Cancer growth and evolutionary games; choosing the right model for including an Allee effect

The current state of the art for treating cancer is using the maximum tolerated dose (MTD) of one or more cytotoxic agents. The goal is to drive the cancer cell population to extinction and therefore cure the patient. However, this strategy might fail and the tumour relapses. Even worse, the relapsed tumour often becomes resistant to the applied chemotherapy. One possible and commonly used explanation for this failure is based on the heterogenetic nature of tumours, which consist of multiple cancer cell types competing for shared nutrients. This motivates modelling tumour growth in terms of competing species models.

Combining approaches from evolutionary game theory, dynamical systems, data science and stochastic differential equations, we propose a model that describes the deterministic nature of tumour growth and the stochastic nature of carcinogenesis (onset of cancer).