Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together.