Optimal control for a stochastic model of cancer chemotherapy.

Chemotherapy is useful in a number of cancers to reduce or eliminate residual disease. When used in this way the objective is to maximise the likelihood that the cancer will be eliminated. In this article, we extend a stochastic model of chemotherapy for cancer to incorporate its concomitant effect on the normal system and derive overall measures of outcome. The model includes the development of drug resistance and is sufficiently flexible to include a variety of tumour and normal system growth functions. The model is then applied to situations previously examined in the literature and it is shown that early intensification is a common feature of successful regimens in situations where drug resistance is likely. The model is also applied to data collected from clinical trials analysing the effect of adriamycin, and cyclophosphamide, methotrexate and 5-flourouracil (CMF) therapy in the treatment of operable breast cancer. The model is able to mimic the data and provides a description of the optimal regimen.