It has been demonstrated experimentally and theoretically that the dispersion coefficients of non-fluid particles in isotropic turbulent flows can exceed the dispersion coefficient of fluid particles. This "inertia effect" cannot be allowed for in eddy interaction models in which it has been shown that the long-time dispersion coefficient of non-fluid particles is always less than that of fluid particles. In the limit of infinitely heavy particles, the difference between the dispersion coefficients is due to the difference between the Lagrangian and Eulerian integral time scales tau(E) and tau(L), and it can be shown that tau(E) < tau(L) in existent eddy interaction models. In this paper, the relationship between tau(E) and tau(L) is investigated for a modified eddy interaction model for which it is possible that tau(E) > tau(L), which will lead to greater long-time dispersion of heavy non-fluid particles than of fluid particles. Numerical simulations are carried out to quantify the effect of the modifications on the dispersion of finite size particles.