Models of Finite Population with Interaction

Abstract

We now want to model the interaction between individuals in our population, so that the resulting process will no longer be a branching process. We consider in this chapter a continuous time model for a finite population with interaction, in which each individual, independently of the others, gives birth naturally at rate b and dies naturally at rate d. Moreover, we suppose that each individual gives birth and dies because of interaction with others at rates which depend upon the current population size. We exclude multiple births at any given time and we define the interaction rule through a continuous function f which again satisfies