The bifurcation analysis of an epidemiological model involving two diseases in predator

In this paper, the local bifurcation conditions that occurrence near each of the equilibrium points of the eco-epidemiological system of one prey population apparition with two diseases in the same population of predator have been studied and analyzed, near E-1, E-2, E-3, E-4 and E-5, a transcritical bifurcation can occurred, a saddle-node bifurcation happened near E-5. Pitchfork bifurcation was occurrences at E-2, E-3, E-4 and E-5. Moreover conditions for Hopf- bifurcation was studied near both of one disease stable point E-3, E-4 and E-5. About elucidation the status of local bifurcation the associated of the set of hypothetical of parameters with numerical results which assert our analytical results of this model.