Mathematical Modelling of Extinction Therapy: Preventing Evolutionary Rescue in Cancer Populations

Abstract

Evolutionary therapies for cancer understand malignancies as adapting populations under Darwinian selection. They use concepts from ecology and evolutionary biology to deal with the emergence of resistance in these malignancies – a big problem in cancer treatments. Extinction Therapy (ET) is an evolutionary therapy that aims for the complete eradication of the tumour. It fights the emergence of resistance with the smart and effective use of drugs/treatments to exploit the vulnerability of a small or declining population using multiple strikes (in the form of drugs, surgery, etc). In other words, extinction therapy “kicks the tumour while it’s down”. In this thesis, we model ET analytically using evolutionary rescue theory and run stochastic simulations to understand the behaviour of a cancer population undergoing ET. We also perform predictive mathematical modelling to aid the design and analysis of future experiments in ET. We find that the timing of subsequent strikes (after the primary therapy) is a very important determinant of the extinction probability. We calculate the optimal timing for these strikes and show how it changes with other model parameters. This work is one of the first few models of ET and sets the stage for future analytical and computational work in the field.