Modeling the Allee effects induced by cost of predation fear and its carry-over effects

•We investigate the role of fear and its carry-over effects in a prey-predator model.•Predation-driven Allee effects can be observed in our model with type I response.•Single species model shows three types of growth (logistic, weak and strong Allee).•Fear and its carry-over effects have important role even with type I response.•Paradox of enrichment can be observed in our model with type I functional response.