Dynamics of a delayed eco-epidemic model with disease in the prey

Resumen

This paper presents the mathematical analysis of a delayed eco-epidemic model that incorporates the effect of disease within the prey population. The stability of the model, both with and without delay, is analyzed. The Hopf bifurcation of the model is discussed by considering the time delay as a bifurcation parameter. Moreover, a behavioral change is observed in the system as it moves from a stable to an unstable state when the delay parameter crosses the threshold value, leading to a Hopf bifurcation from positive equilibrium. In addition, the stochastic stability of the model at the positive equilibrium is investigated. To demonstrate the validity of the theoretical analysis, some numerical simulations are presented.