Understanding Coronavirus with Numbers -Critical Cases

How many people are in critical condition due to coronavirus and need ventilators? What’s the capacity of hospitals to help those patients?

In order to be able to help with the COVID-19 pandemic, we must first understand the potential problems that arise and quantify them so that we can minimize suffering (measured as the number of deaths, the number of infected).

As a mathematician I’ve decided to venture into numbers trying to understand capacity of hospitals, what’s needed and what’s lacking around the world. I have no medical training and so you should consult this text with an expert before acting upon it.

I’ve gathered data from publicly available sources, publications, press: from general statistics to particular needs when it comes to ventilators or hospital beds. I did it to understand how difficult might be the situation if we don’t act now.

Main takeaways from this text:

  • around 5% of infected need to be hospitalised
  • around 2% of infected need ventilators (= 40% of hospitalised)
  • current max capacity of hospitals around the world allows for up to 6% of population being infected in a given region.

Update: since publishing this story a couple of people contacted me to indicate that some of the hospitals are already at their max capacity, even though the % of population infected is much lower for that. The reason for that seems to be that in certain regions many ICU beds are already used by non-COVID-19 patients. This shows that 6% is really rather an upper bound and most hospitals have much lower capacity.

It’s also worth noting that if hospitals are above their capacity then the mortality rate of patients go up drastically. As was explained here:

  • Regions that are prepared have a fatality rate of ~0.5% (South Korea) to 0.9% (rest of China).
  • Regions that are overwhelmed have a fatality rate between ~3%-5% or even higher (Italy has a fatality rate of 7%-9%, as of March 22th there are 53,578 coronavirus cases and 4,825 deaths which gives 9% death ratio).

That’s why it’s extremely important to fight the number of coronavirus cases and keep them below capacity of hospitals while raising this capacity at the same time by building more ventilators, ICU beds and recruiting more medical staff whenever possible.

General statistics on cases

First of all most people will not get severely ill, but the evidence from other countries suggests that around 15 per cent will become severely ill and a further 5 per cent will become critically ill. You can have a look at data here to verify that 5% are in a critical condition. As of 20th March 2020 there are 158,588 currently infected patients of which 7,636 (5%) are in a critical condition. In the same statistics we can check current cases per 1M population: Italy has 679, Switzerland 567, Spain 437 (though this doesn’t say anything about distribution throughout regions).

I’d like to understand what’s the maximum percentage of population that can be infected at the same time for hospitals and medical staff to be able to still help everyone in a critical condition.

The answer to this question will hugely depend on a region of course, but I’d like to arrive at rough estimates of scale we can deal with.

Beds and intensive care hospitalization

In the United States there are fewer than 100,000 ICU (Intensive Care Unit) beds according to a recent analysis by Johns Hopkins Center for Health Security.

In the UK the NHS currently has just under 150,000 beds in total, around 4,000 of which are for critical care.

By EU standards, there should be 4–10% ICU beds in hospitals. In EU the average is 529 beds per 100,000 people, with lowest in the UK (280), highest in Germany (818). Taking upper bounds we should expect 52 ICUs per 100,000 people, or 5,2 per 10,000 people.

As we have seen around 5% of infected patients will need ICU beds — being in critical condition — which means that hospitals at their maximum capacity (assuming beds are used only for COVID-19 patients) can host all patients only if there are less than 20x 5,2 = 1050 cases per 10,000 population, or in other words, roughly less than 10% of the population is infected. This scenario depends on a region, % of ICU beds in hospitals in a given region, non-COVID-19 patients already in hospitals, etc. Presumably the actual maximum capacity number for hospitals is lower than 10% due to other conditions, like the number of medical staff, number of ICU beds, number of ventilators.

Now this statistics doesn’t take into account ventilators, as patients in critical conditions need them to sustain their health.


ICU are not enough because we need also ventilators to accompany most of beds, the lower bound being around 40% of hospitalized need ventilators, so 2% of all infected (confirmed also here).

Germany: German hospitals already are among the best equipped in Europe when it comes to both intensive care beds and the availability of ventilators. According to the government, Germany has around 28,000 intensive care beds, of which 25,000 are equipped with ventilators. So this is almost an ideal scenario when most of ICU beds are equipped with ventilators. With a population of 82 million in Germany up to 6% of the population can get infected before hospitals reach their maximum capacity.

USA: A 2010 survey reported U.S. hospitals had 62,188 full-featured mechanical ventilators. Currently still less than 100,000 (I’ve seen other estimates putting it at 160,000).

Hospitals in Washington, the state hit hardest by the epidemic, had 12.8 ventilators per 100,000 people, the second-lowest per-capita supply, ahead of only Idaho. This would mean that 3% of population in Washington infected is already over the capacity of hospitals.

A survey conducted by outfit of Thomas Kallstrom, the chief executive officer of the American Association for Respiratory Care, five years ago determined there were about 155,000 respiratory therapists in the United States, with a vast majority of them working in ICUs. Kallstrom notes that on average a single respiratory therapist can manage ten patients at once.

This would indicate that a larger problem in the US is having enough ventilators, rather than enough respiratory therapists (assuming majority of them works). Again, this depends on a particular state or region.

UK: The National Health Service has just 5,000 ventilators or 6,700 ventilators, which are crucial in caring for patients in a critical condition. This means that there are less than 1 ventilator per 10,000 population, so maximum capacity of hospitals is reached when 2% of the population is infected.

Predictions state that UK would need probably 20,000 ventilators, which would mean that there are 400,000 cases expected. As of 20th March, there 3,269 cases in the UK.

Poland: In Poland there are 10,000 ventilators. which is less than 3 per 10,000 population or in other words, no more than 6% of population can be infected for hospitals to be able to help everyone in critical condition.


This short text was to show that in order for hospitals and medical staff cope with the COVID-19 only a small percentage of population can be infected. If we surpass 5–6% of the population infected (and that depends on the region) the death toll will be much larger.

From the point of view of practical help you can:

  • produce more ventilators
  • prepare more ICU beds
  • recruit more medical staff

to boost region’s hospitals capacity in fighting COVID-19. On the other hand, everyone else (non-medical staff) should stay home. Just don’t go out — it’s really the best solution for now to stop spreading the virus — unless you can directly help those infected or medical staff in their amazing job.


P.S. If you’re looking for a perspective on what might happen to our global economy because of COVID-19, have a look here.

Written by

CEO Contentyze, the text editor 2.0, PhD in maths, Forbes 30 under 30 — → Sign up for free at https://app.contentyze.com

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store