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

In this paper, the local bifurcation conditions that occur 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 E1,E2,E3,E4 and E5, a transcritical bifurcation can occur, a saddle-node bifurcation happened near E5. Pitchfork bifurcation was occurrences at E2,E3,E4 and E5. Moreover conditions for Hopf- bifurcation was studied near both of one disease stable point E3,E4 and E5 . About elucidation of the status of local bifurcation the associated of the set of hypothetical parameters with numerical results which assert our analytical results of this model.