In the 18th century, Daniel Bernoulli—the son, nephew and brother of mathematicians Johann, Jacob and Nicolaus II Bernoulli, respectively—made one of the first great mathematical contributions to infectious disease control. While formally trained in medicine, Bernoulli is known for his research in biomechanics, hydrodynamics, economics, and astronomy. He also played an important role in the eradication of smallpox from Europe, which was likely introduced there in the early 16th century and was endemic (maintained constantly) by the 18th century. Variolation is an inoculation technique whereby a scab or pus from an individual with a mild smallpox infection is introduced into the nose or mouth of healthy individuals. This practice began as early as 1000 AD in China and India and was introduced into England in 1717, where it was initially controversial. While variolation reduced the mortality probability of infected individuals from 30% to 1%, there was a small chance that the procedure would lead to death from a full-blown case of smallpox.

Bernoulli developed a mathematical model with which he argued that the gain from variolation in life expectancy through the eradication of smallpox far out-weighed associated risks … Using overall survivorship estimates calculated by Edmund Halley (of comet fame), he then used equation (2) to predict the mortality rates in every age class in a steady-state population with a birth class of size 1300. Inoculation via variolation of all newborns would confer widespread immunity, yet entail some mortality due to variolation-induced smallpox. Bernoulli compared the annual mortality rates and average life expectancy predicted by his model to those predicted assuming universal inoculation and found that variolation saves lives even if the mortality rate associated with variolation is quite high (with his parameters, as high as 10.6%).

Bernoulli’s calculations clarified the benefits of widespread inoculation even when there are significant risks. England began widely administering variolation in the 1750’s, and upon the development of the smallpox vaccine in 1796, mandated the inoculation of all infants. Thanks to these efforts, smallpox was eradicated from England by the end of the 19th century. (more)

The method was first used in China and the Middle East before it was introduced into England and North America in the 1720s in the face of some opposition. The method is no longer used today. It was replaced by smallpox vaccine, a safer alternative. This in turn led to the development of the many vaccines now available against other diseases. (more)

For the last few weeks I’ve spent a lot of time trying to more carefully make the case for deliberate infection plus immediate isolation, via the effect of flattening the curve to avoid overwhelming the medical system. (See my model, and models by Zach Hess and Kevin Simler.) Especially via exposing the voluntary young and healthy while isolating the old and sick. However, a few days ago I realized there’s a much stronger reason for deliberate infection: mortality varies greatly by the size of initial infectious dose, and deliberate infection allows for much lower doses. As the above indicates, this practice is a thousand years old.

As soon as your body notices an infection, it immediately tries to grow a response while the virus tries to grow itself. From then on, it is a race to see which can grow biggest fastest. And the virus gets a big advantage in this race if its initial dose of infecting virus is larger. This effect is widely known and acknowledged by experts, and it is one of the main rationales given for wearing masks, gloves etc. That’s not just to cut the chance of an infection, but also to cut the initial dose.

Many studies have found big effects of initial virus dose on many outcomes. For covid19 we know that patients with more viruses in their blood (higher “viral load”) show more severe symptoms. And for other viruses we see that such patients also die more often. But in terms of the most direct sort of evidence, I’ve only been able to find these empirical studies connecting initial virus dose size to human death rates:

1. Deliberate infection with low doses of smallpox is reported to have cut death rates of infected from 30% to 1-2%, or from 1 in 5-6 to 1 in 50.

2. Among 126 African kids infected with measles, the first in a family to get it had a 14x lower death rate relative to other kids in the same families. Presumably that first kid gets it from outside the family, via a low dose, while other kids in the same family are infected at home, via a larger dose.

3. In a Hong Kong high-rise, one resident infected many others with SARS, possibly via aerosols, but those who lived physically closer got a higher dose, and saw 3x the death rate.

4. This New Yorker article mentions 2 more cases, but I can’t yet find cites to studies.

The first case, of a deliberate low dose infection, saw effects in the range 8-30x, while the other two cases of observing a natural difference in dose saw effects of 3x and 14x, giving only lower bounds on deliberate dose effects. So while we can’t at all be sure of the deliberate dose effect for Covid19, we have good reason to expect it to be at least a factor of 3. And maybe a factor of 30 or more.

I hope to include this dose effect in my spreadsheet model soon, but clearly this effect adds greatly to other benefits of deliberate infection, including not just flattening the curve, but also creating good places for controlled experiments and medical training.

The articles quoted above says that this policy was opposed and controversial back in the 1700s, and I’ve seen how many react badly when I’ve tweeted it. Twitter recently locked the account that linked to an op-ed making a similar suggestion. Many have told me privately that I should not write on this in public. But it seems to be far too important to suppress.

We are today proud of having anesthetics, and would think it cruel to do surgery on someone without it. But long ago they had no anesthetics, and so had to be cruel. And today we’d choose to be cruel again if surgery were essential but anesthetics were unavailable, such as on a battlefield. Similarly, humanity is proud of having replaced variolation (i.e, deliberate low-dose infection) with less-cruel vaccines. But in this crisis we don’t have vaccines, while variolation remains quite feasible. We should thus stand ready to swallow our pride, and use variolation if that’s our best remaining option. (As others have been also been suggesting.)

Dose effects seem good candidates for explaining much of the wide variation in observed Covid19 death rates across regions and subpopulations, in addition to age, comorbidity, selection effects, virus strain variations, genetic susceptibility differences, and overwhelming of medical systems. Medical workers plausibly get high doses, and the first few cases in a region would be from travelers who were likely infected with low doses. Places where large families live together closely would have higher doses. And lockdowns that limit non-family contact may similarly induce higher doses, raising death rates.

If lockdowns increase typical infection doses, that makes more difficult the tradeoff between on the one hand (a) that higher-dose mortality cost, (b) large costs of lockdown economic and social disruption, and (c) risks from centralizing power and losing freedoms, and on the other hand benefits of: (1) more time to grow medical resources, (2) flattening the curve of medical demand over time, and (3) hope for a complete suppression until a strong medical treatment arrives, so that most are never infected.

This tradeoff isn’t obvious to me; I’d like to see more detailed cost-benefit analyses. (The very idea of which apparently offends many.) But the bigger the mortality cuts from deliberate infection, the more I’m tempted to take that bird in the hand, rather than gamble on the two bush birds of being able to achieve even larger gains via complete suppression until a vaccine.

We now sit at a great pandemic poker table, playing a huge hand with nature. We could fold and lose the ante we’ve put in, accepting many regrettable deaths due to deliberate infection. Or we can push in 3-30 times as many chips as we have so far, in the form of human lives at risk, hoping for full suppression until strong treatment, just to win back our ante (no bigger pot at stake). Do you feel lucky, punk? I don’t.

Added 8Sep: More data suggesting dose effects: