  We develop a rigorous formalism for the description of the kinetic evolution
of interacting entities modeling systems in mathematical biology within the
framework of the evolution of marginal observables. For this purpose we
construct the mean field asymptotic behavior of a solution of the Cauchy
problem of the dual BBGKY hierarchy for marginal observables of the dynamical
systems based on the Markov jump processes, exhibiting the intrinsic properties
of the living entities. The constructed scaling limit is governed by the set of
recurrence evolution equations, namely by the dual Vlasov-type hierarchy.
Moreover, the relationships of the dual Vlasov hierarchy for the limit marginal
observables with the Vlasov-type kinetic equation is established.
