Farr's law is a law formulated by Dr. William Farr when he made the observation that epidemic events rise and fall in a roughly symmetrical pattern. The time-evolution behavior could be captured by a single mathematical formula that could be approximated by a

bell-shaped curve In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is t ...

Background

In 1840, Farr submitted a letter to the ''Annual Report of the Registrar General of Births, Deaths and Marriages in England''. In that letter, he applied mathematics to the records of deaths during a recent smallpox epidemic, proposing that:

"If the latent cause of epidemics cannot be discovered, the mode in which it operates may be investigated. The laws of its action may be determined by observation, as well as the circumstances in which epidemics arise, or by which they may be controlled."

He showed that during the smallpox epidemic, a plot of the number of deaths per quarter followed a roughly bell-shaped or " normal curve", and that recent epidemics of other diseases had followed a similar pattern.(Farr, 1840), p. 98. "Table (q) exhibits the progress of four more epidemic diseases in the metropolis, — measles, typhus, hooping-cough, and scarlatina, — which have not yet been effectively controlled by medical science. They exhibit the same regularity, but the laws which govern their course will be more conveniently discussed when the abstract of the observations has been extended over another year."

References

Epidemiology Statistical algorithms {{Med-stub