# Predicting Hospital Capacity: Why to Act Early, How to Think About Lag Time, and a Model You Can Use

NOTE FROM TIM: The following was written by a close friend who has decades of experience in healthcare systems and advanced training in computer science and healthcare data science. He preferred to publish anonymously to avoid political headaches, so I’ll call him “Felix.”

We are publishing this quickly for reasons that will soon be obvious, so please excuse any typos. This is a work in progress, and we encourage leaving comments if you have any suggestions for improvement.

### Enter Felix…

During this coronavirus crisis, the paramount objective has become avoiding hospital overflow, which would make the mortality rate skyrocket. We’re trying to accomplish this with voluntary social distancing, but it’s evident that that’s not going to be enough. So how early should governments start introducing mandatory quarantines? The answer is much, much earlier than you might think.

In the following example, we can show mathematically that a city that institutes a city-wide quarantine when its hospitals are anywhere from 4% to 20% full can still easily exceed its total hospital capacity. The assumptions underlying this model are at the high end of current estimates in order to make a point, but they are well within the realm of possibility.

There are two important concepts here that humans are not wired to understand, and it takes some time to wrap your head around them.  Exponential growth, when combined with lag time, can create some wildly counterintuitive effects. Say you have a city (let’s call it Springfield) where new COVID infections per day are growing. The numbers are doubling every 5 days:

10–20% of infected people will need to be hospitalized. From the day a person gets infected, it takes an average of 10 days for them to seek hospital care. So if we had 1000 new cases of coronavirus on Day 1, using the high end of the estimate, we can expect 200 cases to arrive at the hospital on Day 11. We can chart the new daily hospital cases for our beloved city of Springfield.

Let’s also say that the average hospital stay is 12 days. So coronavirus cases start to accumulate in the hospital:

Now, let’s say there are 5000 total hospital beds in all of Springfield. The mayor is watching dutifully, but his team, overwhelmed with other duties, aren’t carefully considering exponential growth in combination with lag time. He sees that about 80% (4000) of his beds are occupied on Day 20, and realizes the city needs to do a full quarantine. He orders it promptly on Day 20, so that he can avoid his hospitals overflowing. New infections reliably start to fall on Day 21 and continue to fall forevermore:

What happens to new daily hospital cases? Remember there’s a 10-day lag. So on Day 21 you’ll get 20% of Day 11’s new infections:

Hospital cases continue to increase after Day 20 even though we instituted a quarantine! On Day 20 we were only getting Day 10’s victims into the hospital.  The people infected on Day 20 won’t show up at the hospital until Day 30. Will we overflow our hospitals? How many total beds will we need? Remember: the patients will accumulate since it takes 12 days to be discharged. Let’s extend our Total Beds Occupied graph:

Total hospital beds needed doesn’t peak until Day 35, even though we quarantined on Day 20. It peaks at around 22,000—more than 4 times as many beds as there are in Springfield. Given the numerical assumptions above, if you quarantine when your hospitals are 80% full, you can expect to exceed your total number of hospital beds by more than 300%. You can see this playing out in Italy right now. They’ve quarantined, but the hospital cases will still rise for many days after the quarantine is instituted.

So how early should we start the quarantine in order to avoid our hospitals overflowing? Let’s see what the max hospital bed need is for different points of quarantine:

If you quarantine at 50% full on Day 17, you’ll still have a peak hospital need of 16,812 beds. (Remember: there are only 5000 total hospital beds in all of Springfield)

If you quarantine at 25% full on Day 14, you’ll still have a peak hospital need of 11,092 beds.

If you quarantine at 4% full on Day 10, you’ll still have a peak hospital need of 6,370 beds.

In this example, if you want to avoid hospital overflow, you have to start quarantining when your hospitals are 3% full. Of course, this extreme example starts at 1,000 cases on Day 1 with only 5000 total beds. The effects of exponential growth are less extreme if you start with a smaller number of initial cases. Nevertheless, it’s valuable to have this example drive the point home that in order to prevent hospital overflow, you have to quarantine surprisingly early.

There are some fundamental assumptions I’ve made up here that you may disagree with, such as the initial case count, growth rate, the hospitalization rate, etc. If you’d like a rough estimate of when would be the appropriate time to quarantine for your particular geographic region, you can modify all the numerical assumptions and run different scenarios by copying the template here:

[Note from Tim: This spreadsheet is read-only. Click on File –> Make a Copy to duplicate it for your own scenarios.]

The author is a data scientist but not an epidemiologist. Any feedback from epidemiology experts about underlying factors is encouraged in the comments.

The underlying assumptions have been pulled from papers about COVID-19 published in recent months. They are at the high end of estimated ranges but not outside of what experts believe to be the possible ranges.

There are far more sophisticated ways to model epidemics, such as SIR and stochastic input modeling. The point of this article is to spread understanding so we chose to use the simplest possible model that still shows the dangers of exponential growth.

The Tim Ferriss Show is one of the most popular podcasts in the world with more than 600 million downloads. It has been selected for "Best of Apple Podcasts" three times, it is often the #1 interview podcast across all of Apple Podcasts, and it's been ranked #1 out of 400,000+ podcasts on many occasions. To listen to any of the past episodes for free, check out this page.

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## 145 Replies to “Predicting Hospital Capacity: Why to Act Early, How to Think About Lag Time, and a Model You Can Use”

1. bakerandcohealth says:

Brilliant. Thanks for bringing up such important points which most governments clearly seem to be either forgetting or just outright ignoring: Exponential growth & lag time.
Good luck everybody.

2. Phillip Neal says:

Thank you for doing this. Now we need to model out ventilators, respirators, and other essential hospital equipment.

1. Rafael says:

Yes ventilators! Im Portuguese…In Portugal there are 1200 ( (numbers given by the prime minister) …scary … Italy is denning ventilators to people with more than 60 years! Because they just don’t have them !

2. A says:

I think it’s extremely important the public understand that respirators and non-invasive ventilation therapies are NOT treatment protocol right now in the majority of hospitals without enough protective equipment/negative pressure rooms for people who are still viral as these therapies spread droplets. It’s not just number of beds… it’s capacity to treat which means appropriate rooms and protective equipment otherwise the therapies can’t be delivered.

1. Katie Dawson says:

I also read that when a patient requires a ventilator and gets one, outcomes are not very good. IOW 97% of ventilated patients are dying.

2. Cory says:

Thank you. This needs to be bumped up and more widely known.

3. Avalanche says:

Check out the blog called Raconteur — long-time ER nurse/ex military — his posts are reports from the front-lines, by the equivalent to a old-time/long-time Sarge-Major or Master-Chief… He goes into some depth on what hospital care may or will not be available. Read esp:

https://raconteurreport.blogspot.com/2020/03/kung-flu-update-etc.html
[Raconteur (goes by “Aesop”):] …
Some people have expressed the hope/belief/fond wish/delusional fairytale expectation that, like many outbreaks, this one will wane once Spring is sprung, and the sun comes out. Look at the John Hopkins map in Peter’s post header, and mentally pencil in the equator in that picture.

To wit: Australia (Oz, affectionately) is in late summer. It isn’t helping their outbreak a bit. Singapore is equatorial. It hasn’t mattered there either.

YMMV, but were I you, I would abandon all hope of weather saving you, and rejoice if it does, which seems entirely unlikely.
Period.

