We consider modified versions of a cell population model for periodic chemotherapy treatment of tumors. These models contain both proliferating and quiescent cells, and treats the transitions between the two types of cells. Our models are defined by replacing the loss term function, μ(t, c), in Webb's model by a constant. This corresponds to having a constant infusion of the drug rather than having a periodic chemotherapy treatment. We compare our results with those of Webb who shows that shorter periods of treatment are advantageous.