A Control Delay Differential Equations Model of Evolution of Normal and Leukemic Cell Populations Under Treatment

摘要

The dynamics and evolution of leukemia is determined by the interactions between normal and leukemic cells populations at every phase of the development of hematopoietic cells. For both types of cell populations, two subpopulations are considered, namely the stem-like cell population (i.e. with unlimited self-renew ability) and a more mature, differentiated one, possessing only the capability to undergo limited reproduction. Treatment effects are included in the model as functions of time and a cost functional is considered. The optimal control is obtained using a discretization scheme. Numerical results are discussed in relation to the medical interpretation.