============
[Elsewhere:] …
Economies all around the world are going to be hit hard. We’ve discussed that in these pages several times, most recently on Monday. [https://bayourenaissanceman.blogspot.com/2020/03/covid-19-time-for-dose-of-realism.html] Do please read the discussion on container shipping in that article – it’s one of the keystones of why economies are going to suffer. China used to handle over 700,000 TEU shipping containers per day. That hasn’t happened for over a month now. Do the math – that means over 21,000,000 (yes, twenty-one million) TEU containers that should have been emptied, or filled, or moved, but haven’t been. That’s an economic disaster in the making in anyone’s language – and it’s still like that. China claims it’s clearing the backlog of containers in its domestic facilities [https://gcaptain.com/chinas-top-container-ports-unclog-backlog-as-virus-curbs-ease/], but no-one knows for sure whether that’s true or not; information out of that country is rigidly controlled and censored, so facts are suspect until verified.

============
1) The fact that they’re doing point-of-care one-time testing, on a disease that incubates for 2-14 days, and perhaps as many as 24 or 28, guarantees the spread of asymptomatic virus carriers into the country, to propagate it hither and yon widespread in a few days, to a couple of weeks. This is the bio-defense version of putting the entire defensive team on the line of scrimmage, and then looking shocked and dismayed when the other team passes over their heads for 3000 yards, and beats you 210-0. Your tax dollars at work.

3. John Dziki says:

Sorry but, the figure that 10-20% of infected people need to be admitted to hospital is crazy. Only a very small percentage of the people who test positive actually develop a serious enough case that they need to be admitted. And even then it is people in there 80’s who make up the actual death rate.

1. Felix says:

Hi John, you can put in your own hospitalization rate in the sheet I shared. Funnily enough, you’ll see that the hospitalization rate doesn’t change the math of hospital beds. It just changes the number of people out there who are not going to the hospital. Thanks for reading!

1. Ed D. says:

Felix – John’s comment is a fair one – and your reply is fair given that hospital beds are indeed finite. But that said – you haven’t addressed his core issue – which is the assumption YOU’VE made about hospitalization rates overall, and from which you’re drawing conclusions. John’s point is that you’re assuming far too high a hospitalization rate.

2. pokaaaahh (@pokaaaahh) says:

Sorry John D, but in risk management we were taught to get the worst case scenario first and plan according to it. What do you suggest as “very small percentage”?
I see 10% of people hospitalized a very possible one given the old populations living in Europe.

3. Ed D. says:

@Pokaaaahh – populations may be older in mother Europe, but they’re not THAT much older. By what about do you suggest changing the Hospitalization Rate, and would it make a material difference? I suspect fiddling with hospitalization rates in EUR vs USA is to miss the point, to miss the big picture, and an utter waste of time. But go ahead if your time and priorities allow. Just make sure your hospitalization estimates are soundly based on real population distributions.

4. JRP says:

It’s my understanding that the virus is mutating and that there is an uptick in young adults (20s and 30s) requiring hospitalization as well.

2. Jason Borowicz says:

It seems from other countries that actual need for hospitalization is around 18%.

3. Alex Allman says:

The last data I saw said 1.3% death rate for men in their 50s. Would you go on an airplane if you knew it had a 1.3% chance of going down? It’s around 0.3% for people in their 20s and 30s… but again, would you go on an airplane if you knew that 3 times out of 1000 it was going down in a fireball? Being dismissive about the deaths of octogenarians is not the game we want to win in any case.

1. Ed D. says:

Alex – a 1.3pct death rate is ABSURD – whatever the age bracket. Please stop signal-amplifying nonsense.

2. mike says:

Alex –

With all due respect, what you have posited is an example of the fallacy of false dilemma. You have proposed that the only choices are (A) get on the plane and have a 0.3% chance of dying IN A PLANE CRASH, or (B) not getting on that plane and having an assumed zero chance of dying (during the same time period).

What your argument ignores is the fact that people get on planes for reasons and that planes are only one option for travel. If someone must travel to a distant point, he can fly or drive (he could also walk or hitchhike, etc., but we’ll just leave it at fly versus drive). You are far safer flying than driving and if not traveling is not a viable option – you would lose your job and your family would starve – the safer option may be to fly.

You have also made another serious error. You have assumed that contracting or not contracting COVID19 is a binary choice like chasing to fly or not fly. Because there is no upside, most people (Ferriss may be the exception) would chose not to get infected with COVID19 no matter what the mortality rate. We can make choices that might (according to our best knowledge) reduce our chance of getting infected or at least postpone getting infected. As Felix will acknowledge, if we don’t get infected, we don’t have to worry about dying from COVID19 and if enough people postpone getting sick, the curve he has drawn is flattened, i.e. the peak of sick patients occurs later and isn’t so high giving the system time to respond and handle the load of sick patients.

4. DS says:

Like Tom Hanks, Rita Wilson, Rudy Gobert, to name a few. Over 80? Nope.

1. EQ says:

John is referring to people in their eighties making up the actual death rate. The people you listed are alive AFAIK.

5. Jones kelley says:

Thank you!

6. Nanou De Ridder says:

Tim is right. The statistics worldwide are showing that around 20% of cases require hospitalization, with about 5% requiring ICU (in the first case it is usually oxygen and in the second ventilation).

4. Bartosz says:

In the template, cell B15 should be “=B3”, not hard-coded to 250.

1. Felix says:

Thanks for the tip Bartosz, this is fixed. Fortunately it doesn’t affect the analysis in the article, the conclusions are still the same.

5. Jessee Turner says:

In OZ Our public hospitals are at more like 120% capacity with ambulances unable to get their patients into ER beds for hours, before this started. But people are trying to stay home. Much less traffic on the roads and heaps parking available where there normally is none.

1. Freyja says:

This is interesting – we haven’t yet factored how many beds are already allocated to other patients (some potentially serious and allocated for a matter of weeks) and new cases from other illness/accidents.
Also factoring in all of the non hospitalized but still ill people, many of whom will be bed ridden at home, needing care. If you’ve ever had a bad flu without needing to go to hospital it’s still pretty bad. Who takes care of them?

2. mike says:

Capacity (at least in the USA) is a nebulous term. It means the number of beds the hospital is licensed to use. In many cases, a hospital can ramp up its physical plant if needed, and while it takes time to train skilled personnel, there are many recently retired or idle health care workers who can be recruited if the reward is right.

1. chet says:

I read that in the early fight over in Wuhan, the government ordered 42,000 health workers to the city from other provinces to join in the fight.

In the USA, we do not have that capacity nor the government leadership to make that happen. From what I have ascertained, China flattened the curve utilizing draconian measures of lockdown, surveillance, testing, and massive centralized manpower.

I don’t see that happening here unfortunately and I don’t see the American public heeding the advice of officials due to the laissez faire attitude of Mr. Trump.

2. Avalanche says:

And there’s your “to fly or not fly” choice. If you’re a retired health care worker, and thus likely either old or caring for your young children furloughed from the school-prison, what reward would be sufficient to put yourself, and your family at risk? Pretty dreadful knife’s-edge calculation — on insufficient data.

6. drluvcatz says:

Thanks Tim this is an easy and well thought out way to show people the importance of early prevention. Lock down is the only thing we have now to slow this. I have been following the virus since Jan and became alarmed early Feb when I saw things were right on track for a Black Swan event. Keep up the good work.

1. nigel walker says:

It’s not a Black Swan event, not even close. Pandemics are regulary predicted hence the existence of programs [before Trump] to predict them.

Brilliant analysis by “Felix”! Could incorporate onte Carlo analysis around the assumptions (infection rate, 10-day lag, etc) could be done — keeping in mind (modeling to take into account) that the spread of the disease will inform the public about the risks and CHANGE people’s behaviors (self-quarantining, better self-care, etc — and changes not always for the better) that will affect the parameters in non-linear ways.

