Acute Promyelocytic Leukemia (APL) is a rare and potentially lethal condition in which risk-based therapy often leads to better outcomes. Because of its rarity and relatively high overall survival rate, prospective randomized trials to investigate alternative APL treatment schedules are challenging. Mathematical models may provide useful information in this regard. We collected clinical data from 38 patients treated for APL under the International Consortium on Acute Leukemia (ICAL) protocol and laboratory data during induction therapy. We propose a mathematical model that represents the dynamics of leukocytes in peripheral blood and the effect of ICAL treatment on the disease's dynamics. We observe that our cohort presents demographic characteristics and clinical outcomes similar to previous clinical trials on APL. Over a follow-up period of 41.8 months, the relapse-free survival and overall survival at two years are both found to be 78.7%. For two selected patients, the model produces a good fit to the clinical data. Information such as the response to treatment and risk of relapse can be derived from the model, and this may assist in clinical practice and the design of clinical trials.