Stochastic vs. Deterministic Models for Systems with Delays

We consider population models with nodal delays which result in dynamical systems with delays. For small population models the appropriate models are discrete stochastic systems with delays. We consider these delay systems and present new theoretical and computational results for such systems. In particular, in this note we summarize results on the effects of different types of delays (a fixed delay and a random delay) on the dynamics of stochastic system as well as their relationship with each other in the context of a just-in-time network model. In addition, we numerically explore the corresponding deterministic approximations for the stochastic systems with these two different types of delays.