Abstract
Invariance is a crucial property for many mathematical models of biological or biomedical systems,meaning that the solutions necessarily take values in a given range. Thisproperty reflects physical or biological constraints of the system and is independent ofthe model under consideration. While most classical deterministic models respectinvariance, many recent stochastic extensions violate thisfundamental property. Based on an invariance criterion for systems of stochasticdifferential equations we discuss several stochastic models exhibitingthis behavior and propose classes of modified, admissible models as possible resolutions.Numerical simulations are presented to illustrate the model behavior.
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