Many biological systems follow a deterministic model which is typically described in terms of a difference equation or differential equation. Often the deterministic model has a stochastic analogue based on birth-and-death processes, diffusion processes or branching processes. For example, in population models where the population size never becomes too small, a deterministic approach may provide sufficient biological understanding. However, if the population size is small, then a stochastic analysis is vital. Among the many biological applications, we stress the areas of epidemiology and population dynamics.