Stability and bifurcation analysis of an eco-epidemiological model with multiple delays

We propose and analyze an eco-epidemic model with disease in predator. The model dynamics is studied with gestation delay in predator and incubation delay in disease transmission along with four different incidence functions. Our findings re-establish the claim of de Jong et al. that the mass action and standard incidence functions behave in a similar fashion. In the absence of timedelay, the stability conditions of the equilibrium points are derived in terms of basic reproduction numbers. We observe that disease has a stabilization effect. Further, we study the stability dynamics of the interior equilibrium for various combinations of the delay factors and observe that the delay may produce oscillations through a Hopf bifurcation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Our analytical results are illustrated by numerical simulations.