Deterministic vs CTMC vs SDE models

These approaches can describe related biological mechanisms at different mathematical levels.

Deterministic model

ODEs produce a single smooth trajectory for fixed initial conditions and parameters. They describe systematic population-level change but not intrinsic event-to-event variability.

CTMC model

A CTMC keeps discrete states and individual random events. Event times and event types are random, making extinction and other discrete outcomes natural.

SDE model

An SDE uses continuous state variables with continuous stochastic fluctuations. It can provide a useful diffusion approximation when population counts are sufficiently large and discrete jumps are relatively small.

Choosing a model

No representation is universally best. The appropriate choice depends on population size, the biological question, the importance of discrete events and the required computational detail.