A class of individual–based models

Abstract

We discuss a class of mathematical models  of biological populations at microscopic level — i.e. at the level of interacting individuals of the population. The class leads to partially integral Markov semigroups. We state the conditions guaranteeing the asymptotic stability. In particular under some assumption it may be shown that any, even non–factorized, initial probability density tends in the evolution to a factorized equilibrium probability density. We discuss possible applications of the general theory - redistribution of individuals, thermal denaturation of DNA, and tendon healing process ...