• Josh Schiffer

April 19, 2020

I hope everyone is doing well, keeping sane and enjoying extra time with family. An incredible amount of information has emerged in the last week and I can barely keep up. This still remains a fun project. I hope it is useful and very much appreciate the support from friends near and distant.


Revised R0. A colleague and friend Ruian Ke is senior author on a paper that is getting a great deal of attention to the tune of >10000 tweets. He predicts a higher R0 in Wuhan of 5.7 (95% confidence interval 3.8-8.9) than originally suggested.

As a starting point, I will point out that this is not such a big difference from other modeling groups. The Imperial College estimates ~4 for many European countries, pre-intervention (see the right panel pre-intervention in Figure 2). The 95% confidence intervals of the two groups overlap somewhat.

For Seattle, the Institute of Disease Modeling suggests a value of ~3.7 pre-social distancing (Figure 1)

Perhaps the outlier is the London School of Hygiene & Tropical Medicine giving estimates of 2-3 before social distancing in many countries (far left estimate of each panel, Figure 2 & 4).

So why do these models differ? And why does it matter? R0, as discussed previously, is the average number of people infected by a single person at the start of an epidemic before there is any herd immunity or intervention. R0<1 means no local epidemic. R0>1 means there is a high likelihood of local spread.

You can also assign each individual a “personal R0” which will be distributed around the population R0 to give you an idea of whether an epidemic is propagated by spread to a few people by many people, or a high rate spread to many people by a few people (super-spreader events).

R0 is important for two reasons. First, it is one of two variables which dictates the rate of exponential growth. For those with math allergies, another way to think of exponential growth is the time it takes for the number of cases to double at the beginning of an epidemic. The other key, and often overlooked, variable is the generation time which is the average time from being infected to infecting. Viruses differ. Measles has an extremely high R0 (~15) but a generation time of a couple of weeks. Influenza has a lower R0 (~1.5) but a narrow generation time of a few days. Both spread rapidly through non-immune populations but for different reasons.

The other reason R0 matters is that it determines the percent of the population that must be infected and/or immunized to generate herd immunity. The equation is 1 – 1/R0: if R0 is 1.5, like with influenza, then only ~33% of people need to be infected for herd immunity to predominate. For measles, the number is ~95%. It is therefore of consequence whether R0 is 2.5 or 5 for COVID, because it determines whether 60 or 80% will need to become infected before the rest are protected.

Before I move onto the reason why the papers are not in agreement, I want to emphasize that the percentages above are high estimates because the formula assumes homogeneous mixing of the population which is not reality. Age structuring suggests that some groups are more likely to avoid infection than others and will require less population level infection than others to gain herd immunity.

I also doubt whether R0 during the first wave is completely relevant for the second wave. We are a fundamentally changed species at the moment and some form of social distancing will remain a part of our fabric for the next 2 years. Our effective reproductive number (Reffective) before the second wave will undoubtedly be lower than R0 before the first wave. Fewer people will need to be infected for herd immunity to kick in.

Finally, herd immunity is gradual. Even if we do not achieve the threshold necessary for the epidemic to die out (Reffective <1), as we move towards this threshold the new rate of infections will already be slowing down considerably.

Now to the papers and why their results differ: one possibility is that the authors use different model structures. Imperial College has a detailed, very cool agent-based model that follows every theoretical case globally. It essentially an updated version of this flu model published many years ago. Check out the movies in the supplementary info (scroll to the bottom):

( The Los Alamos group uses a simplified, but equally valid system of differential equations that captures numbers but not spatial spread of the epidemic. Despite these huge dissimilarities, I do not think that the difference in estimated R0 values are due to the models themselves.

I also do not think that the difference has to do with assumptions about percent asymptomatic cases. This is a critical variable for assessing herd immunity. Yet, provided that the proportion of asymptomatic infectives remains stable over time, it does not impact estimates of exponential growth or R0.

Rather, I think the models arrive at different estimates for R0 based on different inputs for generation time (defined above). Remember, if a mathematician has a valid estimate for exponential growth rate and for generation time, then R0 can be back calculated. For the same rate of exponential growth, R0 can be increased by increasing the generation time and vice versa.

This is where things get tricky because different articles propose different generation times. This paper estimates an interval of ~4 days (directly from data) from 468 transmissions in China. However, these estimates are outside of Wuhan. Social distancing had already kicked in at this point and many infections occurred before people became symptomatic. This naturally lowers the generation time relative to Wuhan. The authors do a great job of acknowledging this and other limitations of their data.

This paper uses data from Shenzen and estimates a much longer serial interval (an approximation of generation time of 6.3 days). In the absence of isolation, the serial interval is even longer (8 days). The Los Alamos group used this longer serial interval as they felt it was more accurate and as a result estimated a higher R0.

