ON STABILITY OF A COMBINED GLEEVEC AND IMMUNE MODEL IN CHRONIC LEUKEMIA: EXPLOITING DELAY SYSTEM STRUCTURE

Abstract This paper focuses on the stability analysis of a delay-differential system encountered in modeling immune dynamics during Gleevec treatment for chronic myelogenous leukemia. A simple algorithm is proposed for the analysis of delay effects on the stability. The analysis shows that the model yields two fixed points, one stable and one unstable. The stable fixed point corresponds to some equilibrium solution in which the leukemia population is kept below the cytogenetic remission level. This result implies that, during Gleevec treatment, the resulting anti-leukemia immune response can serve to control the leukemia population. However, the rate of approach to the stable fixed point is very slow, indicating that the immune response is largely ineffective at driving the leukemia population towards the stable fixed point. Finally, a few remarks are made about possible treatment strategies that can be used to accelerate the approach of the leukemia and immune populations towards this stable equilibrium.