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If host-specific equilibrium mean burden has a gamma distribution, conditional Poisson distributions produce a Poisson-gamma mixture, hence a negative binomial distribution. With mean $m$ and shape $k$, its zero-burden probability is $(1+m/k{)}^{-k}$. Decreasing $k$ increases aggregation: a smaller infected-host prevalence can accompany the same mean burden and more heavily infected individuals.

A prion disease of cattle. A positive surveillance test is an observed diagnostic outcome, whose frequency need not equal true infection prevalence unless test performance and sampling are accounted for.

The within-host parasite burden is the number of parasites, or a specified parasite-load measure, carried by one host. A population's mean burden and its infected-host prevalence are different summaries of the burden distribution.