This very cool paper uses transmission pairs to get at the number and estimates 5.8 days. Figure 1a in this paper is so useful. It highlights how shedding may relate to transmission, how the serial interval is estimated and shows influenza and SARS 2003 as examples. The relationship of the serial interval to incubation period (time from getting infected to having symptoms) demonstrates why some transmissions occur during the pre-symptomatic phase of COVID-19.

After getting somewhat deep in the weeds, I still am honestly not sure what the best estimate for R0 is. Even the authors of all 3 articles project wide 95% confidence intervals which overlap at their extremes. Overall, I do favor a longer mean serial interval and suspect that R0 is higher than the original estimates between 2 and 3.

What really matters at this point is the % infected that would be required for herd immunity. This value will depend on Reffective at the start of the second wave, not the original R0. I think this will vary from country to country and I have zero confidence in my own ability to estimate correct values. I would hazard a guess that if a region hits 50% infected, then herd immunity will be likely to impact local transmission in a very significant way.

We are not there yet.


IHME model. As I mentioned in a prior post, this model, which is being cited widely and used by policy makers, is not an epidemiologic model. It does not intend to capture the mechanisms underlying epidemics, which makes it hard to use as a tool to estimate the impact of key policies. It does not consider basic structural features of infectious diseases epidemiology such as R0 and the generation time.

I love IHME’s work in general, but do not think their COVID model is useful. I am glad some experts diplomatically agree.


Life for the next 2 years.This is a clever modeling paper which predicts second and third waves of infection through 2022. To limit the extent of subsequent outbreaks will require repeated periods of social distancing to prevent health care catastrophe. This conclusion is not new.

The novel twist is the use of past data from two widely circulating less virulent coronaviruses, OC43 and HKU1 as possible models for what will happen with SARS-CoV-2. The model predicts that subsequent new waves of COVID may have seasonality and be most fierce in the winter. Like most modeling papers which attempt to project the future, the models are limited by how much we do not know. Model projections could be radically altered by any of the following: misleading current estimates of the percentage of infected people who are asymptomatic, the availability and effectiveness of future treatments, cross immune protection between different coronaviruses, and duration and extent of immunity against COVID post-infection. Perhaps most obviously, we do not know if SARS-CoV-2 will really mimic OC43 and HKU1. Nevertheless, this model serves as a nice starting point to consider what comes next.

For a broader perspective, read the article below. Ed Yong is such a gifted writer and thinker. This piece is a mandatory read and re-read in 2 weeks. It highlights the sobering realities of reopening the economy, drug scarcity, economic hardship, the growing burden of non-COVID conditions remaining untreated, public transport as a form of mass crowding, lack of central government organization, and privacy, among other things. It is one of the signature essays of the pandemic, similar in its scope and thoughtfulness to the Hammer and the Dance piece by Tomas Pueyo.

I thought this paragraph on the limitations of serology in a low prevalence setting was particularly instructive. Even a great serology test will not guarantee that people can get back to work completely safely:

 “Consider the test produced by Cellex—the only one thus far with emergency use authorization from the FDA. The test has a 93.8 percent chance of correctly identifying people with antibodies against the new coronavirus, and a 95.6 percent chance of correctly identifying people who lack those antibodies. Those numbers sound great, but if only a minority of Americans have been infected, the test would return far more false positives than true ones. Put it this way: If you have a positive result, the odds that you actually have any relevant antibodies are roughly one in two if 5 percent of the U.S. has been infected, and just one in six if only 1 percent has been infected. Scientists can correct for these errors if they use serological tests to assess immunity in a population, but it’s much harder on a person-by-person basis.”


What is the best prevention strategy for the economy?Speaking of Tomas Pueyo, this is another tome that outlines a bipartisan policy plan for emerging from this in one piece. Chart 17b is fascinating. It demonstrates data from the 1918 influenza epidemic showing that cities with the longest implementation of social distancing generally had the lowest influenza mortality but also the smallest hit on the local number of jobs. Who knows if this correlative plot (not causation!) will carry forward to the modern economy? However, it is worth at least considering the possibility that stopping social distancing earlier, will not necessarily lead to the best economic outcome. The desire to help struggling businesses in the short term is noble, but may prove more harmful in the long run.


There is no widespread herd immunity yet. We need to disavow ourselves of this Pollyannish notion which could lead to destructive policy decisions.

Seroprevalence data is starting to emerge which is fantastic! Recall that serology tests measure antibodies against the virus (in blood) and give an estimate of the percent of a given population that have already been infected This data gives us an early insight about the true range of infection in a population and the mysteriously difficult to measure percent of asymptomatic cases.

