Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population

This manuscript aims to consider a variety of fractional predator-prey models in the presence of an infection developed in the predator population. The crowding behavior plays an essential role in some species surviving, which is a useful strategy for defending the inside group prey. The purpose of considering the fractional-order-derivative is to study the memory effects on the mutual interactions, which has been confirmed to be an intrinsic feature of a dynamic biological system. From the perspective of mathematical results, the local behavior of the equilibrium points, and the existence of Hopf bifurcation are obtained. Besides, the influence of some crucial parameters as memory rate, herd shape, the infection rate in determining the asymptotic behavior of prey and predator are investigated. Further, an efficient numerical technique has been employed to illustrate some illustrative representations for numerical approximation for the solutions. This iterative scheme has been designed using the fundamental theorem of calculus in the fractional sense, and linear polynomial interpolation. (c) 2020 Elsevier Ltd. All rights reserved.