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

Document Type : Research Paper


1 Department of Applied Science, University of Technology, Iraq

2 Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq


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 $E_1,E_2,E_3,E_4$  and $E_5$, a transcritical bifurcation can occur, 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 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.