Stability Study of a Ratio-Dependent Eco-epidemiology Model of the Salton Sea Using the Optimal Derivative

In this paper, we proposed a study on a ratio-dependent model which describes the evolution of tilapia and pelican population in the Salton Sea. This largest lake of California is now facing problems due to its massive fish and bird mortality. The model is defined by three non-linear differential equations consisting of susceptible Tilapia fish, infected Tilapia fish and their predator, the Pelican. The aim of this paper was to present a parametric analysis of the stability and global dynamics near the origin of a ratio-dependant predator–prey system arising in halieutic, using the Optimal Derivative. This method was introduced by Arino–Benouaz and can be applied when the classical linearization cannot be used at the origin. We also studied the stability of this model in the vicinity of the positive interior equilibrium E^* using the same method of the optimal derivative. Some computer simulations were presented to illustrate the possibilities given by this method.