Analysis of a fractional-order prey-predator model with prey refuge and predator harvest using the consumption number: Holling type III functional response

Abstract In this article, we study a fractional-order prey-predator model incorporating prey refuge and predator harvesting, employing a Holling type III functional response. The model’s dynamics are explored using the consumption number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:math> {C}_{0} , providing a comprehensive understanding of its ecological implications. We establish the existence and uniqueness of the solution, ensuring the model’s mathematical robustness. Stability analysis is conducted to determine the conditions under which the system remains in equilibrium. Sensitivity analysis is performed to assess the importance of various parameters on the system’s behaviour with respect to the consumption number. Additionally, we investigate the occurrence of transcritical bifurcations, utilizing the prey refuge as a bifurcation parameter. Numerical simulations are carried out to illustrate the theoretical results and to provide deeper insights into the model’s dynamics. Our findings contribute to the understanding of fractional-order systems in ecological modelling and offer valuable perspectives on the management of predator-prey interactions in the presence of prey refuge and predator harvesting.