Cosmic coincidence problem in interacting holographic dark energy models

•An appropriate interaction between HDE and DM is checked.•By using the numerical simulation parameters of the model are determined.•The transition from accelerated phase to decelerated one of the universe and coincidence problem are discussed. It is well known fact that almost the cosmological models for dark energy are suppressed by the coincidence problem. It is worth while studying holographic dark energy model which requires considering the interaction between dark energy and dark matter. In this paper we propose a method for determining parameters of the models so as for the transition redshift zt and the present deceleration parameter q0 to agree with the previous study by means of numerical simulation. By considering the variation of coincidence parameter with the redshift based on the proposed models, we demonstrate that α-model is the most appropriate to explain coincidence problem. Also, this work shows that the direction of flow must be from dark energy to dark matter.