Solutions of weakly reversible chemical reaction networks are bounded and persistent

We present extensions to chemical reaction network theory which are relevant to the analysis of models of biochemical systems. We show that, for positive initial conditions, solutions of a weakly reversible chemical reaction network are bounded and remain in the positive orthant. Thus, weak reversibility implies persistence as conjectured by Martin Feinberg. Our result provides a qualitative criterion to establish that a biochemical network will not diverge or converge to the boundary, where some concentration levels are zero. It relies on checking structural properties of the graph of the reaction network solely. It can also be used to characterise certain bifurcations from stationary to oscillatory behaviour. We illustrate the use of our result through applications.