In the proposed model with interaction between dark energy and dark matter, we consider cosmological scenarios with different equations of state (w d ) for dark energy. For both constant and variable equation of state, we analyze solutions for dark energy and dark matter in seven variants of the model. We investigate exact analytic solutions for w d = constant equation of state, and several variants of the model for variable w d . These scenarios are tested with the current astronomical data from Type Ia Supernovae, baryon acoustic oscillations, Hubble parameter H(z) and the cosmic microwave background radiation. Finally, we make a statistical comparison of our interacting model with ΛCDM as well as with some other well known non-interacting cosmological models. The current accelerated expansion of the universe ascertained from several astronomical sources [1][2][3][4][5][6][7] is one of the appealing fields of research in modern cosmology. To explain such accelerated expansion, either one needs some hypothetical dark energy fluid in the framework of general relativity or claims direct modifications into the gravitational sector leading to several modified gravity theories. However, a large number of observational data favor the existence of ΛCDM-cosmology where the cosmological constant fluid acts as a hypothetical dark energy fluid occupying almost two third of the total energy density of the universe and the cold dark matter (CDM) fluid is responsible for the structure formation of the universe. Nevertheless, the cosmological constant problem [8] and the cosmic coincidence problem [9] associated with the ΛCDM cosmology lead to several alternative descriptions aiming to decode the dynamics of the universe, such as the dynamical dark energy models, modified gravity models, and some others. For a comprehensive discussions on such models and their effects on the dynamics of the universe, we refer [10].Amongst several dark energy and modified gravity models, interacting dark energy models have gained significant attention due to having a reasonable explanation to the cosmic coincidence problem. A number of investigations in this direction have been performed during last couple of years [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Recently, a series of analysis shows that the current observational data prefer a nonzero interaction in the dark sector [28][29][30][31][32][33]. On the other hand, the dark sector's interaction may alleviate the current tension on local value of the Hubble constant and on σ 8 as well [31,32,[34][35][36]. Further, it has been discussed that some appropriate choice of an interaction between the dark components can influence effectively on the perturbation analysis which results in quite no- * Electronic address: span@iiserkol.ac.in † Electronic address: Sharov.GS@tversu.ru table differences in the lowest multipoles of the cosmic microwave background spectrum [37,38]. And sometimes it is possible to address the phantom universe [39][40][41][42][43][44] by a non...