Preventing evolutionary rescue in cancer.

Extinction therapy aims to eradicate tumours by optimally scheduling multiple treatment strikes to exploit the vulnerability of small cell populations to stochastic extinction. This concept was recently shown to be theoretically sound but has not been subjected to thorough mathematical analysis. Here we obtain quantitative estimates of tumour extinction probabilities using a deterministic analytical model and a stochastic simulation model of two-strike extinction therapy, based on evolutionary rescue theory. We find that the optimal time for the second strike is when the tumour is close to its minimum size before relapse. Given that this exact time point may be difficult to determine in practice, we show that striking slightly after the relapse has begun is typically better than switching too early. We further reveal and explain how demographic and environmental parameters influence the treatment outcome. Surprisingly, a low dose in the first strike paired with a high dose in the second is shown to be optimal. As one of the first investigations of extinction therapy, our work establishes a foundation for further theoretical and experimental studies of this promising evolutionarily-informed cancer treatment strategy.