Editing Stochastic process (section)

=== Applications in Biology ===

==== Population Dynamics ====
One of the primary applications of stochastic processes in biology is in '''[[population dynamics]]'''. In contrast to [[deterministic model]]s, which assume that populations change in predictable ways, stochastic models account for the inherent randomness in births, deaths, and migration. The '''[[birth-death process]]''',<ref name="Ross 2010">{{Cite book |last=Ross |first=Sheldon M. |title=Introduction to probability models |date=2010 |publisher=Elsevier |isbn=978-0-12-375686-2 |edition=10th |location=Amsterdam Heidelberg}}</ref> a simple stochastic model, describes how populations fluctuate over time due to random births and deaths. These models are particularly important when dealing with small populations, where random events can have large impacts, such as in the case of endangered species or small microbial populations.

Another example is the '''[[branching process]]''',<ref name="Ross 2010"/> which models the growth of a population where each individual reproduces independently. The branching process is often used to describe population extinction or explosion, particularly in epidemiology, where it can model the spread of infectious diseases within a population.