Kinetic equations modelling population dynamics

This paper deals with the analysis of a class of models of population dynam ics with competition and kinetic interactions. Several models are proposed to describe the dynamics of large populations of individuals undergoing kin etic (stochastic) interactions which modify the states of the interacting p air. Models are characterized by time and space structure, and are motivate d by recent research activity in mathematical immunology. The evolution equ ations are stated in terms of nonlinear integrodifferential equations which are similar to the Boltzmann equation. This paper deals with modelling and qualitative analysis of the related Cauchy problem.