Forager with intermittent rest: Better for survival?

We study the fate of a forager who searches for food performing a random walk on lattices. The forager consumes the available food on the site it visits and leaves it depleted but can survive up to S steps without food. We introduce the concept of intermittent rest in the dynamics which allows the forager to rest with probability p upon consumption of food. The parameter p significantly affects the lifetime of the forager, showing that the intermittent rest can be beneficial for the forager for chosen parameter values. The study of various other quantities reveals interesting scaling behavior with p and also departure from usual diffusive behavior for 0.5