UKC

I'm aware of my almost total ignorance regarding stats, and aware that what looks like an obvious or intuitive conclusion to draw from stats is often wrong.

So, here's my question.  I've read that (IIRC) each corona-infected person will infect 2 others.  I'm assuming this means if we don't self-isolate.  If we do self-isolate, this number would drop, but would still be significant.  It seems logical to me - and this is probably where I'm going wrong - that this means the entire population of the planet will become infected, and this in turn will mean a death toll in the 10s or 100s of millions. 

This universal infection level, and the death toll, sounds wrong to me, but I don't know why.  The numbers seem (to me) to imply it.  Could someone please explain how I've gone wrong?  Layman's language would be much appreciated 

In reply to Thrudge:

The much discussed paper now informing government policy comes out not so far from a simple estimate like yours for a “do nothing” scenario (at the UK level).  That’s not to knock it; they model many different scenarios (not all and arguably not the one we should be following).

This is nowhere near the most terrifying pandemic one could imagine.

In developed nations, the death toll is highly dependant on if healthcare is overwhelmed or not; this could make a 10x difference to total deaths and this is where slowing the spread down counts.  Not in total infections but in what fraction of those can get potentially life saving medical help,

If it’s slowed down enough by social distancing and isolation of the infected, then something interesting starts to happen; more and more of the person-person contacts that normally spread the disease now involve at least one recovered/immune person and this reduces transmission.  This means the disease can die out infecting less than half the people out there.  

In reply to Thrudge:

For a simple model where each case infects R others, the behaviour is different for the case where R is more than one and the case where R is less than 1.  If R is two, then the infection grows 1,2,4,8... Thats bad.

But lets think about the case where R=0.5, and ofr the sake of argument we have 1000 cases.  These will create 500 new cases. That 500 will infect 250, then 125, 64, 32, 16, 8, 4, 2, 1. That last case may infect one more, and maybe one more after that, but it stops there.  Total cases, adding all those numbers together, is about 2000. So it doesn't grow to infect everyone.  Obviously it won't go exactly half each time, there will be a load of random fluctuations, but the overall pattern still works.

So the aim with all the social distancing and self isolation is to push R down to less than one, in which case the epidemic will slowly peter out.  This is what happened in China.  It will be much, much more difficult to do this worldwide though.

In reply to Jack B:

Thank you, gentlemen, that is very informative.

In reply to Thrudge:

I found this useful : https://gabgoh.github.io/COVID/index.html

In reply to Jack B:

The full aim is not to let the epidemic die out from lack of transmission (which would take months to years of worldwide isolation, and would be very fragile) - it's to buy enough time until a vaccine can be developed.
There are cases in the past (e.g. 1918 flu pandemic) where the lockdown was eased off, and the virus resumed exponential growth to reach a 2nd higher peak. We are not safe until we have reached 60%~ immunity in the population (which will only be gained through a vaccine or developed immunity - but this second path means a lot of death, even with a flat curve).

In reply to Jack B: very good simple explanation which should be made clear to everybody .

In reply to Jack B:

Pretty good explanation! Epidemics only grow at (roughly) exponential in the early stages, which is where the UK is now. There may be some 'saturating' effect which limits growth, due to contact network structure, and makes the growth more like linear -- this appeared to happen in the West Africa Ebola outbreak 2013-16, there was a lot of sub-exponential growth -- I can try and find an old slide that illustrates this if anyone is interested. 

In reply to Jon Read:

Yes please .

In reply to Thrudge:

Ive been pretty addicted to this worldwide table-

https://www.worldometers.info/coronavirus/

Can anyone explain how Germany has about 25,000 cases yet only about 90 deaths? This seems to completely buck the trend.

In reply to Dave 88:

Remember that its “detected cases” not total cases.  Germany are testing more people than most places and this means they catch more of the mild, non fatal cases.

An article in the FT said they’re gearing up to test 160,000 people a week.  The UK has tested about 72,000 people total since this began.

Extensive contact tracing and testing/retesting a few days later looks like the only good way to have fewer deaths without almost indefinite lockdown.

Italy has more deaths proportionally as healthcare is overwhelmed in places, and as they have had this underway in number for longer - it can take weeks I think to go from a detected case to a death.
 

In reply to Thrudge:

Yes, pretty much, in the same way that nearly everyone has had colds and flu at some point.  Though, once lots of people have had it, and are immune, it then makes it harder for the virus to spread (because there are far fewer non-immune people to infect). 

What then happens is that the virus mutates, so can re-infect people who have had it before (which is why we still get colds and flu, even if we've had them before).  But then the previous exposure usually gives partial immunity and means it's much milder than the first time.

Of course an effective vaccine could change the above and mean that most people don't get it -- but then, virus mutations mean that vaccines are usually not totally effective (cf colds & flu), but a partially effective vaccine can give you some immunity, so you still get it but more mildly. 

Yes, over time, and worldwide, deaths could well be tens of millions.   But then realise that, worldwide, several tens of millions will die every year anyhow of everything else.

Flu kills half a million a year, worldwide.  The long-term future is likely that, once we've all built up some degree of herd immunity, covid19 might settle down into something similar. 

In reply to Jack B:

I think most studies are putting R0 between 2.2-2.4. The important point is like you mention that infections will also decrease exponentially once R is below 1. I read that for Hubei it was reduced to 0.32 (take the Chinese statistics with a pinch of salt), and the daily rate may be beginning to drop in Italy also, after 2 weeks of lockdown measures. All of the other variables in the equation (CFR, hospitalisation rate) have a limited effect on the disease burden compared to R, but it is also the variable that most of us can actually affect by our actions.

In reply to Thrudge:

I've just started 'The Rules of Contagion' and its a great read. Written before Covid-19 became big, it nevertheless is a fascinating and accessible read on epidemiology and also how non-virus phenomena can spread, such as ideas, fashion trends, banking decisions, memes etc.

One point to remember about spreading diseases is that the R number only affects the susceptible population. In traditional epidemics, those that recover become immune, so the R number has a smaller and smaller pool to infect, and therefore the number of total new cases decreases. 

We're not sure if this is the case for Covid-19 but self-isolation essentially works in the same way but the lockdowns should decrease the number of potential transmissions while we understand it more.

In reply to wintertree:

Ah ok, well explained thank you

In reply to Dave 88:

There's an article currently on the Guardian website discussing the German figures. It's interesting.

In reply to Dave 88:

I should be clear - it’s not a definitive explanation.  I don’t know the total number tested in Germany, only what press report of their plans, and I don’t know about differences in clinical care in the two countries.  But the difference in testing rates is one factor.

In reply to mike123:

Let me know if this works.

https://livelancsac-my.sharepoint.com/:b:/g/personal/readj2_lancaster_ac_uk...

In reply to Jon Read:

Yes, that works.