Community and Ecology Volume 1 Issue 1 (2023) doi: 10.59429/ce.v1i1.105 Received: 4 August 2023 Accepted: 7 October 2023 Available online: 4 December 2023 Copyright © 2023 by author(s). Community and Ecology is published by Arts and Science Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), permitting distribution and reproduction in any medium, provided the original work is cited. Original Research Article Habitat complexity of a discrete predator-prey model with Hassell-Varley type functional response S. Kundu 1 , J. Alzabut 2,3* , M. E. Samei 4 , H. Khan 5 1 Department of Mathematics, School of Advanced Sciences, VIT-AP University, Andhra Pradesh-522237, India 2 Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia 3 Department of Industrial Engineering, OSTI˙M Technical University, 06374 Ankara, Tu¨rkiye 4 Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran 5 Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper 18000, Khyber Pakhtunkhwa, Pakistan *Corresponding Author: soumenkundu75@gmail.com (S. Kundu), jalzabut@psu.edu.sa;jehad.alzabut@ostimteknik.edu.tr (J. Alzabut), mesamei@basu.ac.ir, mesamei@gmail.com (M.E. Samei), hasibkhan13@yahoo.com (H. Khan). Abstract: Prey-predator models with a refuge effect are particularly significant in ecology. The two common conceptions of refuge in the literature are continual refuge and refuge pro-portionate to prey. Academics are already paying attention to new types of refuge concepts. Prey-predator interaction has become a prominent issue in recent biomathe-matical studies due to its environmental influence. In this paper, the habitat complexity of a predator-prey model with Hassell-Varley type functional response is considered. For this, we focused our study on the question of existence and uniqueness in Sec. 2. And Sec. 3 is devoted to show a generalized stability. Note that this representation also al-lows us to generalize the results obtained recently in the literature. In Sec. 4, we have studied the numerical algorithm for the suggested problem. The paper is ended by two examples illustrating our results. Keywords: Predator-prey model, Hassell-Varley type functional response. 1. Introduction of the model In ecology, prey-predator models featuring a refuge effect are extremely important. In the available literature, the most prominent notions of refuge are constant refuge and refuge proportionate to prey. New forms of refuge concepts are already drawing academics’ attention. Because of its impact on the environment, prey-predator interaction has become a hot topic in the contemporary biomathematical studies. Many researchers have worked in investigatingvarious aspects of the dynamical behaviour of this subject matter in ecology, as well as the accompanying growth of population models. Some prey populations benefit from natural protection in the form of refuge dimensions. In other cases, several aspects allow for a longer prey-predator contact, lowering the risk of extinction owing to predation. Many scholars in the discrete area of waste concepts have studied this phenomenon extensively. We refer for reference to the work in [1–5] .