Many biological phenomena can be modelled using SDEs or other stochastic models. For example, disease transmission models which keep track of the numbers of infected $I$ and susceptible $S$ individuals in a population. Stochastic models can capture the observed phenomenon that $S$ and $I$ are typically negatively correlated (because, when an individual becomes infected, $I$ increases by $1$ and $S$ decreases by $1$). Not something that can easily be modelled deterministically.

More generally, compartmental models for biological populations, with processes such as disease transmission, births, deaths, etc. can typically be modelled using something like a discrete state space continuous time process. Such populations are typically subject to both demographic and environmental stochasticity. As the population size increases, demographic stochasticity decreases but environmental stochasticity doesn't - it's for larger populations that applications for SDEs are typically found. For example this article handles large populations using a SDE model which is constructed as a limit of a discrete state space continuous time Markov process. Also, this book, An Introduction to Stochastic Processes with Applications to Biology by Linda Allen, has a chapter on biological applications of SDEs.

Many biological phenomena can be modelled using SDEs or other stochastic models. For example, disease transmission models which keep track of the numbers of infected $I$ and susceptible $S$ individuals in a population. Stochastic models can capture the observed phenomenon that $S$ and $I$ are typically negatively correlated (because, when an individual becomes infected, $I$ increases by $1$ and $S$ decreases by $1$). Not something that can easily be modelled deterministically.

More generally, compartmental models for biological populations, with processes such as disease transmission, births, deaths, etc. can typically be modelled using something like a discrete state space continuous time process. Such populations are typically subject to both demographic and environmental stochasticity. As the population size increases, demographic stochasticity decreases but environmental stochasticity doesn't - it's for larger populations that applications for SDEs are typically found. For example this article handles large populations using a SDE model which is constructed as a limit of a discrete state space continuous time Markov process.

For a general comparison of deterministic and stochastic models in the context of disease transmission, see this book, Mathematical Tools for Understanding Infectious Disease Dynamics by Odo Diekmann, Hans Heesterbeek, and Tom Britton.

Also, this book, An Introduction to Stochastic Processes with Applications to Biology by Linda Allen, has a chapter on biological applications of SDEs.

Many biological phenomena can be modelled using SDEs or other stochastic models. For example, disease transmission models which keep track of the numbers of infected $I$ and susceptible $S$ individuals in a population. Stochastic models can capture the observed phenomenon that $S$ and $I$ are typically negatively correlated (because, when an individual becomes infected, $S$ increases by $1$ and $I$ decreases by $1$). Not something that can easily be modelled deterministically.

More generally, compartmental models for biological populations, with processes such as disease transmission, births, deaths, etc. can typically be modelled using something like a discrete state space continuous time process. Such populations are typically subject to both demographic and environmental stochasticity. As the population size increases, demographic stochasticity decreases but environmental stochasticity doesn't - it's for larger populations that applications for SDEs are typically found. For example this article handles large populations using a SDE model which is constructed as a limit of a discrete state space continuous time Markov process. Also, this book, An Introduction to Stochastic Processes with Applications to Biology by Linda Allen, has a chapter on biological applications of SDEs.

Many biological phenomena can be modelled using SDEs or other stochastic models. For example, disease transmission models which keep track of the numbers of infected $I$ and susceptible $S$ individuals in a population. Stochastic models can capture the observed phenomenon that $S$ and $I$ are typically negatively correlated (because, when an individual becomes infected, $I$ increases by $1$ and $S$ decreases by $1$). Not something that can easily be modelled deterministically.

More generally, compartmental models for biological populations, with processes such as disease transmission, births, deaths, etc. can typically be modelled using something like a discrete state space continuous time process. Such populations are typically subject to both demographic and environmental stochasticity. As the population size increases, demographic stochasticity decreases but environmental stochasticity doesn't - it's for larger populations that applications for SDEs are typically found. For example this article handles large populations using a SDE model which is constructed as a limit of a discrete state space continuous time Markov process. Also, this book, An Introduction to Stochastic Processes with Applications to Biology by Linda Allen, has a chapter on biological applications of SDEs.