A fluid model replaces discrete counts by continuous quantities whose evolution follows averaged large-scale drifts. A heuristic drift calculation motivates such a model; proving a fluid limit requires a separate convergence argument.
A nonnegative fluid model drains in finite time if all its coordinates approach zero at a finite terminal time. A ratio-based ordinary differential equation can become undefined at that endpoint; an absorbing extension is an additional modeling convention.
A fluid limit is a scaling limit of a stochastic process obtained by scaling space and time so that random fluctuations vanish and a deterministic trajectory remains. It can justify a fluid model when the required convergence conditions hold.
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