Hopf bifurcation and stability in a delay model with disease in prey and predator species

In this paper, a delay predator−prey model is proposed with logistic growth in the prey population that includes an SIS infection in the prey and predator population. After dealing with disease in the prey population, in the predator population is considered. We prove the existence of Hopf bifurcation for this systems by analysing characteristic equations. Important thresholds R1 and R2 are identified. Our theoretical study indicates that threshold R1 is important when a transmissible disease runs among the prey population. Threshold R2 is important when the predators are disease