Sustained Co-evolution in a Stochastic Model of the Cancer-Immune Interaction

The dynamical interaction between a growing cancer population and the adaptive immune system generates diverse evolutionary trajectories which ultimately result in tumor clearance or immune escape. Here, we create a simple mathematical model coupling T-cell recognition with an evolving cancer population which may randomly produce evasive subclones, imparting transient protection against the effector T-cells. We demonstrate that T-cell turnover declines and evasion rates together explain differential probabilities in early incidence data for almost all cancer types. Fitting the model to TRACERx evolutionary data argues in favor of substantial and sustained immune pressure exerted on a developing tumor, suggesting that measured incidence is a small proportion of all cancer initiation events. Most generally, dynamical models promise to increase our quantitative understanding of many immune escape contexts, with applications to cancer and intracellular pathogenic infections.