Non-explosivity of endotactic stochastic reaction systems

Abstract

Reaction networks have been widely used as generic models in diverse areas of applied science, such as biology, chemistry, ecology, epidemiology, and computer science. Reaction networks incorporating noisy effect are modelled as continuous time Markov chains (CTMC), and are called stochastic reaction systems. Non-explosivity is a concept that characterizes regularity of CTMCs. In this paper, we study non-explosivity of stochastic reaction systems, in the sense of their underlying CTMCs. By constructing a simple linear Lyapunov function, we obtain non-explosivity for a class of endotactic stochastic reaction systems containing second-order endotactic stochastic mass-action systems as a subset. As a consequence, we prove that every bimolecular weakly reversible stochastic mass-action system is non-explosive. We apply our results to diverse models in biochemistry, epidemiology, ecology, and synthetic biology in the literature.