Mathematical Modelling of Tumour Dormancy

Department of Mathematics, UCL, London WC1E 6BT, UK

Corresponding author: kpage@math.ucl.ac.uk

Abstract

Many tumours undergo periods in which they apparently do not grow but remain at a roughly constant size for extended periods. This is termed tumour dormancy. The mechanisms responsible for dormancy include failure to develop an internal blood supply, individual tumour cells exiting the cell cycle and a balance between the tumour and the immune response to it. Tumour dormancy is of considerable importance in the natural history of cancer. In many cancers, and in particular in breast cancer, recurrence can occur many years after surgery to remove the primary tumour, following a long period of occult disease. Mathematical modelling suggested that continuous growth of tumours was incompatible with data of the times of recurrence in breast cancer, suggesting that tumour dormancy was a common phenomenon. Modelling has also been applied to understanding the mechanisms responsible for dormancy, how they can be manipulated and the implications for cancer therapy. Here, the literature on mathematical modelling of tumour dormancy is reviewed. In conclusion, promising future directions for research are discussed.