Intraguild Predation Model with Stage Structure and Cannibalism in Prey Population

Abstract

This paper concerns an intraguild predator model with stage structure and cannibalism in the prey population, where the prey population is divided into two stages, namely, a juvenile stage, and an adult stage. We investigated the dynamics of this model. We obtained the  quilibrium points, the conditions of existence, and the condition for stability using the  Jacobian matrix and Routh Hurwitz criterion. We use numerical simulation to illustrate the dynamics of the model over time. Furthermore, we illustrate the effects of the maturation rate on the adult prey population and the carrying capacity of the basal resources on the existence and stability region of the model. We also analysed the transcritical bifurcation with the maturation rate selected as the primary bifurcation parameter. We demonstrate herein that each equilibriumpoint undergoes stability switching of the equilibria with the change of maturation rate either from stable to unstable to stable, or unstable to stable to unstable. The obtained result indicates that a large maturation rate can lead to a system where the prey population can escape from predation yet negatively impacts the survival rate of basal resources in the ecosystem. Whereas, an intermediate maturation rate indicates that the species could co-exist whereby theoretically, it can ensure that the optimal predator population exists in the ecosystem. This is in parallel able to stabilise the effect of overpopulation of predators with competition factor. An ecosystem with all species coexists could ensure a healthy ecological interaction for a sustainable environment.