= Fluid limit of the SIRS Markov chain
{title2=$\dot s=-\lambda si+\nu r,\quad\dot i=\lambda si-\gamma i,\quad\dot r=\gamma i-\nu r$}
For convergent initial proportions, the scaled <SIRS Markov chain> converges uniformly in probability on each fixed finite interval to the solution of these equations. The <Poisson time-change representation of a Markov chain> writes it as its integrated drift plus centered Poisson errors. Bounded rates, Poisson concentration and the <Gronwall inequality> control the error. This finite-time limit does not by itself justify an approximation over time intervals growing with the population size.
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