(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
In ecology, it is of great significance to research the influence of gestation period on the dynamics of eco-epidemiology. In the paper, we establish and explore a delayed predator-pest model with disease in pest. We first analyze the existence and local stability of each equilibrium of the model. Then, we investigate the existence of Hopf bifurcation at the coexistence equilibrium. Moreover, we calculate the normal form to examine the properties of Hopf bifurcation. Some numerical simulations are conducted to verify the theoretical results obtained and explore how the delay affects the biomass of pest. Our findings may contribute to a better understanding of the mechanisms of interaction between species in eco-epidemiology. At the same time, this study also provides an insightful perspective into the control of pests in ecosystems.