First, from Santa Clara, an estimated population prevalence of 2.8%. This value is way too low for herd immunity but has generated intense interest as it suggests a high percentage of asymptomatic cases. The caveat is that even an excellent serology test may have a higher number of false positives than true positives when applied to a low prevalence population (like Santa Clara where infection is still uncommon): see Ed Yong’s explanation above. This is in contrast with New York or Madrid where a positive test is far more likely to be a true positive. Importantly, the proportion of false positives is extremely sensitive to even slight deviations in the performance ability of the antibody assay. Therefore, the Santa Clara numbers might be overestimates, but by how much is difficult to know.

First reported domestically in the Bandera County Courier (I think), in the hardest hit city in Germany, seroprevalence is 15%. This is high but not again not enough for herd immunity.

An astonishing 14% of asymptomatic pregnant women at Columbia in New York were positive by nasal swab at delivery. This is incredible and sobering. Given that this was by PCR and not serology, it does not include women who had past infection that they already cleared. Therefore, seroprevalence may be even higher in this section of the city. I still doubt that New York is in herd immunity territory. Incidentally, at UWMC in Seattle, we are screening women at deliveries and the % is really low who are positive.

I will add that it is reassuring that so few of these women were sick.

In summary, herd immunity is something we should be tracking. However, it is not yet a reality in most (?all) places. We are in this for much longer. This is a resource for serology testing for anyone interested. I am not keeping up with this research space at all.


Delay in therapeutic trials.This is an important article highlighting yet another government failure. There is a distinct lack of organization in how trials are being conceived, prioritized and performed. The diversity of medicines being tested is too low. The number of hydroxychloroquine trials is far too high (two well done studies would be plenty). Outbreaks are raging in too many cities without any studies being done. Far too many patients are receiving unproven treatments: in my view that includes anyone who is receiving hydroxychloroquine &/or azithromycin outside of a research study.

Few studies are being conducted in outpatients when there is an opportunity to nip the disease in the bud before it spirals out of control.

In short, there is no centralized organizational structure guiding this process. The expertise is available. Our country has a proud history of successful networks to address large problems within infectious diseases, HIV treatment & HIV vaccines being the best examples. Our failure to do this for COVID must be considered a direct result of cutting government programs for pandemic preparedness.

This is a beautifully designed and organized website started by colleagues David Spach and Gretchen Snoeyenbos at UW. In time, this will likely be a leading resource for guiding rational therapeutic decisions. Unfortunately, at the moment, the site highlights the disarray in the field, a pile of inadequately controlled studies which provide very limited evidence for rational clinical decision making. That is simply our reality at the moment but will hopefully soon change. Physicians are still practicing somewhat in the dark. We should definitely have more informative treatment data by this point.


Viral kinetics / antibody kinetics. A remarkable study of 67 patients in Chongqing showing the average viral loads, symptom load and antibody levels over time. Viral loads turned negative on an average of 14 days from nasal swabs, over 30 days in sputum and 20 days in stool with slight differences between severe and non-severe cases. They also show the timing of fever and cough, and that people start developing antibody responses 10-14 after infection. This is the type of data my group devours. I have been begging these scientists to share their data but no luck. So if you happen to know them and can out in a good word. :)

Early evidence suggests SARS Co-V-2 may be shed for a prolonged time though I have yet to see published papers beyond a month of sampling.

The issue of prolonged shedding is of great interest and importance. At the individual level, I doubt that prolonged shedders will become sick with high frequency and also doubt they are very infectious. However, even one infection event could re-ignite a local epidemic. Zika had this pattern as well in blood, semen and vaginal secretions but this did not turn out to be enough to sustain the epidemic. We’ll see for COVID.


COVID did not start in January in Seattle. Thanks to Trevor Bedford for putting this notion to bed with this thread. If you were ill in January, it was something else. I love slide 6/18 showing all of the other viruses that circulate on a given year. Like COVID, these viruses are sometimes not symptomatic but can sometimes cause several days of misery. Unlike COVID, few of these (influenza and RSV excepted) typically involve the lung in people with normal immune systems. Also look at the sharp drop off in cases on 3/1: the impact of social distancing may be evident on other viruses as well, though seasonality is certainly another possible explanation. -----

Vaccines.This is a magnificent read from the Economist which gives an overview of COVID vaccine development, but also postulates the fascinating political implications of one country, perhaps China, discovering an effective vaccine first. One stop shopping for learning about vaccines if you knew nothing before.

This is an exhaustive resource for keeping track of all vaccine products under consideration. The diversity is remarkably high. I am not a vaccinologist and it is less clear to me how many of the products that are listed have any real chance of making it past phase I trials Antiviral approaches are listed as well.


