Understanding the Role of Intraspecific Disease Transmission and Quarantine on the Dynamics of Eco-Epidemiological Fractional Order Model

Abstract

An eco-epidemiological model involving competition regarding the predator and quarantine on infected prey is studied. The prey is divided into three compartments, namely susceptible, infected, and quarantine prey, while the predator only attacks the infected prey due to its weak condition caused by disease. To include the memory effect, the Caputo fractional derivative is employed. The model is validated by showing the existence, uniqueness, non-negativity, and boundedness of the solution. Three equilibrium points are obtained, namely predator-disease-free, predator-free-endemic, and predator-endemic points, which, respectively, represent the extinction of both predator and disease, the extinction of predator only, and the existence of all compartments. The local and global stability properties are investigated using the Matignon condition and the Lyapunov direct method. The numerical simulations using a predictor–corrector scheme are provided not only to confirm the analytical findings but also to explore more the dynamical behaviors, such as the impact of intraspecific competition, memory effect, and the occurrence of bifurcations.