Séminaire des Doctorants et Doctorantes

Mathematical modeling of chronic Myeloid leukemia

by Kyriaki Dariva

M435 (ENS Lyon)


ENS Lyon


The Chronic Myeloid leukemia (CML) is a blood cancer attributed to mutations in the white blood cells. The leukemic cells tend to proliferate rapidly and to have better survival capacities than healthy cells, while the immune system plays an important role in the long term response. We develop a system of PDEs that describes the interactions of leukemic and immune cells. The purpose of this work was primarily to see if the PDE model can better describe the real distribution of differentiated cells compared to ODE systems that already exist and do the stability analysis. The model is based on a non-monotonic immune response. At low levels, immune response increases with the tumor load whereas for high levels tumor is suppressing the effect of immune response (immunosuppression). In particular, under certain hypothesis, immune response grows fast at intermediate levels (in the ‘immune window’). With this model we find an unstable disease free-equilibrium point and alternated stability of high equilibria (high tumor load), the highest one being stable. For the remission equilibrium point the stability is not guaranteed. There are cases where this point is stable and others where stability is perturbed. We will investigate the robustness of the stability result.