  In a predator-prey interaction, many factors are present that affect the
growth of the species, either positively or negatively. Fear of predation is
such a factor that causes psychological stress in a prey species, so their
overall growth starts to decline. In this work, a predator-prey model is
proposed where the prey species faces a reduction in their growth out of fear,
and the predator is also provided with an alternative food source that helps
the prey to hide in a safer place. The dynamics produce a wide range of
interesting results, including the significance of the presence of a certain
amount of fear or even prey refuge for population coexistence. The analysis is
extended later to the nonlocal model to analyze how the non-equilibrium
phenomena influence the dynamical behaviour. It is observed through numerical
simulations that the scope of pattern formation reduces with the increase of
fear level in the spatio-temporal model, whereas the incorporation of nonlocal
interaction further increases the chance of species colonization.
