THE DYNAMICS OF AN ECO-TOXICANT-EPIDEMIOLOGICAL MODEL WITH THE IMPACT OF ALLEE-EFFECT AND MICHAELIS-MENTEN TYPE OF HARVESTING OF SUSCEPTIBLE PREDATORS

Abstract

In this research, a toxicant-epidemiological model has been constructed, with Allee effects and Michaelis–Menten-type harvesting on healthy predators, as well as food addition to healthy predator populations. It was assumed that preys were consumed by predators through The modified Holling Type II functional response. The existence, uniqueness, and boundedness of the solution were examined., both local and global stability conditions were established. The objective of this study was defined as the assessment of the system’s susceptibility to toxicity, In addition, the Allee effect and Michaelis-Menten-type nonlinear harvesting have an impact on the proposed system's stability. It was shown that these elements have a major impact on the regulation of system stability. Finally, numerical simulations were run in MATLAB to validate the analytical results.