Pelican–Tilapia interaction in Salton sea: an eco-epidemiological model with strong Allee effect and additional food

Abstract

The effect of diseases in ecological system is an important issue from mathematical and experimental points of view. We have analysed the dynamic nature of an eco-epidemiological model consisting of susceptible Tilapia fish, infected Tilapia fish and their predator the Pelican birds. Again, the susceptible prey population is subjected to a strong Allee effect. Moreover, the provision of additional food to predator is one of the momentous concepts in the field of biological control. Beddington–DeAngelis-type functional response has been taken to represent the interaction between susceptible prey and predator, whereas predator consumes the infected prey as Volterra-type (Holling type I) functional response. Feeding on infected prey increases the death rate of predator and is regarded to contribute negative growth, whereas consumption of susceptible prey enhances predator growth rate and is regarded to contribute positive growth. It is assumed that the predator population has sufficient resistance power to overcome the effect of environmental toxicants and so they are free from transmission of infection. In this work, we have studied some basic properties, such as non-negativity, uniform boundedness, and stability criteria of all feasible equilibria. The existence of transcritical bifurcations has been observed around the planer equilibrium points taking the mortality rate of predator and transmission rate as bifurcation parameters. Also, we have incorporated gestation delay in the system to examine the changing nature of the delay parameter via Hopf bifurcation. Further, the formulae for direction, period, and the stability of bifurcating periodic solutions have been established. Several numerical simulations are illustrated using MATLAB to validate all the theoretical results.