Chance of staying well until herd immunity is reached?

[Bongleur]

Here is something for the math-oriented to pass the time:

Chance of staying well until herd immunity

Is it possible to determine the _relative_ chances of avoiding infection until herd immunity is reached? ie odds of success if herd immunity is at 40% instead of worst cast (say 80%). In other words, a dimensionless Risk Factor.

We don't know actual "time" in days to reach Herd Immunity. But maybe we can drop out "time" by making other factors relative to each other.

The time you have spent actively avoiding infection is either an investment or a sunk cost. Might the way you view it determine how you write the equation?

To remain well, you have to win a coin flip every day. But we don't know the chance of failure per day, so you can't use the simple equation of "success = 1 minus the (cumulative) chance of losing."

But it is also like radioactive decay. Which is the same as compound interest, only the Half Life has a negative sign, and compound interest Doubling Time has a positive sign.

Both of those can be re-written as "percentage per day." - except we don't know the actual value of that number.

If we set a worst case for "fraction to achieve herd immunity" - say at 80%,

then is it possible to figure out that "the chance of staying well until herd immunity is reached, IF herd immunity is actually reached at 40%, is 5 times better than if it is at 80%."

We won't know how many days 5x better adds up to, but its a dimensionless Risk Factor.

You can graph this and get a decay curve -- the chance of staying well long enough becomes smaller, as the actual % needed for Herd Immunity rises. Can we get a curve whose shape informs us of something useful?

A more sophisticated equation might use not only the worst case % for herd immunity, but the fact that "today" we have not achieved it, and the reasonably-estimated fraction who have been infected is (whatever percent). So you would have a lower bound as well as the upper bound to constrain the curve.

Herd Immunity is a function of both % of population, and time to reach that % (but we don't know the number of days).

Can "time" be dropped out of the equation or normalized to equal 1, so everything else is relative?

Another factor which drops out is your Personal Avoidance Factor. You know that staying home is better than being a dentist. But it won't change the _relative_ difference for _you_ between Herd Immunity At 40% vs 80%.

The unknown _absolute_ difference will be quite large for stay-home vs dentist, at every value of "Actual % For Herd Immunity." Those would be different curves that stack atop each other (shape is the same).

There are a lot of Factors, but I wonder if it can be structured to answer this particular question in relative terms.

EDIT: and of course the "Actual % For Herd Immunity" is a function of R0. Something that epidemiologist blogger Trevor Bedford said seems to indicate it is a linear correlation, if it was quoted right. ie reduction of R0 by a given percentage reduces the Herd Immunity number by the same percent. Not sure about this though.

 

[OldShooter]

If herd immunity is defined as 80% being resistant to the disease, then eight chances out of ten you will become immune . If half of the herd becomes immune through vaccination, then the raw odds say that it's four out of ten that you will get the disease. But (#1) as an upper-class old and rich American your chances of being immunized are probably better than random. But (#2) there may not be a successful vaccine. The Clint Eastwood question applies: " .. you've gotta ask yourself one question: "Do I feel lucky?"

 

[Sunset]

Herd immunity really only means the virus will not spread much within the community, and often will die out in spots as it cannot find anyone else to spread to, as the next bunch of candidates are all immune.

It does not mean, vulnerable people (those without immunity) won't get infected.

 

[Bongleur]

If herd immunity is defined as 80% being resistant to the disease, then eight chances out of ten you will become immune . If half of the herd becomes immune through vaccination, then the raw odds say that it's four out of ten that you will get the disease.

This has nothing to do with the question posed.
Herd immunity is when it NO LONGER spreads within a given population.
If that is 80% then 80% WILL be infected before it stops spreading.

Becoming immune, either after infection or via vaccine, has nothing to do with the question. Its about AVOIDING infection.

You have to win a coin flip every day, and you have to play until herd immunity is reached. Since "time" (number of flips) is not known, it can only be expressed as "my chances are x times as good if Herd Immunity is at 40%, than if it is at 80%."

 

[OldShooter]

This has nothing to do with the question posed.
Herd immunity is when it NO LONGER spreads within a given population.
If that is 80% then 80% WILL be infected before it stops spreading.

Becoming immune, either after infection or via vaccine, has nothing to do with the question. Its about AVOIDING infection.

You have to win a coin flip every day, and you have to play until herd immunity is reached. Since "time" (number of flips) is not known, it can only be expressed as "my chances are x times as good if Herd Immunity is at 40%, than if it is at 80%."

I'm not even going to try to deal with that, but I would observe that one's chances of becoming infected on a given day are not 50/50.

 

[frayne]

Is herd immunity even possible for a virus that keeps on giving, like the flu or a cold ? Even though we know little about this specific virus, it does sound like one can be re-infected.

