Where does incidence collide?

In epidemiology, incidence is the rate at which new cases of a disease or condition appear in a population over a period of time. It counts only cases that begin during the observation window, so it measures how fast a condition is arising, not how much of it is already present. Porta's A Dictionary of Epidemiology defines it in deliberate contrast with prevalence, which counts all existing cases at a point in time regardless of when they began. Incidence is usually reported as a proportion of the population at risk, or as a rate per unit of person-time such as cases per 1,000 person-years. The referent is a flow of new events into a population, timed and counted, and it is not the angle of a ray, the burden of a tax, or a point lying on a line.[1]

Unit

New cases per population at risk over time, often per person-time

Recovery means

Not applicable

Measured by

Counted from surveillance or cohort follow-up as new cases divided by the population at risk or the person-time accumulated

In public finance, tax incidence is the question of who actually bears the economic burden of a tax, as opposed to who is legally required to hand the money to the government. The party that remits the tax (statutory incidence) is often not the party whose income falls (economic incidence), because prices adjust until the burden settles on whichever side of the market can least avoid it. As a rule the load falls more heavily on the less elastic side of a transaction, so a tax on a good with few substitutes is paid largely by buyers whoever writes the cheque. Harberger's The Incidence of the Corporation Income Tax traced how a tax levied on companies is shifted through capital and labour markets to fall on people the statute never names. The referent is the final resting place of a tax burden in an economy, and it has nothing to do with new disease cases, reflected light, or points on a line.[2]

Unit

The share of a tax burden borne by each party, in money or welfare

Recovery means

Not applicable

Measured by

Estimated from how prices, wages, and returns shift after a tax, using elasticities of supply and demand or general-equilibrium models

In optics, the angle of incidence is the angle between an incoming ray of light and the normal, the line drawn perpendicular to the surface at the point where the ray strikes. It is measured from that normal, not from the surface itself, which is a frequent source of error. The law of reflection says the reflected ray leaves at an equal angle on the other side of the normal, and Snell's law relates the angle of incidence to the angle of refraction through the two media's refractive indices. Hecht's Optics sets out both laws and the geometry of the incident, reflected, and refracted rays. See also reflection and refraction, which describe what becomes of the ray once its angle of incidence is fixed. The referent is a geometric angle at a boundary, and it shares only its spelling with a rate of new disease cases, a tax burden, or a point lying on a line.[3]

Unit

An angle from the surface normal, in degrees or radians

Recovery means

Not applicable

Measured by

Read as the angle between the incident ray and the surface normal, using a protractor, goniometer, or optical bench

In geometry and graph theory, incidence is the bare relationship of a point lying on a line, or a vertex being an endpoint of an edge, with no notion of distance or angle attached. An incidence structure records only which points belong to which lines, and it can be written as an incidence matrix whose rows and columns are the two kinds of object and whose entries mark each touching pair with a one. Bondy and Murty's Graph Theory defines the vertex-edge incidence relation and the incidence matrix that encodes it. Because it keeps only what contains or touches what, incidence is among the most primitive relations in mathematics, underlying projective planes, combinatorial designs, and the structure of graphs. The referent is a pure containment relation between objects, and it is unrelated to new disease cases, a tax burden, or the angle of a ray.[4]

Unit

A yes-or-no relation between a point and a line, or a vertex and an edge

Recovery means

Not applicable

Measured by

Recorded as an incidence matrix or incidence list marking which points lie on which lines, or which vertices meet which edges