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

Rodica Radulescu*, Doina Candea and Andrei Halanay

The dynamics and evolution of a type 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. Moreover, it is assumed that homeostatic mechanisms sustain the hematopoietic stem cell population at a constant level. Treatment is included in the model as a function of time, $u(t)$, 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.

Mathematics Subject Classification: 93C23 34K35 92C50

Keywords: leukemia; delay differential system; optimal control; discretization.

Minisymposion: Analysis and Control of Evolution Equations and Inclusions