2026-09-20T16:56:31Zhttps://digital.lib.washington.edu/server/oai/request

oai:digital.lib.washington.edu:1773/492502026-02-16T02:47:07Zcom_1773_4888col_1773_4891

Bozic, Ivana Zhang, Ruibo 2022-09-23T20:42:21Z 2022-09-23 2022 Zhang_washington_0250O_24697.pdf http://hdl.handle.net/1773/49250 Thesis (Master's)--University of Washington, 2022 We study a multi-type branching process model associated with a transitional network between types. In particular, we are interested in determining the waiting time to each type in the network, employing an approximation of the process by its large time limit. We first present a literature review of results on large time limits and classify the dynamics of branching processes by their mean value matrices. For the special case when the transitional network is a single pathway, we present two approaches regarding approximating the waiting time for each type. To apply our theory to a real world problem, we use a multi-type branching process to model the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting time distributions of novel driver mutations. application/pdf en_US CC BY-NC-ND Branching process Cancer Applied mathematics Applied mathematics Branching process models for cancer evolution: overview and an application to colorectal cancer initiation Thesis Restrict to UW for 1 year -- then make Open Access 2023-09-23T20:42:21Z open.access