Hydroxychloroquine. This is the best study yet. This trial was randomized (good) not blinded (less good as report of symptoms in particular may be biased by knowing whether one received drug or placebo), medium-sized (150 people), not yet peer reviewed, and showed no difference in time to viral clearance. People on HCQ felt better sooner but had more serious adverse events. Not great evidence for this drug but properly blinded studies are in the works. My favorite part is the first sentence of the 3rdparagraph: these scientists from Shanghai put “wonder drug” in quotes. This is not the typical dispassionate language of the scientific literature. These cats do not like DT and/or Rudy Giuliani and/or the drug.


Group homes. A major story nationwide are the numerous outbreaks in these assisted living facilities and skilled nursing facilities. It is a terrible set up. Many of the workers put in long hours at numerous locations and need to do so in order to make ends meet. At some locations, these are immigrants who lack sufficient money to own their own car and therefore are also using public transportation to get to work. The work is physically intimate as many in assisted care need close daily attention (showering, toileting, eating) which makes the transmission risk extremely high between residents and staff.

I started doing a bit of volunteer work with a group of UW clinical staff going to various local group homes to swab all residents. Some locations have had no infected people. Others have had as many as 65% infected. Once the virus hits, particularly in an underfunded facility, it is very hard to contain. Very sad and a vexing problem.


Advice from Wuhan.The politicization of the pandemic is natural and China’s role as a political entity deserves great scrutiny. See the lead in this week’s economist for an overview:

However, the notion that the Chinese people have not suffered from this is absurd. Their shared humanity is so nicely highlighted in this BBC video. “The lockdown isn’t about taking away your freedom, it’s a scientific method to fight an infectious disease, so that you regain your freedom as soon as possible.” Very well stated.

Dr. Feng’s description of the chaos and the need for creativity and toughness in the early days of the epidemic is extraordinary. I am sure physicians in Madrid, Milan and New York would feel enormous kinship with her.


Vietnam.This story remains a glimmer of hope for me. Vietnam, one of the most crowded countries in the world, has not had extensive local spread. All done on the cheap with local ingenuity and a collective sense of responsibility. Bravo.


Health care workers. First reports of the number of health care workers infected in the US so far. 9200. Surely a huge underestimate.

Helen Ouyang describes a descent into near chaos at Columbia. New York will face its next round of national heroes who will face PTSD and guilt. Let’s do better than we did after 9/11 with first responders.


On social distancing.Navigating the micro-decisions of daily life is a challenge for us all. I thought this was a fair critique of the minority of people who are actively outing the rest of us at risk.

However, it does not reflect my experience locally. Chihana and I took a 25-mile bike ride today and went through several typically very crowded parks. It is a perfect 65-degree sunny day here. The mountains are out. Indeed, lots of people were out. I counted ~10 minor instances where people other than family were congregating in groups but saw no red card violations of physical distancing. The 6 foot rule was quite obviously on people’s minds.

People are doing their part and it shows. See this new data from Seattle SCAN. Zero out of 1392 without symptoms came back positive (nasal PCR). 1.6% of 2700 samples in people with symptoms came back positive. Very encouraging.


Expertise & uncertainty. I thought this article by conservative columnist Ross Douthat was superb. Expertise is our guiding light during the pandemic. Expertise is why we can trace the spread of SARS CoV-2 using genetics; it is what will get us a vaccine; it ensures that we perform clinical trials correctly; I could go on and on. Of great importance, expertise also puts the spotlight on areas of greatest uncertainty.

Yet, it is vital to recognize the limitations of expertise. First, experts sometimes drop the ball. The FDA’s bumbling of early testing is one example. Our lack of readiness to nimbly perform clinical trials is another.

Moreover, expertise can’t eliminate uncertainty. Every decision we make on a daily basis is based on huge ambiguity. An expert is no better poised to make decisions about cloth vs medical masks at the grocery store, whether or not to jog in a somewhat crowded park, or precisely how to slowly open the economy. I thought this article nicely captures what will follow: trial and error, adaptation and then more trial and error. Most policy decisions will be tradeoffs with unavoidable downsides and upsides.


Contact tracing.This partnership between Apple and Google seems like a necessary step for efficient contact tracing via to allow efficient self-quarantine or isolation. Perfect for Asian countries where buy in more universal. Who knows whether this will work in our country where libertarian philosophy is fairly widespread?


The United States. Three damning pieces about the state of our union. The first essay by the great Charles Blow describes that the epidemic is now disproportionately impacting people of color. Not surprising, but depressing and enraging.

The second describes the abject neglect within the executive office during January and February which is at least partially responsible for so much of current predicament.

One of my favorite writers Viet Thank Nguyen describes what this must look like to the rest of the world.


Rural COVID. Some incredible journalism from the Arctic.

The fragility of rural health care systems with fixed overheads is frightening. Examples from the south, the Midwest and eastern Washington.


Personalizing the pandemic.Touching obituaries highlighting the diversity in age, race, and region of those who have passed.


RIP John Prine.An American legend is gone.

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