Impact of fear on a delayed eco-epidemiological model for migratory birds

Abstract In this paper, a delayed eco-epidemiological model including susceptible migratory birds, infected migratory birds and predator population is proposed by us. The interaction between predator and prey is represented by functional response of Leslie–Gower Holling-type II. Fear effect is considered in the model. We assume that the growth rate and activity of prey population can be reduced because of fear effect of predator, and this series of behaviors will indirectly slow down the spread of diseases. Positivity, boundedness, persistence criterion, and stability of equilibrium points of the system are analyzed. Transcritical bifurcation and Hopf-bifurcation respect to important parameters of the system have been discussed both analytically and numerically (e.g. fear of predator, disease transmission rate of prey, and delay). Numerical simulation results show that fear can not only eliminate the oscillation behavior caused by high disease transmission rate and long delay in the model system, but also eliminate the disease.