# How long until most of us have been infected?



## SPC100 (4 Apr 2020)

One way the restrictions/crisis ends is when everyone (or a significant percentage) of us are infected. 

Exponential growth is hard to understand.

How many times does infection have to double to reach 4 million?

Based on current growth how long will that take.


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## SPC100 (4 Apr 2020)

Taking 4million as most of us, and 4k as current infections.

4000 x 2^x = 4million
2^x = 1000
X = log (1000,2)
X is 9.6

I.e. after ten doublings 4million will be infected.

Iirc we are doubling infections every 5 days at the moment. 

I realise that a lot of things can change the growth rate.

Within 50 (10x5) days at current growth rates the infection crisis will have passed.

This is a lower bound for how long it will last


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## Brendan Burgess (4 Apr 2020)

I don't think it's the right question, but this is what it looks like if it did double 10 times


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## Brendan Burgess (4 Apr 2020)

4,273 is the number of confirmed cases. 
These tests were probably taken, on average, a week ago.

So there were 4,273 confirmed cases a week ago.

In reality, there were far more cases as most infected people were not tested.

You are assuming that everyone who is exposed to it will get it. This might be right, but it could be that some people in the population will be resistant to it.

I think that a herd immunity develops much earlier than 80% infection.  ( 4m out of a population of 5m)

And, of course, the rate of increase will be determined by our own behaviour. 

Brendan


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## Oisin19 (4 Apr 2020)

It doesn't work like that. Exponetial growth stalls as it goes through the population and people build up immunity. Also by flattening the curve you extend this period. 

I think if no mitigation factors were put in place there virus would fizzle out after 3 months.

By flattening the curve the virus will be around for nearly 2 years as we have to reduce the spread to keep the ICU demand at its max level for a longer period of time. The hope is that a vaccine comes into place to kill it off. There is a lot of factors at play and its a fine balancing act!


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## SPC100 (4 Apr 2020)

I agree the growth rate will slow (and time to double will increase) due to measures but also as you say as percentage infected/immune increase i.e. the doubling time will increase over time.

I agree the starting number is wrong.

But we can still use the current growth rate to have a rough prediction how long it will take for a significant percent of population to be infected.

The prediction will of course change drastically as growth rate changes.


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## SPC100 (4 Apr 2020)

Let's say Herd immunity is 60 percent i.e. 3 million it's still ten doublings to get there.


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## joer (4 Apr 2020)

Dont forget that we are all working on if,s but,s and maybe,s. No one really knows for sure.


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## SPC100 (15 Apr 2020)

406 deaths /.37% infection fatality rate estimates that 109729 were infected.

That assumes that the infection fatality rate holds true for Ireland.

That puts us at 5 doublings away from herd immunity/most of us being infected.

Deaths are currently doubling about every 7 days, if that rate continued it implies about 35 more days.

Hospital and icu admissions are trending towards doubling every month, which would imply 5 months.


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