ALSO,

would be SUPER-GREAT if soi-disant Felix incorporated another parameter of ACTUAL coronavirus needs-hospitalization vs. not-need hospitalization (people go to hospitals THINKING they have coronavirus, say, or even that could SELF-MEDICATE AT HOME just as, if not more, effectively as the care they’d get at hospitals (with all the OTHER risks they face at hospitals — BY THE WAY, SURVIVAL RATES probably go WAY DOWN as the capacity utilization increases, yet another dependent variable),

AND FINALLY

Introduce another parameter of NON-coronavirus cases seeking help at hospitals who will be DISPLACED by coronavirus patients — some significant % of which could be dismissed to go home — and what happens to THEM and their survival rates.

So to summarize the additional variables to be modeled:

1. Lag time as a function of reported cases (not simply 10-days)

2. % infection in a community changing behaviors that influence other variables (contagion rate, etc)

3. Coronavirus hospitalization-seekers who (A) need hospitalization or (B) don’t need hospitalization

4. Non-coronavirus hospitalization-seekers who (A) need hospitalization or (B) don’t need hospitalization, and the number of hospital beds taken up by coronavirus hospitilization-seekers.

5. MORTALITY rates (with probability distributions) for 3A and 3B and 4A and 4B,

Assigning probability distributions around ALL of the variables (some of which are not indepenent), and then running Monte Carlo analyses to determine the distribution of potential deaths.

Outstanding modeling “Felix”!

1. Tim Ferriss says:

Thanks for the very thoughtful and helpful comment, Adam! Good to see you here again 🙂 And thanks to everyone for their comments. We are reading them all.

2. Rob says:

Are there any additional behaviors or strategies that could reverse the growth rate to a similar degree as social distancing or quarantine that aren’t being discussed or haven’t been considered?

Everyone is very focused on distancing strategies obviously due to their effectiveness however are there any other potentials?

1. Mannan Javid says:

I wonder about supplementing hydroxichloroquine or chloroquine as Elon musk mentioned. Or other immunity improving supplements (“athletic greens” as Tim would mention)

2. Enrique says:

Yes ! There are other options. Much like a persons metabolism can vary wildly due to behaviors so can ones own immunity. I’ve not been sick in years even though I teach in public schools. Lotsa Sunshine and 2,000 mg Vitamin C is the secret. My family (wife and 2 kids) rarely get sick also. All depends how much sun they get as I get best results due to working outdoors ( I’m a garden teacher). Sunshine contains vitamins A&D and turns the food we do eat into fuel our body can use

8. Mark Esslinger says:

Thanks for providing relevant information and insights on this fast changing situation. It does not make anyone feel better to be right about the virus but it can save lives and get us back to “normal” sooner. Herd immunity will be the goal and its a brutal path to achieve the desired 60 – 70% will take many months and unfortunate losses of life. Support your medical health professionals, doctors, etc. and help everyone by taking steps to slow the virus – keeping life saving resources available to more people.

9. John Long Gone says:

Yes but:
>Springfield’s hospitals are probably already running at 80 to 90 % on a normal basis. The 5000 beds are the beds the town needs for day to day emergencies that do not stop because of the virus. In other words, 5.000 beds doesn’t mean 5.000 free beds to begin with.
>The infection rate greately increases when quarentine is announced and everybody runs to the stores at the same time. People who were not infected do get infected on day -1 of the quarentine, because they go to the store along wth the infected.

1. R. Gee says:

Agreed, this is an important distinction. Hospitals normally run 70-80% capacity or they shut down.

10. John Long Gone says:

A big problem hospitals are finding here in Spain is shortage of nurses. Many nurses get infected and have to go through long periods of home isolation as soon as they test positive. Which really complicates things, because you have less and less people to run the hospital and more and more patients.
(In our case this happened because of extreme ineptitude in all levels of decisionmakers who failed to provide basic equipment to nurses and doctors who are in highly contagious environments. It’s really a no brainer that keeping nurses and doctors healhy should be a number one priority in a situation like this, but some people just don’t get it).

1. Lidia says:

Exactly. The reason why people in the street should NOT be wearing masks, and hand the ones they have to the nurses and doctors. In the Netherlands, doctors found a way to reuse the masks by plasma sterilization. Hopefully this will help.

1. MaoZhou says:

Former FDA Head Scott Gottlieb (sp) today emphasizes that while N95 masks should not be worn by anyone other than doctors or ICU personnel masks can help to: 1) Prevent infection of others if you’re infected but asymptomatic (see US LAGGING in testing)
2) Help prevent getting exposed to virus.
Taiwan has also used this approach. Some sort of mask is BETTER than no mask.

2. Dirk Woods says:

Exactly! It’s the people stupid! As an ER doctor in the currently locked down Bay Area it is crystal clear to me that few are looking at this crisis in the correct way. Most of the calculations about capacity assume you will be able to staff a bed. Many ICU beds go unfilled in good times because of staffing shortages of nurses. If they have to stay at home with a fever for 14 days you have just increased the weakness of the currently weakest link.
While it is awesome to figure out how to make one ventilator ventilate 8 people it doesn’t help a bit if the extremely valuable resource of a qualified ICU nurse to watch the patient isn’t there. Keeping a ventilator patient alive and not having them die from complications is rocket science and if our rocket scientists are dropping like flies our fellow citizens are screwed. Why the most powerful man in the world work with 3M and other businesses to create adequate protective gear for all providers is beyond me- oh yeah, he has placed people without any experience or competence in positions of authority and they have no idea what they are doing in a crisis, just like Michael Lewis predicted in his last book. Awesome, just awesome.

1. Kelley says:

Truth. “Many ICU beds go unfilled in good times due to staffing shortages…” Beds or no beds…the ventilators don’t run themselves! Not to mention the amount of fluids, vasopressors, antibiotics, sedatives, pain medications and paralytics that critically ill patients require. Protect those of us on the front line first so we can protect the masses! Airlines get it: in the event of a cabin pressure change, the oxygen mask will drop down. Place YOUR OWN mask on first so you can help others. We’re being mandated to ration appropriate PPE in the hospital. It’s very scary.
(Also, thank you for showing such respect for my role as an ICU nurse. It’s really, really refreshing and appreciated)

11. LLvDelft says:

Thanks Tim. You are definitely a trusted voice of reason through all this. I sent it to the powers at be in my city. It’s about to turn into mayhem here. There is no way in hell we only have 2 people infected in my city. What is striking to me is that the information as to HOW MANY PEOPLE TOTAL have been tested instead of just positive is not available here. Curated half-information like we are all idiots or something.

Stay safe. Keep posting the realness.

Best regards,
Lucy

12. Jeff Stafford says:

Tim – I have spoken with a friend of mine who is an anesthesiologist. He feels pretty confident we have enough ventilators in the US to manage the spike. The problem is they won’t all be in the right place at the right time. It seems like the government or some consortium of really smart people need to create a Ventilators on the Go service to make sure the ventilators get to the right hospitals in the country. Sounds like a job for Mick Ebeling at Not Impossible Labs!

1. Gavin says:

Interestingly, in South Africa the plan is to move around the equipment as needed. Similar problems exist with equipment not being in the right place at the right time.

2. jennifer schroeder says:

Jeff,
Writing this from my bed in Seattle with a case of (presumed)Covid19. Can’t get a test though, and when my breathing became labored, was told not to go to hospital unless it was debilitating.

I contracted it from my friend, a nurse at Evergreen Hospital (the site of the 1st US death). She is Alonso in quarantine until symptoms are gone plus 72 hours.
So down one nurse.

The other nurses I know – all 30 year surgical veterans and supervisors are scrambling to test everyone walking in, cancel elective events, change over OR’s to isolation rooms, and find and monitor even basic supplies- masks- to keep the healers healthy.
The only hospital with a new pre-planned isolation unit is at capacity and they are at 90% ventilator use.

