Abstract
The research presents a qualitative investigation of a fractional-order consumer-resource system with the hunting cooperation interaction functional and an infection developed in the resources population. The existence of the equilibria is discussed where there are many scenarios that have been distinguished as the extinction of both populations, the extinction of the infection, the persistence of the infection, and the two populations. The influence of the hunting cooperation interaction functional is also investigated where it can influence the existence of equilibria and their stability. A proper numerical scheme is used for building a proper graphical representation for the goal of confirming the theoretical results.
Highlights
1 Introduction Interaction functional is the number of resources successfully hunted per predator consumer, and it highlights the degree of successfulness of the consumer attacks to the predators, the behavior of both resources and consumers
We look for the disease-free equilibrium (DFE) which is written as 3 = (N, S, 0), where (N, S) is the positive solution of the following system:
4 Conclusion We dealt in this research with the consumer-resource system where we investigated the influence of the hunting cooperation on the spread of the disease developed in the consumer population
Summary
Interaction functional is the number of resources (prey) successfully hunted per predator consumer, and it highlights the degree of successfulness of the consumer attacks to the predators, the behavior of both resources and consumers. One of the first interaction functionals is the Holling type functional response where he proposes three different interaction functionals for modeling different behavior of some animals. His functionals were used widely, see for example the papers [1–4]. The main remark for Holling interaction functional is the dependence of the behavior of the resources population, which has been named the prey dependent interaction functional. The dependence can be on the consumer population there are some works that model this case as Hassell–Varley intermingling functional [5, 6], ratio-dependent intermingling functional [7], Beddington–DeAngelis intermingling functional [8], Crowley–Martin intermingling functional [9], and fractional calculus or different applications [10–34]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
