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 proportionate to prey. Academics are already paying attention to new types of refuge concepts. Prey-predator interaction has become a prominent issue in recent biomathematical 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 focus our study on the question of existence and uniqueness and show a generalized stability. Note that this representation also allows us to generalize the results obtained recently in the literature. Furthermore, we have studied the numerical algorithm for the suggested problem. The paper is ended by two examples illustrating our results.
