  Mathematical modeling based on time-delay differential equations is an
important tool to study the role of delay in biological systems and to evaluate
its impact on the asymptotic behavior of their dynamics. Delays are indeed
found in many biological, physical, and engineering systems and are a
consequence of the limited speed at which physiological, chemical, or
biological processes are transmitted from one place to another. Since real
biological systems are always subject to perturbations that are not fully
understood or cannot be explicitly modeled, stochastic delay differential
systems (SDDEs) provide a more realistic approximation to these models. In this
work, we study the predator-prey system considering three time delay models:
one deterministic and two types of stochastic models. Our numerical results
show relevant differences in their respective asymptotic behaviors.
