Modeling on Eco-System Consisting of Two Hosts-One Commensal with Mortality Rates for the Second and Third Species

Abstract

In this paper, the system comprises of two hosts S1, S2 and one commensal S3 ie., S1 and S2 both benefit S3, without getting themselves affected either positively or adversely. Further, S1 and S2 are neutral. Here all the three species posses limited resources. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex. The global stability of the system is established with the aid of suitably constructed Liapunov’s functions and the numerical solutions for the growth rate equations are computed using Runge-Kutta fourth order scheme.