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Section: New Results
Chronic myelogenous leukemia
Participants : Frédéric Mazenc, Siviu Niculescu, Peter Kim [Univ. of Sydney] .
The paper [26]
focuses on the stability analysis of a delay-differential system encountered in modeling immune
dynamics during imatinib treatment for chronic myelogenous leukemia (CML).
A simple algorithm is proposed for the analysis of delay effects on the stability.
Such an algorithm takes advantage of the particular structure of the dynamical interconnections
of the model. The analysis shows that the model yields three fixed points, two of which are
always unstable and one of which is sometimes stable. The stable fixed point corresponds to an
equilibrium solution in which the leukemia population is kept below the cytogenetic remission level.
This result implies that, during imatinib 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. To extend the stability analysis with respect to the
delay parameter, we conduct a global nonlinear analysis to demonstrate the existence of
unbounded solutions. We provide sufficient conditions based on initial cell concentrations that
guarantee unbounded solutions and comment on how these conditions can serve to predict whether
imatinib treatment will result in a sustained remission based on a patient's initial leukemia load
and initial anti-leukemia