The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative

In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency.

Automated summary

This research explores the influence of an infectious disease on the evolution of ecological species using a computational predator-prey model of fractional order. It is found that predators exhibit cooperative hunting behavior, and the transmission rate of the infection affects the evolution of predator-prey interactions. Graphical representations of the mathematical results are provided through a precise numerical scheme.