Optimal chemotherapy: a case study with drug resistance, saturation effect, and toxicity

A system of differential equations for the control of tumour cell growth in a cycle-nonspecific chemotherapy is presented. A rate-of-kill term of saturation type, drug resistance, and toxicity are taken into account in a class of optimal control problems. Some results are obtained for general tumour cell growth rates. A detailed analysis is presented for the Malthusian cell growth, which shows a variety of optimal treatments according to the values of the model parameters and initial tumour level.