On persistence of chemical reaction networks with time-dependent kinetics and no global conservation laws

New checkable criteria for persistence of chemical reaction networks are proposed, which extend those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying, thus incorporating the effects of external signals, and also relax the assumption of existence of global conservation laws, thus allowing for inflows (production) and outflows (degradation). As an illustration, a hypoxia network is analyzed.