This paper analyzes a cosmological model containing the fermion field, scalar field and vector field with Yukawa interaction. Such a model allows one to research the contribution of various types of matter to the dynamics of the universe. In flat, homogeneous, and isotropic space-time, this coupling can provide the acceleration expansion of the universe. Cosmological reconstruction of dynamical equations is obtained using hybrid solution. This solution is researched by cosmography and energy condition. In the model under study, a zero energy condition, a strong energy condition, and a dominant energy condition are satisfied, and a weak energy condition, which is not mandatory, is not satisfied. It is shown how the cosmographic parameters – the parameters of deceleration q, jerk j, and snap s – can be related to the hybrid value of the scale factor. The resulting analysis makes it possible to relate the model-independent results obtained from cosmography to theoretically substantiated assumptions of gravity. The total density and pressure of the energy of the gravitational field are found in the form of the sum of contributions, which are associated with the bosonic, fermionic, vector fields, as well as the Yukawa type potential. In the model under study, in the early epoch, the bosonic field is responsible for the accelerated regime. Fermionic and vector fields have a positive pressure value, and therefore slow down the accelerated expansion of the universe. At a later time, a transition to a slow mode occurs, as the total pressure tends to zero.

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