In this paper, a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced angiogenesis, using patient data, is presented. The dynamics of colon cancer is given by a stochastic process that captures the inherent randomness in the system. The stochastic framework is based on the Fokker-Planck equation that represents the evolution of the probability density function corresponding to the stochastic process. An optimization problem is formulated that takes input individual patient data with randomness present, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, sensitivity analysis of the optimal parameter set is performed to determine the parameters that need to be controlled, thus, providing information of the type of drugs that can be used for treatment.
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