• Josh Schiffer

March 25, 2020

A paper from Sunetra Gupta (Oxford) that may have profound implications on the pandemic. Essentially, they use the simplest form of an epidemic model (an SIR model) to predict that the first reported death in a city may signal that 1000s of people have already been infected (as opposed to 100s as I had previously thought). By the time things look really bad in hospitals (Lombardy, New York), they predict that herd immunity is already setting in. However, the degree of herd immunity depends on the parameter in the model which estimates the proportion of people at risk of severe disease, and this parameter is currently unknown.

In other words, while we have reasonable estimates of case fatality rate (case = sick enough to seek care and get diagnosed), we really NEED estimates of infection fatality rate (infection = everyone who gets infected, diagnosis or no diagnosis, inclusive of people with no symptoms at all). I knew this from the beginning and wrote about it in early posts. However, I confess to underestimating the effect that percentage of asymptomatic cases could have on herd immunity, which in retrospect is sort of a silly oversight.

Figure 3 is the key. If parameter p is lower, this means a lower proportion of infected people have any chance of getting sick (higher % are asymptomatic). As this number goes down, the total number infected goes up, the number of “susceptibles” (y-axis) goes down, meaning that herd immunity has set in. If herd immunity exceeds a certain threshold, then that particularly city is a bad garden for the virus to grow any further (ie, R<1).

If true, the implications are substantial:

  • First, with this degree of silent spread in the community, only herculean physical distancing efforts will lower R<1 before herd immunity is achieved because so many infected people do not even know it. Makes me wonder about the mild cough I developed today.

  • Second, if herd immunity is already setting in, then there may not be a large second wave in places that were hit really hard. Ironically, East Asia may be more at risk for a heavy second wave than Northern Italy.

  • Third, on a personal level, there is a higher chance you have already been infected.

  • Fourth, the Imperial college report which has had a major effect on policy making in the UK & US barely mentions herd immunity so this might have been a key omission.

I am still digesting this information, both in terms of the paper’s methodology and its implications on the pandemic and the best way to optimize social distancing. I am lacking a strong opinion. Other than this….

This paper points to the urgent need for serologic surveys in broad segments of the population to understand the burden of asymptomatic infection. In the US, Seattle is the best spot for this as we were a bit early relative to the rest of the country. Serologic tests look for antibodies which represent a history of infection with a virus. We can use this method to estimate the total % infected in a community, and then extrapolate the true infection fatality rate. We can also determine whether asymptomatic infection is widespread.

This puzzle will be answered very soon. Several countries now have serologic assays. Given the extraordinary pace of information, I am going to gamble and guess that there will be headlines in the next 72 hours. (Or not)


It is a time to be thankful for the many people who are quietly pulling their weight at some personal risk. Clinical & non-clinical hospital workers, farmers, grocers, the police force, and many others. All quiet heroes....


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