Existence and Stability of Limit Cycles in a Two-delays Model of Hematopoiesis Including Asymmetric Division

A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia is considered. All three types of stem cell division (asymmetric division, symmetric renewal and symmetric differentiation) are present in the model. Stability of equilibria is investigated and emergence of periodic solutions of limit cycle type, as a result of a Hopf bifurcation, is eventually shown. The stability of these limit cycles is studied using the first Lyapunov coefficient

A Complex Mathematical Model with Competition in Leukemia with Immune Response - An Optimal Control Approach

International audienceThis paper investigates an optimal control problem associated with a complex nonlinear system of multiple delay differential equations modeling the development of healthy and leukemic cell populations incorporating the immune system. The model takes into account space competition between normal cells and leukemic cells at two phases of the development of hematopoietic cells. The control problem consists in optimizing the treatment effect while minimizing the side effects. The Pontryagin minimum principle is applied and important conclusions about the character of the optimal therapy strategy are drawn