This article is to introduce an exponential growth model that I’ve created for the SARS-nCoV-2 (“COVID-19”) virus pandemic and what specifically it may do within the United States right now. There are lots of charts that are being produced by media and other organizations showing the growth of this virus across the world. But, just as I wrote my original COVID-19 article because I felt that the story was still confusing or inaccurately being protrayed to most people, I feel the same is happening right now when it comes to comprehending the pandemic within the US.
Thus, the purpose of this model is two-fold:
- Show whether an exponential growth of the virus is happening within the US, and
- Illustrate the power of exponentials so they are better understood
Let’s jump directly into what the model is showing as of today, March 19th, 2020, relative to the official statistics. There will be two charts, the first is about the total infected within the US and the second will be the total dead in the US.
The above charts show what the model shows as far as progression of the amount of cases of infected Americans (top) as well as the number of those that have passed away due to the virus (bottom) during the month of March 2020.
Here are the assumptions and parameters used in the construction of this model:
- Model began on March 7, 2020
- 2,000 infected Americans
- Doubling rate of 6 days
- 10% hospitalization or serious rate
- 3% death rate with a 12-day lag from infection
All of the above are assumed to be conservative in that the number are likely more aggressive and larger. For example, infection amount was perhaps around 10,000-20,000. Doubling rate is likely to be quicker at 4-5 days.
Regardless, the model has been and will continue to be updated every 2 days and charted to show how it is holding up as a model for what is happening and to extrapolate into what may happen. Note: I am not making any predictions or treating this subject light-heartedly. The purpose of the model, again, is to share information and to make sure that we are not confused about what’s happening.
I’m not going to get into why things are happening and a lot other things that are better left to others to represent and share. Those that are interested in a steady stream (sometimes hourly) of interesting data points and recommended resources I come across are welcome to follow me on Twitter (@ShawnShafai).
What Does the Model Say Today
I see the model saying the following things as of today, March 19, 2020:
- the US is, indeed, experiencing exponential growth
- the parameters and assumptions that were made were, in fact, conservative
Please note that the model and realities around virus epidemiology mean that the model is reflecting past action and not today’s action. Even if we were to employe all of the best practices in virus containment and management, you still will have a lag of weeks until those results come to fruition and it impacts future manifestation of health outcomes (infections, hospitalizations, and death).
I am encouraged with the steps that have been taken in the past week to help containment and limit the spread of the pandemic (flight restrictions, work from home for many, etc.). Sadly, much more needed to be done weeks ago (and as early as late January 2020) that wasn’t. Even today, there are still many that don’t understand the crisis and think it’s mainly hyped up by the media.
If things continue as they’ve done for the first 12 days of the model, it shows the following for the US:
- End of March – 32,000 infected, 3,200 hospitalized, and 943 dead
- End of April – 1 million infected, 100,000 hospitalized, and almost 16,000 dead
- End of May – 32 million infected, 3.2 million hospitalized, and almost 500,000 dead
Again, let me reiterate, this is not a prediction and not what I expect to happen. This is a model and the parameters are clearly articluated above and after 12 days, it’s proven not only accurate but actually conservative. Conservative in terms of the 2,000 starting count of infections was almost certainly too low. As well, the doubling rate may be more aggressive then every 6 days. Both of these are highly likely in why the official counts above (in Orange) have broken above the model.
Let me state once again, the outcomes above don’t have to be what happens and we should all pray that it doesn’t. But, the purpose of the model is to bring clarity and attention to this topic. I adhere to the phrase that it’s far better to be wrong than to be confused. With such models, we can understand potential and what is happening to take appropriate action. I’ll keep updating this model every 2 days and tweet my updates on Twitter, if you’d like to stay updated.
Why Exponential Functions Can Be Frightening
Why I think many people still can’t grasp the power of this particular pandemic to produce awful far-reaching outcomes is that exponential functions are hard to understand and we don’t deal with them in our daily lives much or at all. I believe this is the same reason certain governments around the world (I won’t name) only in the last few days changed their disastrous course after they got a glimpse of how exponential growth of the virus within their population would lead to catastrophic outcomes.
Here’s an analogy that I like (I didn’t create it):
- imagine that you are sitting in seats at the top of a baseball stadium watching a game
- a drop of water if dropped onto the palm of your hand every minute starting at noon or 12:00pm, starting with 1 drop, then 2 drops the next minute, 4 drops the following minute, and so on
- assume the baseball stadium is watertight
- given this progression of drops of water onto the palm of your hand, when do you think the stadium will be full of water and you’ll be floating at the top, how long will it take — days, weeks, years?
- the answer is at 12:50pm, in less than an hour, the entire stadium will be full of water
- the most poignant part? At 12:45pm, you would only see water way down on the baseball diamond 5 feet deep and the stadium is still 93% empty of water. Yet, in 5 minutes, the stadium will be full of water
This is how exponential functions work. Slow, slow, slow, speed up, speed up, boom.
Let me reiterate one final time, things in the world don’t have to work like a mathematical model. The point of the model is to show what is actually happening and to make sure there is no confusion what can happen if things don’t get in the way of how the virus has been spreading.
I will leave you with a final look at exponential growth, this time, this is the growth of infections outside of China.
What you see above is a logarithmic chart and not a simple linear one. The significance is that if you see a steady straight line and not a flat/horizontal one, it is showing you exponential or geometric growth. More specifically, what you are observing above is an exponential rise of infected people in the world (outside of China) about every 2 weeks.
So, we want from 1,000 cases outside of China on February 18th to 10,000 cases on March 2nd, and finally we achieved 100,000 cases on March 16th. Go to the website and play around with the interactive chart on your own, if you like.
If this continues, we have will have 1 million cases at the end of March and 10 million cases two weeks after that in mid-April and so on.
I’m sorry to repeat myself one final time, but these are just numbers and not a destiny. Yet, they can also be a future outcome if you don’t take things seirously and do the right things. Globally and nationally, we’ve had a lot of challenges with doing the right things as I’m sure everyone will agree. The point is arm yourself with the reality that numbers don’t lie and that they can also suggest things in the future that should make you sit up to attention.
The characteristics of SARS-nCoV-2 (“COVID-19”) that we got a glimpse into during January got the hair on the back of some of our necks standing up on end. Here you had a virus with a “perfect storm” of characteristics of transmissivity, serious complication rate, and death rate that had all of the hallmarks of a potential terrible global pandemic.
Only a handful of countries took immediate “gold-standard” actions (namely Hong Kong, Taiwan, Singapore, and South Korea) and many of the rest didn’t or weren’t able to do so. Those that did have demonstrated how you get this under control. Those that didn’t (and some continue not to do so to this day) demonstrate how we have a real problem on our hands for a while to come.
If you’re not on Twitter, just message me on Facebook if you want updates on what my model shows. I update it every 2 days and will not be publishing updates here on this website.
Good luck & health to all.