AbstractChronic Myeloid Leukemia is a type of cancer that starts in certain blood-forming cells of the bone marrow. Interferon-$$\alpha$$ was once the standard front-line treatment producing remission rates of only 28.3 percent in 1991. After the highly effective drugs first became available in 2001, survival rates have increased immensely. According to the American Cancer Society, one large study of CML patients treated with a drug called imatinib found that about 90 percent of them were still alive 5 years after starting treatment. While imatinib has changed the way oncologists treat CML, remission is common after extended gaps in treatment. In this paper, we will explore the long-term dynamics of CML under treatment through the use of use of theoretical and mathematical components. We closely base our methods upon the approach of Urszula Ledzewicz and Helen Moore. We will introduce our unique model and explain component selections, while we move towards understanding the optimal interactions of imatinib and interferon-$$\alpha$$ against dormant and proliferating CML cells. Our future work involving optimal control dynamics will be briefly introduced and further solutions are currently ongoing.