The Bifurcation and Persistence Conditions of an Eco-Toxicant-Epidemiological Model with the Impact of Michaelis-Menten Type of Harvesting of Susceptible Predators and Allee-effect of Species

This paper investigates the conditions for local bifurcation in a toxicological ecology model containing a susceptible predator, an infected predator, and a prey, with strong Allee-effect and toxicity for both the susceptible predator and the prey, non-linear harvesting of the Michaelis-Menten type in the susceptible predator group, and treatment for the infected predator. The model was studied after transformation into a dimensionless System. The model possesses eleven equilibrium points (equilibria), with the saddle-node bifurcation occurring around the equilibrium points . Additionally, transcritical and pitchfork bifurcations transpired at all other equilibrium points. The Hopf bifurcation of the positive point was studied, and the conditions for this point were determined. The persistence was studied numerically, and its points were determined. The numerical results of a set of hypothetical parameters supported our analytical results for demonstrating local bifurcation and its persistence using C++ and MATLAB software to further refine the results.