Abstract:
The talk is comprised of the mathematical and numerical study of a new mathematical model
of acute leukaemias (blood cancer). The model is defined by a system of nonlinear
ordinary differential equations describing interaction of healthy and leukemic cells. The
model includes multiple feedback mechanisms such as competition for bone marrow space and
competition for hormonal factors. We study the impact of the different feedback loops on
the speed of disease progression and the response to chemotherapy. An interdisciplinary
combination of mathematical models and clinical data will help to identify crucial
mechanisms during evolution and treatment of the disease. The techniques used include:
numerical simulation of dynamical systems and analytical study of ordinary differential
equations (equilibrium points, linearized stability).