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Comment by randomsearch | Hacker News Reader

Surprising to see some of the same “but hospitalisation rates low” comments on HN when we are literally supposed to be the world’s foremost users of complexity theory and big O notation.

Even if hospitalisation rates are a small constant factor lower, doesn’t everyone remember from CS101 that O(k^x) is bad news bears and that constant factor ain’t gonna save your assignment once the problem size grows just a little more.

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When x trends to infinity, which is irrelevant in this case since you're limited by population numbers.

Feel free to plug in population numbers into an exponential growth function and watch the medical system get overwhelmed. This isn't about it collapsing - once a few thousand people have died preventable deaths and a bunch of medical staff quits because of PTSD, we'll stabilize. But at least in the ethical framework dominant in my cultural sphere, that's not really an acceptable path.

Remember that it's not an exponential.

The total number of cases is very similar to a logistic curve that initially can be approximated by an exponential, but later it stabilizes and it looks like a step.

The number of active cases / hospitalizations is similar to the derivative of the logistic curve that initially can be approximated by an exponential, after some time goes to zero. It looks like a bump.

A smaller hospitalization rate means that hopefully the bump is low enough to not saturate the hospitals.

More about some simple models: https://en.wikipedia.org/wiki/Compartmental_models_in_epidem...

The R value model is a doomsday sayers dream, because any increase automatically means exponential growth. Any growth, no matter how tiny, translates to scary graphs.

Of course exponential growth goes quickly. OPs argument was that the constant factor of hospitalization doesn't matter at all, which is ridiculous in the real world.

If you take an exponential growth of 1.5, quite a quickly spreading infection. And a hospitilization factor of 5% vs 0.05%:

day 20: 3.3k cases, 165 vs 1 hospitilization

day 25: 25k. 1.2k vs 13

day 30: 191k 9.5k vs 95

day 35: 1.5m 73k vs 728

day 40: 11m 550k vs 5528

So a 10M people country with ~5k. beds wouldn't have healthcare capacity due to the constant factor, while without they would be overwhelmed within a month.

What is your point? That any growth, no matter how tiny, translates to scary graphs?

Not just that, but after 2 years of pandemic you start having very few new people to infect effectively.

Having been infected with one strain of SARS-CoV-2 doesn't protect you from all other variants. It's not even clear that it protects you from reinfection with the same variant indefinitely.

I was infected with Delta 9 months after one of the initial strains. I was more or less as sick as I was the first time for a full two weeks.

That said, when I looked up studies on that the chances were about 1% for that to happen to me (at that time).

Could you expand on your actual argument beyond "exponential growth bad, we are all doomed"?

Are you suggesting how lethal it is when someone gets it is of no consideration?

A reduced rate of severe cases still is simply a mere constant factor that won't save us. Unless the rate goes down to approx. zero we're back to square one where there is almost no immunity and the number of simultaneous severe cases will easily and quickly rise far beyond the hospital capacity due to the very high rate of infections.

On average, there are hospital beds (of any kind) available for about 0,3% of the population. If 5% of the cases are severe enough to require hospitalization, this means that hospitals get completely overwhelmed when 6% of the population are down with COVID simultaneously. And that's assuming that every hospital bed can be used, which is unrealistic.

> A reduced rate of severe cases still is simply a mere constant factor that won't save us

Yes.

That this has to be explicitly stated here explains my surprise.

We need R0 to be under 1.

Lets imagine cases double every day, and 1 in 1000 go into hospital

Day 1 - 1 cases

Day 11 - 1000 cases, 1 hospitalisation

Day 21 - 1 million cases, 1,000 hospitalisations

Day 31 - 1 billion cases, 1 million hospitalisations

Day 41 - 1 trillion cases, 1 billion hospitalisations

That would be awful. It would be impossible too.

But we only have 7.8 billion people. Or we are Saying people get reinfected multiple times within 33 days.

You assume no reinfection.

It is possible to get to 100% population death if you assume 0.0001% death rate where the 99.9999% reinfected over and over untill they die. That assumes reinfection.

Reinfection in 41 days?

The average hospital stay is much shorter and so you're ignoring queue theory 101 and Little's law.

You are quite correct regarding the big picture.

But as someone who is one of those data numbers, I care very much that I am a lot less likely to end up in hospital.

thanks malthus

People grasp onto hope, even pragmatic thinkers like the hn crowd

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