On the existence of the positive steady states of weakly reversible deficiency-one mass action systems

•The existence of steady states of mass action systems is of key importance.•We investigate in this paper weakly reversible deficiency-one mass action systems.•We prove that such systems always has a positive steady state. In this paper we prove that there exists a positive steady state in each positive stoichiometric class for every weakly reversible deficiency-one mass action system. This qualitative property does not depend on the values of the rate coefficients. Since not all weakly reversible deficiency-one mass action systems satisfy the assumptions of the Deficiency-One Theorem, our result contributes to the theory of deficiency-one mass action systems.