Patch Use under Predation Hazard: Foraging behavior in a Simple Stochastic Environment

I have developed a stochastic dynamic programming model of the situation envisioned by the marginal value theorem, however I have treated prey encounter as a stochastic event, included a consideration of predation hazard and incorporated the use of a refuge. Unlike the marginal value theorem, in my model the forager's objective function is to avoid death, not to maximize its long term rate of energy gain. The model is solved numerically and the resulting optimal policy (strategy for utilizing patches) is then used in computer simulations to generate distributions of predicted patch-residence times. I solve the model to predict differences caused by changes in the parameter values