I’m curious why your friend feels we have enough ventilators? What state is he operating in?
I am in bed with breathing issues, am a healthy 50 yo
And have been turned away from even going to get a test. I am not only quarantining but now in bed so I don’t have to find myself in a position of needing a ventilator and having access.

I agree with you, that medical equipment needs must be orchestrated nationwide, but what is the reality? And which hospital will give there previous equipment up today and risk a need tomorrow?

13. Ali says:

I think it’s extremely important the public understand that respirators and non-invasive ventilation therapies are NOT treatment protocol right now in the majority of hospitals without enough protective equipment/negative pressure rooms for people who are still viral as these therapies spread droplets. It’s not just number of beds… it’s capacity to treat which means appropriate rooms and protective equipment otherwise the therapies can’t be delivered.

14. Erin says:

Thanks Felix. Clear and easy to understand. One aspect that I’m particularly curious about is if hospital capacity can be dramatically increased. Can empty hotels be converted into hospital rooms? Can we increase the production of ventilators? Can we crowdsource the creation of new ventilators by 3D printing parts at home?

While we are all social distancing at home there may be ways we can help.

1. Patrick says:

In Texas, the state government chose to not accept the Medicaid expansion, which would have given medical coverage to 1.6 million Texans. Around 20 rural hospitals have closed because so many patients in their areas cannot pay for care. Most of those hospitals are sitting empty and could be reopened more quickly than retrofitting hotels, apartments or schools.

1. Avalanche says:

“those hospitals are sitting empty and could be reopened more quickly ”

And staffed by whom? And refitted with equipment from where? Everyone keeps “counting beds”: “let’s just roll out WWII Army cots and let people lie in those.”

AND THEN WHAT?!

2. 4uhane says:

As an RN who is acutely aware of how stretched resources already are, I am wondering where we will find the staff for all these extra beds people are proposing…?

1. Tim Ferriss says:

1. Debi says:

That piece kept me home since early last week. Great article, Tim.

2. Tage says:

Fot those of us who are a bit mathematically challenged there’s good video at Khan Academy with easy to understand guidance through this marvel of information.

15. Dustin Jones says:

Hey Tim, there is an excellent college lecture on the exponential function and our lack of understanding on YouTube by Professor Bartlett. The title is similar to your books in that it shouldn’t be too quickly judged because it contains amazing content. It is titled, The most important video you will ever see full lecture. It is an excellent video and he does an amazing job of providing thought experiments to help people better understand the effects of exponential growth. Hope you and yours are safe and well!

16. Marko Bekker says:

Hi Tim. We are in the same team. We all want to help. I think there might be an error in the model. The post references doubling cases every 5 days (14.87% growth per day). The model however more than doubles the total cases every day (114.87% growth). Apologies if I misunderstood the post. Happy to discuss with ‘Felix’. Please let him e-mail me. Would also be useful to add the ALOS and some assumed population numbers into the model. Keep safe.

1. Felix says:

Hi Marko, I double checked and don’t see this bug in the shared google sheet. Perhaps you copied it and then changed the growth rate? Please double check. Thanks!

1. Marko Bekker says:

Hi Felix. I checked. Can I e-mail you my ‘adjusted’ model and you can consider? There are a few other matters (like hospitals not starting at 0% occupancy, total population, mortality, etc..) that I think you should consider.

2. Laurence Hansen says:

I haven’t looked into the spreadsheet, but it’s very common when calculating growth percent of g, that a cell reflecting that growth rate would be calculated as the source cell * (100% + g). For example, if cell A1 holds a value in time and B1 is to reflect the growth of 14.87%, the simple formula in cell B2 would be =A1*1.1487.
(Note: 1.1487 is 114.87%)
So, if that’s the kind of calculation used in the spreadsheet, then it is correct for the 14.87% growth rate.

17. Curtis Long says:

These charts are based on exponential growth. However, actual data indicates that growth of the disease (and deaths, in particular) is not exponential.

The work of scholars Anna Ziff and Robert Ziff, respectively of Duke University and the University of Michigan, presented earlier this month states that the growth rate appears to be following a “small world” path as indicated by power law.

‘The course of the disease is showing something other than the exponential growth that is routinely being tossed around. “This is a large number of fatalities,” the Ziffs observe, “but not nearly as large as if the growth were exponential.”‘

1. Michael Anderson says:

Thank you Tim.
I have been following your insights on this manner since your original 5 bullet friday you dedicated to the potential spread of this event, and sharing the information likening the statistics to Winning the war in Vietnam. I feel like YOU and your TEAM and many followers turned the tide on social distancing with your victory in Austin in regards to SXSW. I can’t thank you enough for your ACTION. You already have improved the lives of many Millions of Americans. You shined the light on the reality of the situation before many could even begin to see it. You turned the tide of blissful ignorance in advance of massive calamity, and your actions and communications were vital for all of us. THANK YOU for the WORK that you do.

2. Sonia says:

Very informative article thank you. I’m in full agreement with the quarantine to happen ASAP and across all borders as it’s necessary for containment and to buy time for the diagnostics which will further help starve the covid -19 bug. What I really believe we need implemented at the same time is the plan for grocery – as it is the stores which are over crowded and lines are long with no 6 ft distance in place. If this bug can indeed remain airborne for upto 30minutes in various temps we really need an alternative shopping arrangement. In China they had it all in Apps and devised a brilliant order and drop- off service which precludes face to face drop offs. In Italy it’s a few people in the store at a time and a distance kept amongst those in line and only one household member in line. In addition I spoke w infectious disease drs in Santa Monica and air travel is a big issue. It appears that in flights longer than 5 hours the circulated air becomes stale and if a person sitting in the last seat in the plane sneezes that germ can end up in the lungs of someone in first class ( I had gotten TB in 2009/ and no one knew how – most likely international air travel / travel abroad) and this what my Dr had explained. We are a nation of very bright & resilient people. It’s all about preparation, logistics, team work and calm – w good leadership/ that’s what we need and we shall overcome.

3. MaoZhou says:

Curtis, what evidence do we have on the ground that would support this theory in the US with our lack of testing and record keeping?

1. Curtis Long says:

Hi, MaoZhou. It appears that this study focuses on data from China, so I don’t know if there is evidence (from European outbreaks, for example) that might inform us as to what to expect in the U.S.

4. LKM says:

Very interesting. Wondering how researchers take into account the impact of active efforts to clamp down on spread of the virus, which would upend usual network behavior by individuals and groups. It seems clear that although individuals vary in how connected they are, and of course take their own steps to avoid contact if deaths get high enough to worry them, deliberate efforts at containment earlier on by centralized factions (governments at various levels) must make it difficult to mathematically model what would happen without those efforts for any particular pathogen.

1. Curtis Long says:

I agree, LKM. It seems like it would vary a lot from country to country and from city to city. Rambo makes a good point below about the massive movement of people in London, which may be very different from, say, Wuhan. (But then again, it may not.)

5. Rambo says:

Hi Curtis

Interesting idea.

My reading of the Ziff and Ziff paper is that the levelling off (slower than exponential growth) that they identify in total fatalities worldwide is _not_ due to a small world effect. it is mainly due to the effects of the lockdown in Hubei and the rest of China, which has stalled the growth in cases in China and therefore has slowed the growth in the global total.

Also… in large cities such as where I live in London (UK) there seems little or no scope for a ‘small world’ effect. A million people travel into the city centre every day, mostly in crowded transport. Another 1-2 million live in the same household as these 1 million. Another 1 million children go to school with children in that 1-2 million group. Another 1-2 million adults live in households with those children. You get to the whole city of 9m pretty quickly – very few people are more than four or five close (shared household or schooling) hops from several people in the core 1m city centre commuters. and thats without considering leisure travel. So the ‘small world’ effect seems likely to be limited to small and/or remote rural settlements.

