A mathematical model for growth of solid tumors and combination therapy with an application to colorectal cancer

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.