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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.

Study of the distribution and determinants of health-related outcomes in populations. Incidence, recurrence and prevalence answer different questions and should not be exchanged when evaluating prevention.

A model in which a binary diagnostic outcome occurs when an underlying continuous liability exceeds a threshold. Genetic and environmental components can influence liability. Estimating liability-scale heritability requires assumptions about prevalence, ascertainment and the liability distribution; crude diagnostic concordance is not a continuous-trait correlation.

Two reasons are selection bias and unequal ascertainment.

The one-day slaughter-inspection yield isor 500 detections per million inspected adult cattle. The routine field detections correspond, using a stable herd size of five million, toper adult-cattle day, or 8 detections per million adult-cattle days. Therefore the numerical one-day comparison isThe annual field rate is $14600/(5\times 10^6)=0.00292$ per cattle-year; comparing the inspection probability directly with this annual proportion would mix observation periods. Applying the random inspection-sample proportion to all 150000 slaughtered adults would predict about 75 detected cases in that slaughter cohort. These arithmetic comparisons describe detection yields, not a 62.5-fold biological disease-risk difference: a cross-sectional inspection estimates a prevalence yield, whereas daily field reporting is an ascertainment rate over animal-time.

A microparasite typically multiplies within an infected host on a much shorter time scale than between-host transmission. A useful first model classifies hosts by infection status. A macroparasite, such as an adult parasitic worm, instead requires a count of parasites per host: two infected hosts can carry very different within-host parasite burdens. These are modelling distinctions rather than a rule determined only by an organism's physical size.

For a microparasite with no lasting immunity, a homogeneous SIS model isThe basic reproduction number is $\beta /\gamma$, and the prevalence $I/N$ describes the infected-host fraction. A SIR model adds an immune class, and a SEIR model adds a latent class. Contact structure, age, susceptibility, recovery rate and infectiousness can require several such classes. Then a next-generation matrix or operator, rather than a single averaged contact rate, sets the invasion threshold. Stochastic epidemic models are relevant to early extinction and finite populations; network or spatial models represent nonuniform contact opportunities.

For a simple macroparasite burden model, let $p_j$ be the fraction of hosts carrying $j$ adult worms. Assume acquisitions at rate $\lambda =\beta L$, independent adult-worm losses at rate $\mu j$, and a number $L$ of infective stages in a well-mixed environmental reservoir. The immigration-death worm-burden model hasThis birth-death process needs the burden distribution or its probability generating function, not just an infected/not-infected partition. Its mean $m={\sum }_{j}j{p}_j$ satisfies $\dot{m}=\beta L-\mu m$. With host number $N$ fixed and each adult producing infective stages at rate $\sigma$, one possible environmental closure isFor this asexual, unsaturated transmission approximation, one worm's basic reproduction number is $(\sigma /\mu )\beta N/(d_L+\beta N)$. Growth above the invasion threshold requires additional density regulation if a finite endemic burden is sought. Sex-dependent mating would change this closure.

With constant external exposure $\lambda$, the equilibrium burden follows a Poisson distribution with mean $m=\lambda /\mu$, giving infected-host prevalence $1-e^{-m}$. If exposure rates vary across hosts as a gamma distribution, the Poisson-gamma mixture gives a negative binomial distribution with mean $m$ and aggregation parameter $k$:The same mean burden can therefore coexist with very different prevalence and highly infected subgroups. Aggregation of macroparasite burdens affects treatment coverage, burden-dependent host mortality, immunity and parasite fecundity. For sexually reproducing worms, hosts need both sexes for fertile output; a mean alone may not determine it. With independent equally likely sexes and Poisson burden, the probability of both sexes is $(1-e^{-m/2}{)}^2$, illustrating mating-limited macroparasite transmission and its low-burden bottleneck.

Both microparasite and macroparasite models need heterogeneous exposure and host responses. The special extra difficulty for macroparasites is translating a distributed worm burden, and possibly worm sex or developmental stage, into transmission and host harm. Conversely, complicated within-host microparasite processes can also require more than a binary host state when the simple fast-within-host approximation fails.

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.