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Bifurcation of an eco-epidemiological model with a nonlinear incidence rate. (English) Zbl 1228.92075
Summary: A predator-prey system with disease in the prey is considered. Assuming that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria. By using bifurcation methods and techniques, we study Bogdanov-Takens bifurcations near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium are analyzed, and one or two limit cycles are also discussed.
##### MSC:
 92D40 Ecology 34C23 Bifurcation (ODE) 34C60 Qualitative investigation and simulation of models (ODE) 34D20 Stability of ODE 65C20 Models (numerical methods)