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 dynamicsÂ is studied with gestation delay in predator and incubation delay in disease transmission alongÂ with four different incidence functions. Our findings re-establish the claim of de Jong et al. that theÂ mass action and standard incidence functions behave in a similar fashion. In the absence of timedelay,Â the stability conditions of the equilibrium points are derived in terms of basic reproductionÂ numbers. We observe that disease has a stabilization effect. Further, we study the stability dynamicsÂ 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 analyticalresults are illustrated by numerical simulations.