Mutual inhibition in presence of a virus in continuous culture

In this paper, we consider two species competing for a limiting substrate such that each species impedes the growth of the other one (Mutual inhibition) in presence of a virus inhibiting one bacterial species. A system of ordinary differential equations is proposed as a mathematical model for this competition. A detailed local qualitative analysis of the system is carried out. We proved that for a general nonlinear growth rates, the Competitive Exclusion Principle still valid, that at least one species goes extinct. For some cases where we have two locally stable equilibrium points, initial species concentrations are important in determining which is the winning species. Obtained results were confirmed by some numerical simulations using Matlab software.