On the derivation of macroscopic hyperbolic equations for binary multicellular growing mixtures

This paper presents an asymptotic theory, based on the hyperbolic scaling, for a large class of Boltzmann-type equations suitable to model the evolution of a binary mixture of multicellular systems in biology. The modelling approach is that of the kinetic theory for active particles. Time scaling related to cell movement and biological activity are shown to play a crucial role in determining the macroscopic equations corresponding to each case. Applications are focused on the immune competition.