Gunnarsson, Einar2022-09-132022-09-132022-06https://hdl.handle.net/11299/241592University of Minnesota Ph.D. dissertation. 2022. Major: Industrial and Systems Engineering. Advisors: Kevin Leder, Jasmine Foo. 1 computer file (PDF); 280 pages.Cancer is a group of diseases characterized by uncontrolled cell proliferation. The initiation of cancer usually involves a series of mutations in genes responsible for regulating the cell cycle. As the cancer-initiating cell expands into a tumor, the tumor cells continue to accumulate mutations, which induces substantial genetic heterogeneity within the tumor. In recent years, it has been increasingly recognized that epigenetic mechanisms, which are chemical changes to DNA or the chromatin structure which houses DNA, play an equally important role in tumor evolution. Due to their reversible and rapid nature, epigenetic mechanisms can enable cancer cells to switch dynamically between two or more phenotypic states, which commonly show differential responses to drug treatments. This dissertation consists of four projects which each involves using a mathematical model to study the evolutionary dynamics of cancer. The projects range from addressing the process of cancer initiation to the evolution of drug resistance, and they take both genetic and non-genetic perspectives. In Chapter 2, we study the dynamics of cancer initiation in multilayered tissue under a two-step mutational model of cancer. In Chapter 3, we study the accumulation of neutral mutations during tumor progression, which are mutations that do not affect the division rate of tumor cells. In Chapter 4, we study the role of phenotypic switching in the evolution of stable drug resistance. Finally, in Chapter 5, we develop a statistical framework for inferring the rates of cell division, cell death and phenotypic switching in cancer.enBranching processesCancer evolutionMathematical biologyMathematical modelingParticle systemsThesis or Dissertation