Accounting for dimensional differences in stochastic domain invasion with applications to precancerous cell removal

We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, stochastically simulated populations invade with a dimension dependent wave speed that can be over twice as fast as their deterministic analogues. Although the wave speed can be analytically derived in the cases of small domains, the probabilistic state space grows exponentially and, thus, we use numeric simulation and curve fitting to predict limiting dynamics. •We have generated a framework for a simple discrete invasion model, which can be solved analytically providing a complete solution.•In large domain cases, such a complete solution is impractical and we provide stochastic simulations (code provided for free on Github) demonstrating how the invasion rate can be extracted from ensemble statistics.•Stochastic invasions are fundamentally different from their deterministic analogues. Specifically, stochastic population can invade faster and their invasion rate depends on the size of domain they are invading.•We have been able to extract a healthy precancerous cell elimination rate. This can be potentially used to predict if patients have impaired pancreatic functions and are, thus, at a higher risk of pancreatic cancer.