= Epidemic curve
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.<Principles of Epidemiology in Public Health Practice by the Centers for Disease Control and Prevention>[Lesson 1, section 11, Epidemic Patterns: onset-time histograms and outbreak patterns]{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 is
$$
\lambda_{\rm onset}(t)=\int_0^\infty\lambda(t-u)f(u)\,du.
$$
This <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.
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