Dynamics of a fractional-order eco-epidemic model with Allee effect and refuge on prey

Abstract

In this article, a fractional-order eco-epidemic model with Allee effect and prey refuge is studied. First we prove the existence and the uniqueness of solution of the proposed model. The non-negativity and the boundedness solutions are also shown. It is found that the model has four equilibrium points, namely the extinction of both prey and predator point (E₀), the disease-prey-free and predator-free point (E^∗), the predator-free point (˜E), and the coexistence point (ˆE). All equilibrium points are locally and globally asymptotically stable with conditions. Those analytical results are confirmed by our numerical simulations. As expected, our analytical and numerical simulations show that the Allee effect may induced the extinction of prey population. The prey refuge, particularly for the case of weak Allee effect, may reduce the possibility of prey extinction.