Your browser version is outdated. We recommend that you update your browser to the latest version.

Podcasts

DENVER UNDERGROUND podcast

Videos

Emergency Department Management of Orthopedic Injuries VIDEOS

The Basic Math of COVID

Posted 3/22/2020

We are all underwater in COVID information. Here are some facts that will hopefully be intellectually stimulating:

R value is key: R represents the number of people that an infected patient will subsequently infect. As long at R>1 then more people get sick. When R<1 the burden of disease goes down. At the end of the year I expect Time Magazine to call “Flattening the Curve” the phrase of the year, and that flattening depends on how big R is and how long it stays above 1.  (Technically R is R naugth, R0—>for this write up it will just be called R.)

If you go back to your middle school math, the basic equation for a line is y=mx+b, where “m” is the slope of the line. While the epidemiological math is non-linear (and complicated by the rate of cure vs new-infection), R is basically “m” (or the slope of the infectious curve graph). When R >1 the slope is positive, when R=1 the slope is 0 (flat) and when R<1 the slope is negative. If R is 2 the cases will follow the following pattern 1 :  2 : 4 : 8 : 16 : 32 : 64 : 128 : 256 : 512 : 1,024.

 

The goal of all our efforts is to control the R/slope of this disease: hand washing, social distancing, testing, quarantine, closing schools/public spaces/work environments.


For a more detailed and eloquent description of all of this go to Bill Rodriguez’s site (Harvard Global Health Physician). It is excellent, detailed and accessible:  
 https://covid19-insights.squarespace.com/


There have been discussion about the tactics that various countries have used to combat the spread of the virus. I have had a hard time figuring out exactly why the different strategies have had different impacts. So let’s dig into that further.
 
Containment has been successful in a couple of countries around the world. Singapore has been one of the examples cited as a system that has handled the virus threat well. The government and medical authorities were active early in the course of the disease. This allowed them to follow the path of the virus by “contact-tracing.” This is where the government interviews everyone with a confirmed case and traces back their contacts for the past week or so (they do this using interviews, review of public surveillance cameras, police investigations and cellphone/app data that shows peoples’ locations over time). Once these movements/contacts are mapped, the Singapore authorities put all of the people who were in close contact with those patients on 14-days of strict house confinement (with jail time and huge fines hanging over their heads if they break quarantine).  Only those who develop symptoms get tested.  

This is a lot like the game they play on the big screen between innings at baseball games. The one where they hide a ball under a cup (or truck or barber shop chair or beer can, depending on what they are trying to sell) and then shuffle the cups around. As long as you pay close attention you can follow the movements and know where the ball is once the cups stop moving, but if you look away for a second it is just a guessing game.  Singapore started following the cup early in the game, so they still know where the virus is. The result is that they have been able to contain the spread of the virus, while limiting mass/unfocused confinement of their citizens.

China: where it all started  

Wuhan is a huge city—11million people live there (L.A. and Moscow have about 12million people in their metropolitan areas), and the province it is in (Hubei) has 60million people in it. They didn’t even know the game was starting, so they lost vision of where the ball was hiding right off the bat. In response they decided to just hold all the cups down on the table once the shuffling stopped.

China not only confined the entire Hubei province, but put around 760million people in the country on home confinement.

The confinement was severe and included the following:
Orders for home confinement except to buy groceries or get medical care
Closing of schools, factories and offices
Shut down of all travel in and out of the province
Banning of private vehicles from driving on the streets
Deployment of police/security to ensure people stayed in their houses
Tracking of people’s movement by tracking their cell phones
Door to door temperature checks
Building of mass confinement tents for those with the virus—>people with the disease were treated outside of their homes

The results of the mass confinement was that in one week R in Wuhan went from around 2  down to 1. . .

. . .let that sink in because it is incredible.

A review in the journal Nature pointed out a number of interesting facts about containment measures. Before this confinement, models predicted that about 40% of China’s population could be infected. There have been around 81,000 cases in China. Putting those data points together, the confinement measures led to a 67-fold reduction in disease transmission. If the confinement had started a week earlier, models predict 2/3 of cases could have been prevented and if started 3-weeks earlier it would have led to a 95% reduction in cases.


Finally, what about the USA

We definitively lost site of the ball and have no idea how many balls are hiding under all the cups in the country. While testing is ramping up, what we do with it will be another question. Because people can shed the virus for days before they are symptomatic, just screening those who are already sick probably will have limited effect. There are promises of tests on the horizon that can give results in hours. That type of testing would allow us to limit quarantines of healthy people and would give those with the disease a definite diagnosis.  The “It may be COVID, or a handful of other viruses including the flu, but you're quarantined for two weeks regardless,” is a frustrating conversation for people on both sides. I also expect people with the virus to be more focused on the health of others if they actually know they have the disease and can cause harm to others.

This brings us to the paths that are soon to diverge in our country. While California is locking down the entire state in an attempt to limit the spread of the disease, this week the Wall Street Journal published an editorial questioning if these measures are worth the financial turmoil they are going to cause. It took China 45 days to lock down the spread of the virus. I don’t know if Americans have 45 days of lock down in them. And if we don’t, there may be a time that we choose the resumption of our economic activities over flattening the viruses curve (choosing $ over R). That will play out in the next couple of months and the path we choose will have an immense impact on our health care system, the health of our population, the consistency of our moral fibers and our overall economic future.

Finally, in the coming days/weeks we will see if our confinement measures have affected R in the same way that it did in China. If the impact is similar, and we have taken R from 2 to1, then our cases should plateau out (this is all back of the napkin math and only based on very data scarce logic).  If it hasn’t been as effective and R stays around 2—>Booooom.


https://www.wired.com/story/everything-you-need-to-know-about-coronavirus-testing/
https://time.com/5796425/china-coronavirus-lockdown/
https://www.nature.com/articles/d41586-020-00741-x?error=server_error&error=server_error&error=server_error&error=server_error&error=server_error&error=server_error&error=server_error
www.bbc/news/world-asia-51866102
https://www.wsj.com/articles/rethinking-the-coronavirus-shutdown-11584659154?mod=hp_opin_pos_1
https://wwwnc.cdc.gov/eid/article/25/1/17-1901_article

Cookie Policy

This site uses cookies to store information on your computer.

Do you accept?