• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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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 $T$ cell concentration.