  We present a mathematical model, based on ordinary differential equations,
for the evolution of solid tumors and their response to treatment. Specifically
the effects of a cytotoxic agent and a monoclonal antibody are included as
control term in the equations. The variables considered here are: the number of
cancerous cells sensitive to chemotherapy, the number of cancerous cells
resistant to chemotherapy, the degree of angiogenesis and the average intensity
of VEGF. The rules that govern the quantities mentioned above are based on a
geometrical argument: we approximate the tumor mass as a sphere and thus derive
basic formulae for the normoxic cells and for VEGF production. The monoclonal
antibody acts on VEGF and thus has in uence to the global degree of
angiogenesis. Numerical estimates on some of the parameters are performed in
order to match the main landmark in tumor progression and reaction to treatment
in the specific case of colorectal cancer.
