The Chronic Myeloid leukemia (CML) is a blood and bone marrow cancer.
It is characterized by mutations in the white blood cells which tend to proliferate rapidly and to have better survival capacities than healthy cells. The immune system plays an important role in the long term response.
We propose a system of PDEs which describes the interactions of immune
and leukemic cells. We consider that differentiation can be described by a
continuous variable which we use to structure our system. 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 the immune system (immunosuppression).
We find that the maturity structure can affect the stability chart of the
system. In particular the remission steady state (unique if it exists), which is
always stable for the ODE corresponding model, can be unstable in the PDE
case. We discuss the influence of the maturity distribution of this steady state
on the stability.