I’d also observe that, unfortunately, relying on such a ‘small world’ effect, as a basis for public health strategy, feels a bit risky. Even if the maths and the logic look okay.

1. Curtis Long says:

Your points are well-taken, Rambo. It’s early stage research. Hopefully further investigation of this theory will prove its validity, in which case smarter public health decisions can be made for future epidemics. If we learn that a full lock-down is more extreme than is necessary to control an outbreak, perhaps we can avoid tanking the world economy and still bring the novel virus to it’s spiky little knees.

18. John Marshall M.D., M.B.A. says:

Hey 4-Hour Family

I’m a working Emergency doc in Texas trying to divert “worried well” from the emergency departments and flatten this curve. Sometimes the Emergency Department is just a place where people go when they are scared…that’s normal. However if you are scared about COVID it would be much better if we could have people use these clinics…and then if you do get sick…come see me…I love my job and am glad to meet you.

My contact details includes a website I started to aggregate all the satellite testing clinics

I’d appreciate any good ideas about how to get the satellite clinics to list their information and then spread the word..

J. Marshall MD

1. Lazyretirementgirl says:

John, Presbyterian Hospitals have testing ( drive up, I believe) in Albuquerque and Santa Fe, New Mexico

19. RKR says:

Thank you for this illustration and data based explanation. I live in Los Angeles area (Pasadena). How do I get this Information to someone who can actually DO SOMETHING about this? Send the link to the Governor? The Mayor? Hopsital heads at Huntington memorial hospital? How can we actually execute in this information?

20. MRD says:

Tim, please thank your data scientist friend who took the time to write this. It is very easy to understand, very well written, informative and timely. We are all working from home via Zoom meetings, and everyone seems normal and healthy. As you said, our brains are not setup to understand exponential growth, and even less equipped to understand how that is impacted by he lag time. I found it simple enough to be easily understood, yet sophisticated enough to be meaningful.

21. w000c2edd3a says:

If the prevailing thought is that the virus cannot be stopped, only slowed, and that 80%+ will experience mild to no symptoms…why wouldn’t we just quarantine the high risk population? It looks like that would be 4-5%. Let the rest of us keep the economy going and provide free services to those in need. Seems to me we are doing this backwards? I’m certain I am missing something but…

1. David says:

That’s interesting. I don’t know the data is fully understood, but general understanding is lower aged, healthy population much more likely to have mild symptoms and less likely to require hospitalization. Quarantine only for 60+ and others who are high risk with health issue for 30 or 60 days. Let the younger population get infected, recover, and jump start herd immunity. In model the % hospitalization would be greatly reduced. Once hospital beds / rooms / personnel peak start releasing older population from quarantine incrementally. Much less damaging to economy and probably not infeasible to execute.

1. Rambo says:

The UK govt was sort of following this policy / strategy… but, in the light of some pretty solid modelling work done by epidemiologists and others at imperial college (London), whic showed that it was highly risky, they have now rowed back from it.

The difficulties with it are that it takes a lot longer than 30-60 days for the under-60 ‘herd’ to get good immunity, 75% say, with under 0.1% newly ill each week. It takes more like 4-6 months maybe longer. and there are still a few under-60s just acquiring the virus for the first time… so when the over 60s do come out of the deep freeze, the virus rips through them just as it would have done if they’d stayed at liberty. An te healthcare system gets swamped with 10x the number of critically ill people that it is designed to cope with. Disaster deferred not averted.

The 20 page Imperial college paper (by Ferguson et al) is worth a read. It covers both the US and the UK in its analysis. This link should work…
https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf

2. JoDi says:

This is what I’ve been wondering as well. I’d like to see this topic addressed as I’ve yet to see anything written on it.

22. Shawn says:

Doctor, nurse, and medical staff and their attrition has to be added to the model. People available to treat will diminish over time as well.

Hospitals do not have enough isolation space, WHOLE hospitals will need to be designated as ID space and/or otherwise use closed buildings for expansion.

Mobilize Army hospitals now to add capacity

Nationalize manufacturing for PPE, ventilator, and other medical equipment.

Nationalize Amazon, UPS, Fedex logistics to get things where needed…when needed.

Nationalize stores like CVS for drive through testing.

1. Ed D. says:

Nationalize? Really? You mean for efficiency? ..like the DMV? Great idea! Why stop with your list here, and just nationalize everything?

23. André Miede says:

Very interesting take on the issue, thank you very much.

Joscha Bach took a very similiar way a few days ago with his short article “Don’t “Flatten the Curve,” stop it!”: https://medium.com/@joschabach/flattening-the-curve-is-a-deadly-delusion-eea324fe9727

The Imperial College in London has released a study that is based on proper simulations and that came to the same conclusions as Joscha’s back-of.the-envelope-calculations: https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf

Hope this helps the discussion and further modeling.

24. PixieApple says:

And what if we just quarantine at risk groups (elderly, underlying health conditions) and those in direct contact with them (carers, immediate family etc)? Does this not stem the flow of hospitalisations but avoids catastrophic damage to the economy and forcing generations into poverty?

25. Nom de Plum says:

Not only that, but MORTALITY will go up disproportionately. As the system gets burdened, more and more of the people entering the care funnel will receive subpar treatment–or be excluded entirely from life saving interventions.

26. Marc says:

Tim, thank you for sharing this – I used it to help form my own personal decision around social distancing for my family based on our already overburdened rural hospital. Will share with the hospital board as well, it is important that people understand the impacts of their decisions.

27. Alex Allman says:

The initial assumption is the scariest part here in NYC where available hospital beds on any given day zero = 0. Typical time lag on any given slow Wednesday afternoon between ER visit and bed available for admission is 24-48 hours before taking CV-19 admissions into account. On a busy day ERs in Manhattan have beds stacked in every walkway like sliding tile puzzles that doctors need to push this way and that to get to a particular patient. It’s gonna be a shit-show.

Hi Tim, for starting cases here in Maryland, I put three, as in three “reported” cases. Am I getting something wrong? The daily increase doesn’t add up, it’s too low on the Google sheet. Thank you for this!

29. Scott Groves says:

One assumption that is inaccurate is the percentage of occupied beds before infections start. Hospitals are typically close to full at any given time.

30. Sharinna Sarmiento says:

Enlightening.

31. Svenhard says:

This assumes a starting point of hospitals being 5% full. Ours is 80% full before the pandemic.

32. Billy Jalbert says:

Thanks for being ahead of this and sharing all you have thus far. New nickname. The Tim Reaper?

33. Anna Mari says:

Great blog post. Thanks for posting it. There are so many more complications to placing patients in hospital beds as some have discussed in the comments. I have been a nursing house supervisor at several large hospitals and a trauma center. I think the public needs to understand that there is a huge wait time to get a bed because of the various levels of acuity (how sick they are) what type of care they need, monitored beds, ICU beds…are they ventilated or not. Are the nursing staffing ratios appropriate to intervene early if patients are becoming sicker? Or are the nurses pushed to the limit and unable to appropriately care for their patients. I don’t even want to talk about dealing with isolation requirements in hospitals without private rooms…I could go on and on as most healthcare professionals could. ( but I will spare you my ramblings.)
I’m glad you are giving out good information. Thank you!

34. Anne B says:

Has anyone looked into modifying one ventilator to support multiple patients? While not ideal, maybe it could save lives

35. Ed D. says:

Invoking the concept of “antifragile” – the more we act to prevent adverse effects now, the worse those adverse effects will be when they regroup and hit us again in the future. (And usually they hit us again in the fairly NEAR future.) So – wouldn’t it behoove us to allow this to happen, albeit with some less-draconian attempts at mitigation, and so be better able to weather this when it reappears down the road? (THIS is never openly discussed so far as I know..)

