In this paper, the system comprises of a commensal (S1), two hosts S2 and S3 ie., S2 and S3 both benefit S1, without getting themselves effected either positively or adversely. Further S2 is a commensal of S3, S3 is a host of both S1, S2 and all the three species have limited resources. The basic equations for this model constitute as three first order non-linear ordinary difference equations. All possible equilibrium points are identified based on the model equations and criteria for their stability are discussed. Further the numerical solutions are computed for specific values of the various parameters and the initial conditions.

This paper deals with an investigation on discrete model of host commensal pair. The model comprises of a commensal (S1), a host (S2) that benefit S1, without getting effected either positively or adversely. The model is characterized by a couple of first order non-linear ordinary differential equations. In all, four equilibrium points of the model would exist and their stability criteria is discussed. The model would be stable if each of the eigen values is numerically less than one. Further the growth rates of the species are numerically estimated using Runge-Kutta fourth order scheme.