Chronic myelogenous leukemia (CML) is a cancer of the white blood cells that results from increased and uncontrolled growth of myeloid cells in the bone marrow and the accumulation of these cells in the blood. The most common form of treatment for CML is imatinib, a tyrosine kinase inhibitor. Although imatinib is an effective treatment for CML and most patients treated with imatinib do attain some form of remission, imatinib does not completely eradicate all leukemia cells, and if treatment is stopped, all patients eventually relapse (Cortes, 2005). In Kim (2008), the authors developed a mathematical model for the dynamics of CML under imatinib treatment that incorporates the anti-leukemia immune response, and in Paquin (2011), the authors used this mathematical model to study strategic treatment interruptions as a potential therapeutic strategy for CML patients. Although the authors presented the results of several numerical simulations in Paquin (2011), the studies in that work did not include the possibility of imatinib-resistant mutations or an initial population of imatinib-resistant leukemia cells. As resistance is a significant consideration in any drug treatment, it is important to study the efficacy of the strategic treatment interruption plan in the presence of imatinib resistance. In this work, we modify the delay differential equations model of Kim (2008), Paquin (2011) to include the possibility of imatinib resistance, and we analyze strategic treatment interruptions as a potential therapeutic tool in the case of patients with imatinib-resistance leukemia cells.



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