36. Louis Rossetto says:

I despair at this kind of simplistic analysis.

1. Growth rates of this virus have not been exponential anywhere, otherwise everyone on the planet would already be infected and/or dead.

As Nobel laureate Biophysicist Michael Levitt put it: “In exponential growth models, you assume that new people can be infected every day, because you keep meeting new people. But, if you consider your own social circle, you basically meet the same people every day. You can meet new people on public transportation, for example; but even on the bus, after some time most passengers will either be infected or immune.” https://www.calcalistech.com/ctech/articles/0,7340,L-3800632,00.html

2. Hospital beds is not the important issue. It’s ICU beds. The US has more ICU beds than anywhere else in the world, literally 3X those in Italy. Check the death rate in Germany, which has almost as many ICU beds/100K as the US. It’s .02% (27 deaths on 11973 cases as of 18 March), about what they say influenza is.

3. This is not a disease that kills everyone equally. On the contrary, this is a disease that kills the oldest. Actually, that is also not accurate; this is a disease that kills the sickest. 97 percent of the people who have died in Italy have not only been old, they’ve been sick.

4. There are literally no studies that prove that extreme suppression (quarantine) is effective – because there have been no controls. Why is it assumed that following the Chinese model works? What might have been going on there was not that everyone was locked down, but that health professionals went door to door to find all the sick and vulnerable.

5. Tanking the global economy is not without life and death costs. People will die in the developed nations because they won’t be eating right, or getting proper nursing home care, or they’re depressed and no one can help them, or their illnesses are deprioritized, or research funding is being diverted from lower priority diseases so the cures won’t be delayed in the future, etc. And many more will die in the developed countries because trade will be stopping, they will stop earning, healthcare will deteriorate, the fertilizer won’t be shipped because the ships are laid up so people won’t be eating, etc.

6. This discussion doesn’t account for natural immunity (how many will never get sick? We don’t know how many, but we know many don’t get sick).

7. No accounting for seasonality of disease (why isn’t it rampant in India?).

8. And no accounting for a real alternative: quarantine the people most at risk, and let the rest get on with their lives and keep the economy humming, the factories cranking, the store shelves full of toilet paper. They sent the kids out of London during the blitz in WWII. Help the sick elderly. It may be that simple.

1. Ed D. says:

My “plus one” to this commenter: “I despair at this kind of simplistic analysis”. So do I. I also despair at the one-size-fits-all, top-down, hysterical response of authority-systems and opinion-formers the world over. Jumped-up authoritarians around the globe are trying on some new powers to force people to stay at home, do this, don’t do that – and the freedoms the people loose in the course of the authoritarian response to the virus will not be easily regained.

37. mjmcmahon says:

In Toronto, Canada where I live, Hospital Capacity was already close to 100% before COVID-19. ☹

38. LKM says:

Thanks for posting this and using your platform to educate. In my area of California, we have only a few *known* cases (but they include community transmission and we had no testing until very, very recently, and have very restrained testing now, so….) and many people don’t seem to fully understand what even the social distancing efforts are intended to prevent.

Tim and Felix – Thanks for posting this, and for sharing the spreadsheet. While plenty of the input assumptions are still unknown, the overarching message that this conveys is critical for people to hear…

One challenging reality that this analysis assumes is that the quarantine will last for 40 (or more) days…otherwise the growth will continue to expand at exponential rates.

Until a vaccine or treatment becomes viable, that may be the only mathematical way to ‘flatten the curve’, although in application, economic and social pressures will make it impossible. Indeed, as a society, we may have to prepare for ‘partial quarantines’ that last even longer, and that still allows CV-19 to spread, but at an ‘acceptable’ rate.

For now, getting the word out about the importance of social distancing and quarantining is the most important step, but soon the key information and educational challenge is going to be answering “how long does this have to last?”…

40. Puveendran Arullendran says:

Key Assumption flaw: you are assuming that when a new case is diagnosed it will take 10 days for them to present to hospital . However in Europe ( I am doctor in UK ) , testing is only done in a patient that is already admitted with respiratory problems ( ie they are already at day 10) There is no universal screening to pick them up before they are symptomatic . I believe this is similar in US.

41. Samo says:

Hi Tim. Greetings from Slovenia (8.730-t, 287-c, 1-d). Virus is not a problem,The problem are sanctions and actions of the government.Its time for changes.

42. Chris Y. says:

Just tried out the model…the other thing to consider is that we are talking about **new** demand for ICU beds…in my city there are around 16 ICU bed & based on published statistics last year they averaged 15.1 ICU cases/day… so there is not a lot of unused ICU beds as it is…people already need ICU for “everyday” things… so the actual supply of ICU space runs out far quicker because we have to consider that ICU beds are already being used for heart attacks, car accidents, etc…

43. Margaret Kosmala says:

This is a good first understanding! But the next question is: if your interventions work to keep demand for the health care system within supply (or even if you don’t), how long are you going to keep everyone quarantined? The answer is many many months. As soon as you unquarantine everyone, you’re going to have the same problem of hospital overflow all over again with such a contagious disease. Can our economy survive a 6-month full quarantine? A 12-month full quarantine? Will our populations tolerate it? Do we unquarantine people gradually so as not to overwhelm the healthcare system? How would we do that in a fair and just way? Would really love to see some people writing on these topics, too.

44. Niels says:

Thanks Felix for sharing this information. It’s very helpful to get a better image of the situation.

However, I’m still wondering a few things which I hope someone here can clarify a bit more.

Beware: I’m not claiming the points below to be facts or scenario’s that are going to happen for sure. I’m not specialised in the material at hand, so I use these points to clarify my way of thinking and the questions I’m still left with after much reading and thinking about this topic.

1. Hospital capacity is not only beds, ventilators or meds, but also the people working in healthcare. Most likely, they get sick sooner or later as well. Doesn’t this bring down the hospital capacity even more, thus resulting in an even bigger overflow?
2. Let’s say a region/the world quarantines early enough and the hospitals won’t overflow. How long do you keep people in quarantine before it’s safe enough again? No matter when you start your quarantine, it seems to me like the virus still circulates somewhere in the world. That means that there are 2 scenario’s (of course there are more, but I’m highlighting the 2 most widely separated cases in a simplified version).
1. Let’s say that you started quarantine too late. Hospitals will have been overflowed big time, a lot of people have died (more than should have died), but on the other side most people will already be immune by the time the quarantine ends (assuming you’re immune after you’ve got it). That means that when breakout ‘starts’ again after quarantine ends, the growth will be a lot less severe due to more immune people around the infected. As a result, probably no more quarantines are needed.
2. Let’s say that you started quarantine early enough. In this case hospitals are not overflowed and a lot of lives have been saved. On the flip side, the virus still has a chance of circulating somewhere, but almost no one is immune yet. Doesn’t this mean that when the breakout ‘starts’ again, you need to quarantine yet another time? And again, and again, until the majority of the population is finally immune, causing the virus to finally die out.

In short for point 2: when, according to experts, should it be safe enough to stop quarantine and how many more quarantines are likely to happen after that in case of quarantining early enough vs. too late during the first ‘wave’? And what are the conditions of a virus dying out?

45. André Miede says:

Thank you very much for your insight.

Did you see Joscha Bach’s recent take of this topic (and his back-of-the-envelope calculations)? https://medium.com/@joschabach/flattening-the-curve-is-a-deadly-delusion-eea324fe9727

The Imperial College in London has released a study that is based on proper simulations. It arrives at the same conclusion as Joscha: the number of cases during the peak of the infection exceeds the available medical resources not by a small factor, but by a magnitude. https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf

Hope this helps the discussion.

