A PDE model for the transport and uptake of doxorubicin in a spherical tumor surrounded by normal tissue is presented. We states its stability with respect the initial and boundary condition and then by using a finite difference method we simulate numerically the drug transport, uptake and loss of tumor density. This is obtained using two examples of drug administration: bolus injection and a continuous infusion. Our results shows that continuous drug infusion is more effective than bolus injection in the loss of tumor density.