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On the 3rd of July, 1638, George Garrard  wrote Viscount Wentworth to tell him:

The Plague is in Cambridge; no Commencement at either of the Universities this year.

On October 2nd of that same year, Cambridge canceled all lectures. Even if history does not repeat (but historians do), one is tempted to look to the past for hints about the future.

From the Annals of Cambridge  (compiled by Charles Henry Cooper ) we learn that the plague combined with the residency requirements for a degree at Oxford, prompted a rush of Oxford students to Cambridge to obtain their Masters of Arts degree. We know this from an anonymous letter to Oxford’s Chancellor:

…..many of Batchelor of Arts of Oxford came this Year for their Degrees of Masters of Arts here, which this Year they could not obtain at Oxford, which I endeavored to prevent……..

This prompted a complaint to Cambridge. Its vice-chancellor replied,

I Pray receive this assurance from me, and I doubt not but the Practice of our University will make it good……

Oxford, in the meantime, maintained country homes for its scholars where they could hide from the Black Death. The plague lowered property values which allowed the colleges to expand their land holdings.

What effect on the intellectual life of the University? Anna Campbell’s 1931 book entitled `The Black Death and Men of Learning‘ estimates that about a third of European intellectual leaders perished during the plague and Universities were in a precarious position.

James Courtenay, writing in 1980  with access to more detailed data about Oxford suggests a less bleak outcome.

The mortality rate was not particularly high , either of brilliant or of marginal scholars and masters. The enrollment levels across the next few decades do not seem to have been seriously affected.

He notes an argument for a drop in the quality of higher education but that would have been a response to a drop in the quality of primary education.

The race to publish COVID-19 related papers is on, and I am already behind. Instead, I will repurpose a paper by Eduard Talamas and myself on networks and infections which is due out in GEB.

It is prompted by the following question: if you are given the option to distribute—without cost to you or anyone else—a perfectly safe but only moderately effective vaccine for a viral infection, should you? That we’ve posed it means the answer must be no or at least maybe not.

Unsurprisingly, it has to do with incentives. When the risk of becoming infected from contact declines, individuals tend to be less circumspect about coming into contact with others. This is risk compensation, first suggested by Charles Adams  in 1879 and popularized by Sam Peltzman in the 1970’s.

Therefore, the introduction of a vaccine has two effects. On the one hand, it reduces the probability that an individual becomes infected upon contact. On the other hand, it decreases individuals’ incentives to take costly measures to avoid contact. If the second effect outweighs the first, there will be an increase in infections upon the introduction of a moderately effective vaccine.

These are statements about infection rates not welfare. Individuals make trade-offs. In this case between the risk of infection and the costs of avoiding it. Therefore, observing that an individual’s infection probability will increase upon introduction of a partially effective vaccine is insufficient to argue against introduction.

In our paper, Eduard and I show that the introduction of a vaccine whose effectiveness falls below some threshold could make everyone worse off, even when each individual is perfectly rational and bears the full cost of becoming infected. If the vaccine is highly effective, this outcome is reversed. This is because risky interactions can be strategic complements. An individual’s optimal amount of risky interactions can be increasing in the amount of risky interactions that others take.

To illustrate, call two individuals that engage in risky interactions partners. Every risky interaction that Ann’s partner Bob has with Chloe affects Ann’s incentives to have risky interactions with Chloe in two countervailing ways. It increases Chloe’s infection probability. But it also increases the probability that Ann is infected conditional on Chloe being infected—because if Chloe is infected, chances are that Ann’s partner Bob is also infected. Given that a risky interaction between Ann and Chloe only increases the probability that Ann becomes infected when Chloe is infected and Ann is not, the combination of these effects can lead to an increase in Ann’s incentives to engage with Chloe and her partners when Bob engages with Chloe.

One might ask, given the huge trove of papers on epidemiological models, this effect must have been identified before and discussed? No, or at least not as far as we could tell. This is because we depart from from a standard feature of these models. We allow agents to strategically choose their partners— instead of only allowing them to choose the number of partners, and then having matches occur uniformly at random.

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