46. LKM says:

Harvard Global Health Institute data set on hospital bed capacity (parsed out by hospital referral region with local population stats) for various infection rates of adult population across different time spans. Still skips staffing issues and equipment issues but covers the problem of avail vs total beds, including for ICU beds. Fascinating/appalling.

Be sure to scroll down below explanation to read the definitions, which explains some assumptions used. (Such as for “potentially” available beds — what that means).

https://globalepidemics.org/2020/03/17/caring-for-covid-19-patients/

Stories based off this data are running in NYT and ProPublica.

47. Brian says:

Thank you Tim and Felix. These things don’t spread exponentially forever, or 90% of the world would be infected already.

People are not meeting new people every day, they generally keep the same social circles, patterns, etc so even if one person infected 10 (made up number) they aren’t meeting 10 NEW people every day, and so on.

The exponential rate actually declines after awhile.

Another “non-epidemiologist” commented on this effect here:

I don’t know if I can post the website so I put it in my login

48. Roger Dooley says:

Thanks for getting the word out, Tim. Here in Austin, people seem to be in denial. Today, I ventured out for the first time in a week to do a curbside grocery pickup at Randalls. That was a fiasco – my order (placed DAYS earlier) was canceled “due to high order volume.” I found this out as I arrived at the store. But, I was amazed at the level of activity on the roads, in parking lots, etc. Busier than normal weekday, far from the sparse traffic I expected. Maybe all the folks working from home decided to go shopping. This is going to get worse quickly, stay well!

49. howard austin hewlett says:

I am very sorry that people will get infected and some will die but I wish we as a society took our daily health/weight as seriously as we are taking the corona virus.

50. JB says:

Great perspective, thanks for providing a data based view of the situation and why the actions being taken are CRITICAL. Heed the warnings!

51. James Fischer says:

Oh for fuck’s sake. That he’s so special he shall be named Felix. Step up to the fucking plate or leave the planet and take your panties with you. Crazy shit.

52. Colleen says:

I appreciate this explanation.
The concern that I have as a front line care provider is that these models fail to recognize that our hospitals are over capacity to begin with.
Fundamentally we need to change how our society practices medicine and utilizes the hospital.

53. Scott E Hardy says:

Thanks Tim. Great analysis. I believe the same principle of exponential growth and lag time are also in play with global warming. But it is a much slower moving trajectory, which is really bad because by the time people realize for sure that we are in trouble, we may be beyond our ability to recover. Climate change should be treated with the same level of urgency and crisis response as we are now starting to see with the novel corona virus. Bernie has the right idea with his plan to address the problem. Hopefully Joe was listening.
– Scott

54. Luiz Finotti says:

Tim, I’m sure you can’t keep up to all comments and replies to your work, but this post helped me gain political support for actions regarding COVID-19 containment in my city, and, being a physician involved in the management of medical services in my city, that could not have come in a better time. Many many thanks!

55. Forrest says:

At what point does the overall impact of quarantine outweigh the relatively small number of deaths? For instance cars – we’ve decided as a society that motor transportation is worth the risk yet it results in many more deaths than coronavirus. What about tobacco or obesity? Why is this such a greater threat?

56. Anke says:

Tim, thank you for the calculation, I am a microbiologist and totally agree with the post! Can you please put the key findings in 5 easy to understand bullet points on top of the post! The calculation is great but non-scientists will get lost in the reading and not get the take-home messages! And it would be great to extend the calculation to the following: Which quarantine measures should be taken at which day in the “cycle”. Clearly most politicians are missing out on having such numbers at their hand at the moment because all their actions are lagging way behind what would be required! iE I am in Australia, we are still relatively early in the cycle with lower infection rates than Europe and schools and childcare are still open. It would be great to have a model how effective each quarantine step is (how many people do you get in contact with) (voluntary self isolation, cancelling events, closing schools and childcare, closing shops, ban on going out) and at which infection rate within a specific population which step should be taken (or: should have been taken, because everybody is lagging behind …)

57. Rambo says:

Hi Tim and Felix

Nice analysis.

Lots of insight from a simply structured well focused model.

Would suggest it is worth looking at the role of front line health care staff and their testing and protection, because i think they could be a big factor in the propogation of the disease (as well as providing the treatment and caring for the sick) … if they arent protected and checked out properly. sick patient gives te virus to paramedic, nurse etc … who gives it to other patients and colleagues, before realising that they have the virus. rinse and repeat. coupled with exponential growth, equals … a further nasty big positive feedback loop.

Proper masks, gowns, regular testing, and possibly increased social distancing amongst the medics, might nip this in the bud. Nil protection and nil testing will leave it free to go into overdrive.

Exponential growth plus lagged effects equals super difficult arena for setting policy.

Covid-19 is a very dramatic example; global warming/heating looks like it is probably another one, albeit in slower time. There are others too eg in the criminal justice system.

Sterman’s book on System Dynamics is a great exposition on this (and more), if anyone wants the full nine yards, but its not a light read … or ‘The Forest and the Trees’ covers it in a bit less depth but easier to digest.

58. Martin G Backe says:

You should see the just released Reason interview with Richard Epstein which basically argues against everything you’ve written here. I’m not saying that you’re wrong, but it’s nice to see the counter arguments.

59. Ann Michele says:

Most hospitals are already at nearly full capacity, canceling elective and non urgent surgery will only gain maybe 20% more beds, the time to quarantine was yesterday in any example. And the number of hospital beds are meaningless, the only statistic that counts is the number of staffed beds, no nurses=no hospital beds. Plus there is not enough PPE to take care of infected patients , this is going to be Italy in about a month.

1. Avalanche says:

Another problem with “elective and non-urgent” is — who decides? My bro-in-law just began chemo for his recurrence of lymphoma. My sister is freaking out because of ALL the times to shut down his immune system?! But it’s his decision. Which is “more urgent”? Should he risk having no immune system during a bad pandemic, or risk cancer spreading over however-many-months corona-chan goes on?

Vox Day, in his blog, drives off questions — and sometimes questioners: “what about meeeeeee?” But there are the many millions of people trying to balance what-about-me — just as we try to balance it about working, finances, and crashing the economy.

But Ann Michele has the center point of it: beds WITHOUT staff are not hospitalization; and ‘unstaffed beds’ are available in homes (and probably more comfortable too).

I’m a moderately healthy 64-yr-old, and 100% NOT counting on the VA to be of any use to me in this. VA is mostly crap in good times; it will be beyond useless if I do get very sick. I’ve laid in all the OTC/self-treatment meds for whatever I can imagine I might need; I WISH I had taken time to update my will; and I began my social isolation a week+ ago. I am highly intelligent and used to be medical affairs director and EMT teacher for an ambulance corps. If *I* am making plans to ‘do-without’ — what are the MPAI supposed to do?

60. Sarah Cartsburg says:

Here in bavaria(germany) we are starting to not to allow any surgery etc that isn´t 100% necessary right now (like cysts, vasektomies, basically all that can wait), building up huge tents next to hospitals and converting gymnastic halls into space with hospital beds.

Most doctors, f.e. trained surgeons, have to undergo special trainings now to learn how to use the lung stuff (don´t know the proper english translation, maybe ventilators?) – and we have ordered medical students into the hospitals – so basically we are really preparing for the worst case. Hospitals are closed for everyone else, and as for now they are empty.

But since we are on the border to italy, and many people went there on their skiing break at the end of february, i think it´s better to be prepared, especially since this exponential curve is so steep.

