Dynamical complexity of a delay-induced eco-epidemic model with Beddington–DeAngelis incidence rate

Abstract

Present article has proposed a general eco-epidemic model with disease in predator population subject to Beddington–DeAngelis type incidence rate with the significance of fear in prey individuals and also analyzed the impact of external food supply to the sound predator. As an additional factor in representing the interplay amongst the predator and prey species, the Holling type-II functional response in the context of intra-specific competition within the prey species is taken into consideration. The model dynamics is studied by employing discrete time-delay in prey and gestation delay in predator in order to generate more authentic and natural dynamics. Positivity, uniform boundedness, and uniform persistence of the solutions for the model system have been explained analytically. Furthermore, the extinction criteria of the predator population have been explored and also illustrated by numerical simulations. For the non-delayed model, the existence and stability conditions of all conceivable critical points are investigated associated with the model parameters. The basic fundamental bifurcation assessments of the model reveal the formation of local bifurcations (Hopf-bifurcation and transcritical bifurcation) and provide the parametric region for occurrence of Bautin bifurcation and Gavrilov–Guckenheimer bifurcation. It is also reported that the provision of supplementary food to the sound predator may enable to remove the infection more promptly. Afterward, the stability dynamics of the coexistence state for different configurations of the delay factors have been scrutinized, as well as the delay parameters may produce oscillations via Hopf-bifurcation if they exceed some threshold value. But, when the gestation delay has been incorporated only in infected predators, no critical point can be obtained at which the Hopf-bifurcation takes place for the considered parameter values. Most of the theoretical discoveries have been certified through several numerical experiments constructed with the application of MATLAB and MATCONT.