Estimating Eradication Time and Probability in Stochastic Tumour Models

Cancer is a leading global cause of death, and biomedical research has long investigated carcinogenesis mechanisms and therapeutic strategies, often leveraging mathematical models. Low-dimensional models facilitate the description of tumour growth and the optimization of drug administration. Recently, Chemical Reaction Networks (CRNs) have enabled the integration of stochastic noise into tumour dynamics, offering an alternative to classical deterministic models. One intrinsic limitation of the deterministic approach is that tumour eradication can only occur asymptotically, i.e., over an infinite time horizon. Conversely, when the number of tumour cells becomes relatively low, the stochastic approach provides a more accurate description of the system and allows for the quantification of the eradication probability. In this note, we extend and refine existing methods for estimating the eradication probability and mean eradication time in stochastic tumour models. We then apply the results to a model of interest, for which stochastic simulations numerically confirm and validate the theoretical results.