What i don´t get: Schools and kindergarden, as well as cinemas, reaturants etc. are closed (and there are rumours about a big shut down of everything on friday) , but as long as everybody still goes shopping for groceries daily – how will the infection rate go down?

It´s no like we have those huge supermarkets like in the US where there is more space that people. People are close together when we shop, stand in line, touch our food and pay, and also the money and coins (or the automatic payment systems, but where you still enter the code) might transfer it too, right?
Why haven´t we started to stop normal postage shipping and all those amazon and DHL and UPS cars have to bring food to the houses instead so that people actually do stay home?

and why is almost NOBODY (at least not the mass media) talking about actually boosting everybodies immune system, fe.e with diet changes etc.?

It is proven that fear slows down your immune system – so preparatio n and care, yes, but all this fear maybe isnt the best.

61. Andreas says:

Thanks for sharing the template! I have a question regarding the model template. How do I get the time factor of the hospitalization working? They don’t seem to be factored in anywhere in the template.

62. Jon says:

Brilliant article. Wonder what is the average occupancy rate of hospital beds. Is it under 3%? Otherwise, alarm bells are not going to ring until much much later.

63. Jim Wang says:

Instituting a quarantine is a great first step but getting these numbers out in front of people is important to maintain the quarantine. Locally, with schools out, a lot of parents were taking their kids to the local parks and having them all play together on the playgrounds. Our county had to shut down the parks to prevent this. Many people aren’t personally touched (yet) by the virus and fail to heed the warnings of people who can project 20 days down the road!

64. DonB says:

Perhaps Social Distancing isn’t the correct term to use? Physical Distancing is necessary, but we need to remain Social.

65. Lorenzo Cagni says:

Our healthcare personnel are working hard and everyone here is oriented towards solving the problem.
We don’t like to be blamed or considered to be greasers.

Felix is ​​absolutely right when he says that we should all be quarantined long before we are in the midst of the general pandemic.

I know there is talk in general, but some think that it was Italy that acted late.
I honestly don’t think we could have acted earlier, there are countries like the UK that still persist in not looking reality in the face.
Yet even Trump had initially allowed travel from the UK and Ireland …

I’m not an expert at all, but this simple reasoning is based on facts. Tell me if I’m wrong in some passage.

I would instead like to see Italy help in the future the other countries that will find themselves in our current condition.

66. CS Russell says:

“Flatten the Curve”
Humbly suggest this easy to digest vid of this same concept. Joe Hanson.
The punchline is well delivered: Philadelphia vs. St Louis in 1912

67. VK Lima says:

Keep calm, wash your hands, all surfaces, phone screens, steering wheels etc. Eat clean, sleep well, drink plenty of clean water, Keep calm, keep calm, keep calm..

If we are all so motivated on fear, living fear based lives, imagine the possibilities the government can hold over us.

Don’t be scared, be smart.

68. Ryan U. says:

Is it possible that COVID-19 arrived in the US earlier (or with more prevalence) than the first “documented cases”? I have not seen this idea discussed much. What if there were affected individuals that mistook the symptoms for seasonal flu and never sought medical treatment? While this article is a study in models and not epidemiology it would affect some of the outcomes.

69. Gabriel White says:

Wouldn’t it change your model drastically if you change the assumption that hospital beds are not static? What if the mayor of Springfield turned the stadium used by the local NBA team (as well as other now vacant public spaces) and immediately began the process of turning them into temporary hospital wards?

Also, what if the assumption that quarantining early cases will prevent the spread of infection is faulty?

There are several news stories from the last few days that show that enforcing an effective quarantine of a population of any meaningful size in the USA is not possible (barring the use of draconian methods of control, such as those used in China, which would not be legal in the USA). You are never going to get a high enough percentage of the population of a city like, say, San Diego, to stay inside for a month.

Even if the governor deployed the national guard, you still aren’t going to achieve anywhere near 50% compliance. What are they going to do, shoot people that violate the quarantine? Right now they can’t even convince people not to hoard toilet paper.

70. Julie says:

Thank you for the analysis, interesting, but a few concerns:

1. It is assuming there are no negative effects to an early quarantine that could themselves cause increased hospitalization – there likely are, look at the increases in hospitalization around times where people become isolated, eg. the holidays.

2. There is unlikely any point in time in North America where hospitals are running at anything under 75% capacity, and most typically run close to or over 100% capacity during normal times.

Current hospital systems/hospital workers are setup to be stretched in normal times. Excesses/redundancies need to be built into the system before pandemics, not during. We shouldn’t be in a position where we are relying on a quarantine to solve this in the first place. This is not an unexpected event – it has been on the brink of happening multiple times, including with SARS, H1N1, Ebola, etc.

71. Julio says:

Comes to my attention the exponential decrease if people seek hospital attention earlier on. Changing those 10 days to 8 made an incredible difference in most scenarios. This should be a front of attention as well.

72. J Tubb says:

3 weeks of quarantine can make a huge difference. See Codigno, Italy. See Singapore. My father was isolated in a TB ward for seven years of his 20’s. He came out alive, with damaged lungs, but maintained a wry, clever, philosophical sense of humor. Had me, his first child, at 34. I can do this quarantine thing- he was a great example. I am high risk. Let’s crush this!

73. Joseph Fischer says:

Felix and Tim, Thanks for stepping out. I really appreciate it. I have been following in my local community – Napa, CA. Just the facts Ma’am — Dragnet parlance. County officials are either witholding information or don’t know / can’t figure it out. Stepping out means people come out of the woodwork with their own baggage on issues / assumptions / etc. Thanks again for putting it out there. Keep your eye on the ball as you see it with input that feel is valid. Best Regards.

74. mike says:

Tim talked about companies like AirBNB and Hilton have stepped up to help our medical heroes have safe places to recoup from long shifts.
Here is another possible solution. ***Especially for remote hospitals**
A call out to the RV, Motorhomes and Trailer dealers. Lend and donate units that can be strategically placed close to hospitals that will provide isolated quarters for Dr’s and other essential medical workers. As we know many of our heroes won’t be able to go home without risk of affecting family members. They will need rest and a quiet place to recharge.
This could also be said for what we used to call the entertainment industry whom is currently on indefinite hiatus. Use their STAR TRAILERS and put them new hospitals for our heroes. History will remember those who step up for our health care workers now.

75. PJ says:

How do you change this model to start hospital occupancy starting at 50% instead of 0%?

76. tMichael says:

Perhaps seeing hospital beds as a fixed number is wrong. With time, ICU’s can be expanded, some patients driven to other hospitals. Space can be made. Imperfect MASH units created. Not immediately but each week, seeing the coming crisis, hospitals out a necessity can get creative.

77. tMichael says:

This is shooting in the dark, hoping that smarter people can answer- If ventilators/respirators weren’t available, would a CPAP machine attached to an oxygen concentrator help? (perhaps concentrator isn’t the right word, but there are oxygen enhancers that can attached to CPAP machines.
thanks.

78. Mathias says:

79. Darren Sands says:

Hi Tim,
We have a ventilator assist system thats is based on AI algorithm, in November it received FDA approval.
It can reduce the time a patient requires IC assistance by up to 25%.
It monitors patients vitals constantly and automatically recommends adjustments which allow lower qualified nurses to control the ventilator.
There is a remote feature which allows doctors to adjust settings remotely removing them from the contagious environment.
Not sure if I can put a link but if you want more info please be in touch and I will leave the website in the details box.
Best regards
Darren Sands

80. Justin says:

Just sent this to an er doc friend of mine to see what he says.
‘we’ really really screwed up on this one by looking at the math. And to think there r still morons out there sticking their heads in the sand or even holding ‘covid parties’

1. darren sands says:

Good news. Thanks Justin, let me know if you need anymore info.