiation phase and the phenotypic plasticity that suggests the existence of a dynamic interaction among Cancer Stem Cells and non-Cancer Stem Cells populations. Using these models, we study several therapy effects on breast cancer in order to obtain the temporal behavior of the cell populations, taking into account different drug concentrations and oncoantigen-driven vaccinations.