Invariance is a crucial property for many mathematical models of biological or biomedical systems, meaning that the solutions necessarily take values within a given range. While invariance criteria are well-known for systems of ODEs and semilinear parabolic PDEs, such results are less known for stochastic systems. In fact, several recent stochastic model extensions violate this fundamental property.

We recall explicit invariance criteria for deterministic models and present their corresponding extensions in the stochastic framework. The results can be used to characterize the class of invariance preserving models, and hence, for model validation, which is illustrated in various biological examples.