Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis

. Objective: Cancer stem cells have been identified as the growth root for various malignant tumours and are thought to be responsible for cancer recurrence following treatment. Materials and methods: Here, a predictive mathematical model for the cancer stem cell hypothesis is used to understand tumour responses to chemotherapeutic drugs and judge the efficacy of treatments in arresting tumour growth. The impact of varying drug efficacies on different abnormal cell populations is investigated through the kinetics associated with their decline in response to therapy. Results and conclusions: The model predicts the clinically established ‘dandelion phenomenon’ and suggests that the best response to chemotherapy occurs when a drug targets abnormal stem cells. We compare continuous and periodic drug infusion. For the latter, we examine the relative importance of the drug cell‐kill rate and the mean time between successive therapies, to identify the key attributes for successful treatment.