Positive dynamic systems resulting from modeling cancer chemotherapy

We consider a specific class of mathematical bilinear models based on cell-cycle kinetics which are used to describe and improve treatment protocols in phase-specific cancer chemotherapy. This class of models contains a two compartmental model of single drug chemotherapy, three compartmental models of multidrug therapy combining blocking and killing actions, and recruitment from quiescence together with killing action, as well as more general multicompartmental model with many drugs. We demonstrate that these models are positive dynamic systems and it is very important from biological point of view. Moreover this property is crucial for elimination of singular controls from candidates for optimality.