We develop a deterministic predator–prey compartmental model to investigate the impact of their velocities on their interactions. Prey hides in a refuge area and comes out of this area when predation pressure declines. To avoid predation, prey can limit their velocity. For antipredator behaviour, we examined that prey mortality increases when either predator or prey velocity increases while raising antipredator behaviour increases prey density. We proved that predator free equilibrium is globally asymptotically stable and co-existing equilibrium will be globally stable under certain conditions. We find that transcritical bifurcations occur at predator-free equilibrium at the certain value of the death rate of the predator.
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