Influence of the presence of a pathogen and leachate recirculation on a bacterial competition

Abstract

In this paper, we proposed and analyzed a five-dimensional system of ordinary differential equations modeling the competition of two competing bacteria in a chemostat under the influence of the leachate recirculation and in the presence of a pathogen associated only with the bacteria 1. We suppose that the nutriment is present into two forms, soluble and insoluble nutriment, and both two forms are continuously added to the chemostat. The proposed model takes the form of an “SI” epidemic model and uses general increasing growth functions and general increasing incidence rate. It admits multiple equilibria that we give the conditions under which we assure both the existence and the local stability of each equilibrium point. The possibility of periodic trajectory was excluded, and the uniform persistence of both types of bacteria was proved. Finally, several numerical examples confirming the theoretical findings are given.