Fractional model of prey-predator interactions in a reserved area with a competitive and toxic environment

Abstract

In this work, a mathematical approach is used to analyze the dynamics of a fractional-order predator-prey model with two effort functions in an environment that is both competitive and toxic. It is assumed that there are two major prey and predator groups; prey groups, moreover, occupy two different zones, one that is protected and the other not so. Susceptible predators are assumed to have access to both zones, infected predators do not have access to the reserved zone. Therefore, susceptible predators seek prey species in both the reserved and free zones. We first demonstrate the bounds of the solution. The existence is then verified. We will then turn to examining the local and the global stability using the Lyapunov method. As a final point, we will use numerical simulations to confirm our results and to verify the population’s response to prey consumption in the reserved region.