Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301The bifurcation analysis of an epidemiological model involving two diseases in predator21952217591510.22075/ijnaa.2022.5915ENAtheer JawadKadhimDepartment of Applied Science, University of Technology, IraqAzhar A. MajeedDepartment of Mathematics, College of Science, University of Baghdad, Baghdad, IraqJournal Article20211106In 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.https://ijnaa.semnan.ac.ir/article_5915_554d660b97b6d42438a296014dbcfb4d.pdf