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A quantitative study on the role of TKI combined with Wnt/$β$-catenin signaling and IFN-$α$ in the treatment of CML through deterministic and stochastic approaches

We propose deterministic and stochastic models for studying the pharmacokinetics of chronic myeloid leukemia (CML), upon administration of IFN-$α$ (the traditional treatment for CML), TKI (the current frontline medication for CML) and Wnt/$β$-catenin signaling (the state-of-the art therapeutic breakthrough for CML). To the best of our knowledge, no mathematical model incorporating all these three therapeutic protocols are available in literature. Further, this work introduces a stochastic approach in the study of CML dynamics. The key contributions of this work are: (1) Determination of the patient condition, contingent upon the patient specific model parameters, which leads to prediction of the appropriate patient specific therapeutic dosage. (2) Addressing the question of how the dual therapy of TKI and Wnt/$β$-catenin signaling or triple combination of all three, offers potentially improved therapeutic responses, particularly in terms of reduced side effects of TKI or IFN-$α$. (3) Prediction of the likelihood of CML extinction/remission based on the level of CML stem cells at detection.