A mathematical analysis of a competition and cooperation model between two enterprises with delay based on ecology theory: Case of Orange and Telmob in Burkina Faso

The work presented in this manuscript is part of the general framework of mathematical problems concerning the economics phenomenon modelling. The main objective is the formulation and study of a competition and cooperation model between two companies with delay based in ecology theory. This model describe the dynamic of two enterprises Orange and Telmob in Burkina Faso. We present some mathematical results concerning the solution existence, the stability of the model equilibria. Moreover the two enterprises are uniformly weakly persistent and the solution goes to a pseudo almost periodic solution if and only if $\mathcal{R}_{\theta} <1$. Some numerical simulations are performed using the economical values, are done to illustrate these results.