ISyE Student Seminar: Zicheng Wang
"Large Deviations Analysis on Cancer Evolution"Presentation by Zicheng Wang Friday, February 21
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Abstract: A major issue in cancer treatment is that cancer cells can develop resistance to treatment. Mathematical modeling can provide advanced understanding in cancer evolution when mutation-induced drug resistance occurs. We model such evolution by a multi-type branching process, and study two important stochastic times: crossover time and recurrence time. Crossover time represents the first time that the total cancer cell population is dominated by the mutant cell population. Recurrence time represents the first time that the mutant cell population exceeds a given proportion of the initial population size of drug-sensitive cells. We show convergence in probability results for both crossover time and recurrence time. We conduct large deviations analysis on the events of early crossover and early recurrence. It is shown that exponential decay speed and speed functions for both stochastic times depend on the initial size of mutant cell population. We then apply our results to analyze the distribution of number of non-extinct clones of mutants at the recurrence time conditioning on the event of early recurrence. |