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A common-source outbreak affects people exposed to the same source of an infectious agent or toxin. A brief exposure gives a point-source pattern; a continuing or intermittent source can produce a broader or repeated pattern. This classifies the exposure mechanism, whereas a propagated outbreak involves transmission between successive hosts.^[ref]

In an illustrative point-exposure model, everyone is exposed at time zero but the incubation period varies between people. Symptom onsets spread over subsequent days even though exposure was simultaneous. If the incubation-time probability density function is $f(u)$ and $M$ exposed people eventually develop symptoms, the expected onset count per unit time is $Mf(t)$, assuming complete observation. The width of the epidemic curve then reflects individual delays rather than the duration of exposure.

An investigator therefore combines an epidemic curve with individual exposure histories and comparison groups. A single peak does not by itself establish a shared source, and a shared source can be followed by secondary propagated outbreaks.

An epidemic is disease occurrence above the expected level for a specified population, place and period. The comparison needs a baseline: an increase in incidence alone does not establish an epidemic, and cases need not be increasing throughout an outbreak. For example, if a hypothetical community normally records two cases per week, a fall from twenty cases to eight still leaves occurrence above that baseline.^[ref]

An epidemic curve plots cases against time, commonly using symptom onset. A common-source outbreak reflects shared exposure, whereas a propagated outbreak reflects transmission between hosts; these mechanisms can also combine.^[ref]

In a closed homogeneous SIR model, let $s$ and $i$ be susceptible and infectious fractions, with transmission coefficient $\beta$ and recovery rate $\gamma >0$. The equations giveFor $i>0$, the infectious compartment grows when the effective reproduction number ${\mathcal{R}}_{0}s$ exceeds one and shrinks below one. This is a dynamical growth threshold, distinct from comparison with an observed baseline. An epidemic invasion threshold concerns growth after a small introduction; a final size relation for an epidemic concerns total susceptible depletion. An endemic equilibrium instead has continuing transmission balanced by the population's other processes.

An epidemic curve is a histogram of cases against a chosen event time, commonly symptom onset. Its axes must specify the case definition, event date and bin width. It helps compare an observed outbreak with common-source outbreak and propagated outbreak mechanisms.^[ref]

Counts per bin differ from an incidence rate: a rate additionally needs the population or person-time at risk. Replacing daily bins by weekly bins also changes bar heights and can hide short peaks.

The displayed timing is delayed from infection. In a model with completely observed symptomatic infections, infection intensity $\lambda (t)$ and an independent, stationary incubation period density $f(u)$, the expected symptom-onset intensity isThis convolution follows by adding infections at each earlier time weighted by their onset-delay probability. Reporting delay would introduce another observation process. A peak in recorded reports therefore need not coincide with a peak in infections; reconstructing transmission requires the relevant delay and ascertainment model.

A propagated outbreak spreads through transmission from infected hosts to further hosts, producing successive infection generations. The transmission route can involve direct contact, a shared vehicle or a vector. Separated peaks in an epidemic curve can be suggestive, but overlapping transmission generations need not give visibly separated waves.^[ref]

For an elementary branching approximation, let $I_k$ count infections in generation $k$ and suppose each infectious host generates an average $R$ new infections while susceptibility remains effectively unchanged. Then $\mathbb{E}[I_{k+1}\mid I_k]=R{I}_k$ and $\mathbb{E}{I}_k=R^k{I}_0$. Starting from one infection with $R=2$ gives expected generation sizes $1,2,4,8$. This is a mean calculation, not a guarantee that every introduction survives: random transmission can produce extinction.

The generation interval controls the timing between infection generations. Depletion of susceptible hosts, changing contacts or interventions can change the effective reproduction number, invalidating the constant-$R$ approximation. A common-source outbreak can seed this mechanism, so distinguishing the initial source from later transmission is part of reconstructing the outbreak.