 

[DrRoy]

I think the question was: what are the odds of being in the 20% that do not get sick?

 

[mpeirce]

Is herd immunity even possible for a virus that keeps on giving, like the flu or a cold ?

There is no “the flu” or “the cold”. Each of these are families of viruses.

If you catch a specific influenza virus and it doesn’t kill you you won’t catch it again. BUT you can certainly catch another influenza virus later.

The challenge with influenza and rhino viruses is that there a many variants of these viruses and new variants appear often.

 

[Sunset]

I'm not even going to try to deal with that, but I would observe that one's chances of becoming infected on a given day are not 50/50.

+1

Day's DW & I stay on our own property, the chance of us getting infected is ZERO.

Day's I have to go pick up groceries, medical appt, etc, are greater than 0 and vary a lot each time, but no real way to quantify it.

 

[Bongleur]

I'm not even going to try to deal with that, but I would observe that one's chances of becoming infected on a given day are not 50/50.

Delete "coin flip" insert "stochastic process."

 

[Redbugdave]

The fly in the ointment is that now the doctors are saying that a person that has had it could catch it again. Possibly another strain?

 

[statsman]

The fly in the ointment is that now the doctors are saying that a person that has had it could catch it again. Possibly another strain?

I wish I could find the article I read related to this topic. The Reader's Digest version was that some viruses would mutate and catch those who were "missed" on a previous go-around. It's unknown if COVID-19 will work like this or just fade away.

 

[audreyh1]

The fly in the ointment is that now the doctors are saying that a person that has had it could catch it again. Possibly another strain?

I think it’s just that some people take a very long time to clear the virus.

 

[RAE]

I think it’s just that some people take a very long time to clear the virus.

I think so too. Most epidemiologists seem to believe that those who get infected with COVID-19 will have some degree of immunity for a while. No way to know what that time period is........could be a year, could be 5 years, could be longer.

With regard to herd immunity, I've seen figures like 60-70% thrown around as the percentage of the population that would need to become infected to approach herd immunity. And, as others have said, that doesn't mean the virus will completely die out...........only that it's rate of transmission will slow way, way down, as it will become increasingly difficult to find new hosts.

If we maintain strict lockdowns all across the country, and people follow the rules, it follows that it will take much longer to approach herd immunity. That is why some scientists are now saying that perhaps the best approach is to relax restrictions somewhat, at least for most people (those with no serious underlying health issues), while still isolating those most vulnerable, if at all possible. That would (theoretically) allow the virus to spread in a semi-controlled fashion across the population to people who are best able to defend against it.

This argument seems to make some sense to me. Otherwise, it's going to be a long, long time (with the economy mostly shut down) before anything close to herd immunity is reached.

 

[Nemo2]

https://www.euronews.com/2020/02/27/coronavirus-can-you-catch-covid-19-twice-euronews-answers

Coronavirus: Can you catch COVID-19 twice?

Although there is "good evidence" to suggest that you can become immune to the virus, how long this lasts has yet to be determined.

"People who work in other coronaviruses say about a year, maybe, which is good," Prof O'Neill said. "If you do get a second infection it is much milder, but we don't fully know as it's a new virus," he said, adding that there is "optimism that if you are infected once you should be protected".

European exit strategies, including in France, have acknowledged the low rate of immunity among their population, estimating it to stand between 1% and 6%, with countries such as Ireland warning that lifting restrictions too soon could lead to a significant rebound in cases.

The question as to whether a person could be infected more than once gained traction back in March, where a local government in Japan said it had recorded the first case of a person who has tested positive after apparently recovering from an earlier bout.

According to NHK, the woman, in her 40s, is a tour bus guide who travelled with tourists from Wuhan, China, in January. She tested positive for COVID-19 on January 29 and was given the all-clear by February 6.

Just weeks later, the woman began exhibiting symptoms and was tested again - only for it to return as another positive result.

We spoke with experts in March, who at the time stressed that nothing is really impossible while research is ongoing to find out everything there is to know about the virus.

But in terms of getting infected twice, they generally said other scenarios are more probable.

Connor Bamford, a virologist at the Wellcome-Wolfson Institute for Experimental Medicine at Queen's University in Belfast, told Euronews it is "unlikely" the woman was re-infected but underlined there was still a lot to learn.

He said: "This is potentially an important development but there’s still a lot we don’t know.

"Also, this is likely to be a rare event so it might not make much of an impact during the outbreak."

Meanwhile, Fabienne Krauer, an epidemiologist in Oslo, Norway, said: "We cannot know if this is a re-infection unless we explicitly know that the woman cleared the virus in between."

She went on to say that if it were the case as stated in Japanese reports that two tests in a month had returned positive, then "we can't tell if this is a real re-infection or a persistent infection."