Simulation of stochastic hybrid systems with switching and reflecting boundaries

Modeling and simulation of biochemical systems are important tasks because they can provide insights into complicated systems where traditional experimentation is expensive or impossible. Stochastic hybrid systems are an ideal modeling paradigm for biochemical systems because they combine continuous and discrete dynamics in a stochastic framework. Simulation of these systems is difficult because of the inherent error which is introduced near the boundaries. In this work we develop a method for stochastic hybrid system simulation that explicitly considers switching and reflective boundaries. We also present a case study of the water/electrolyte balance system in humans and provide simulation results to demonstrate the usefulness of the improved simulation techniques.