# Farr's Law

by Raywat Deonandan, PhD

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00:01 Let's talk now about Farr's law.

00:03 This was put forth by Dr. Farr in the 19th century.

00:08 And he was instrumental in exploring how to use observations of death to better understand epidemics.

00:17 So, Farr's said some interesting things, one of which was, "The death rate is a fact; anything beyond this is an inference." What he meant by this was that when you're observing infections in a population, you only know the cases that you are detecting.

00:35 You don't know the ones who didn't present themselves for testing.

00:38 There is a detection bias at play here.

00:41 We are usually underestimating the true burden of infection in the population.

00:47 We also never know when infection curve has actually shifted in real time, because we can't really test that well.

00:56 And there are delays and lags.

00:58 But Dr. Farr argued, we always know pretty well about death.

01:06 And death is such a serious endeavor that usually the healthcare system is aware of it.

01:12 So, we've made the observation that epidemic events rise and fall in roughly symmetrical patterns.

01:20 That means that the rate of decline of an epidemic, meaning its infection, incidence rate, is going to look a lot like its rate of increase before we got to the peak.

01:33 So, in other words, you can use a bell curve to approximate the shape of the rate of infection in a population.

01:44 Now, he sent a famous letter in 1840, to talk about his theories about smallpox.

01:48 I won't go through the details of the letter.

01:51 But the takeaway is that he noticed that the smallpox incident rate was increasing regularly until it's stopped, and then it decreased.

02:02 And he noticed that the rate of increase looked a lot like the rate of decrease almost step by step.

02:07 There was symmetry in the death rate and the incidence rate.

02:12 And he concluded from this that we can use this symmetry to predict when an epidemic is going to wane.

02:22 So, that brought up this thing called Farr's law, which is not really a law, it's just an observation.

02:27 Farr's law simply says that, once the peak infection has been reached, it will roughly follow the same symmetrical pattern on the downward slope.

02:37 So, this incident, cumulative incident curve, or rather the incidence rate curve will look like a bell shaped.

02:49 The thing is, deaths tend to lag infections.

02:53 Because it takes time.

02:55 You can be infected for several days, you become hospitalized, get sicker, and then you die.

03:02 So, if you were to look at the curve, describing deaths in a population versus the curves describing incident rate, they will be separated.

03:13 They will be a part because the deaths come later.

03:16 They are lagging, but both will be symmetrical.

03:20 So, Dr. Farr was suggesting that by observing the deaths, you can start to make some guesses about the incidence rate.

03:29 So, once the deaths start declining, and you can observe the deaths, you can be confident that the incidence rate in the community has also started declining.

03:39 And you can do some mathematical investigations to backfill the data, and therefore predict when the epidemic is likely to end.

03:51 Now, Farr's law isn't a law, as I mentioned.

03:54 It's just an interesting rule of thumb we could use to make models.

03:58 It's only really valid if all other things are equal.

04:03 Things like incubation time and other dynamics in the population.

04:08 When used to break AIDS deaths, for example, it really failed because the underlying infection processes the transmission dynamics of AIDS were very different.

04:19 So, on the left, there is a projection of HIV/AIDS done in 1990, of when we thought the epidemic would wane based upon Farr's law.

04:32 The actual curve looked a little more dire.

04:36 So, Farr's law did not serve us well here.

04:39 It showed that in the case of HIV/AIDS in the USA, symmetry was not observed.

The lecture Farr's Law by Raywat Deonandan, PhD is from the course Pandemics.

### Included Quiz Questions

1. Infections and deaths
2. Incidence and prevalence
3. Mortality and morbidity
4. Health and disease
5. Age and weight
1. It assumes the underlying infection processes/transmission dynamics of diseases are equal.
2. It assumes no one in the population is dying.
3. It assumes no one in the population is being born.
4. It assumes the infection rate grows faster than it declines.
5. It assumes the death rate and infection rate begin to grow at the same time.

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