Abstract

This paper presents and analyses a modified Leslie-Gower-eco-toxicant-epidemiological model for a food chain that includes one prey, a susceptible predator, an infected predator, and a top predator, integrating fear with cooperative hunting and nonlinear harvesting, using the Leslie-Gower growth and predation function. Prey species are directly exposed to toxins from the susceptible predator and cooperative hunting from the susceptible predator, while the susceptible predator faces predation and cooperative hunting from the top predator. The top predator also experiences the Leslie-Gower growth function, as well as nonlinear harvesting and environmental toxins. The boundedness and qualitative nature of the model have been proven. All equilibrium points of this model were found. All the necessary conditions for achieving local stability of the equilibrium points were identified, leading to the conclusion that all points , where  are locally stable. Additionally, a global stability study was conducted using appropriate Lyapunov functions. In the end, a numerical simulation was conducted for a single set of parameters and varying initial conditions to verify the analytical results and assess the impact of fear and toxins from consumption or the environment, cooperation, nonlinear harvesting, and the Leslie-Gower function on the dynamics of the proposed model.