A on whether we can protect high risk individuals by increasing infections in low risk individuals. Can it work?

We need to be aware of what assumptions have to be true for this to reduce deaths.

First a caveat: I'm focusing on deaths here. There are other things that matter.

If you are arguing for this strategy because of other concerns, that's fine. But too many people suggest this strategy saves lives without understanding what they are talking about.

While reading this, bear in mind that long-term care facilities have many high-risk individuals.

Once it is in, the disease spreads well, no matter how many low-risk individuals have immunity.

It also spreads between facilities by patient transfer or movement of employees.

This strategy cannot help at all once infection gets in to high-risk facilities, but it seems to encourage those introductions.

To simplify our discussion, let's consider a well-mixed population, so the long-term care facility issue is not relevant.

[The argument I'm giving explains the mechanism and can be generalized to include the facilities, but for simplicity I'm ignoring it. Deaths in long-term care are a large fraction of total deaths so policy should focus a lot of attention there.]

Consider a population made up of high-risk and low-risk individuals. There is transmission within each group and between the groups.

Let H(t_0) and L(t_0) denote the number of infections in each group by time t_0. Can we find their final values?

I'll explain the calculation and then we'll talk about what happens if we change the transmission rates during the epidemic.

Let's do a thought experiment.

When we look at the cumulative collection of infected people at some specific time t_0, we take at each person infected so far and make a list of everyone they have infected, and everyone they will infect.

Call this the "transmission list" at time t_0.

The transmission list includes the infected people and some who aren't yet infected.

If the transmission rate is constant, then to find the size of the transmission list at time t_0, you only need to know H(t_0) and L(t_0) and a little probability theory.

The key observation is we don't need to know what H(t) and L(t) were for t<t_0 to find the current transmission list length. I just need their current values.

The epidemic finishes when the transmission list is the same size as H and L (no new infections coming).

This lets us calculate the final size, without having to worry about the specifics of when the peak occurs, how large/wide the peak is, etc.

More detail here: https://link.springer.com/article/10.1007/s11538-012-9749-6

What if we temporarily change a transmission rate?

If we increase transmission rates within the low risk group, could this decrease the final H?

I can't directly calculate the final size without knowing the epidemic timing.

I can show that the original situation was better.

Here's the argument: with no change to transmissions involving H individuals, the number of H and L individuals added to the transmission list per H infection and the number of H individuals per L infection are unchanged.

The number of L individuals per L infection increases.

We can only balance the cumulative infections and the transmission list (which ends the epidemic) if we increase the number of cumulative infections. The additional infections in the low-risk individuals have protected no-one.

Infections in both groups increase.

But - we must have hit the herd immunity threshold sooner, you say? You're right. But when we hit it, we had more active infections, so the number of people infected *after* the threshold was reached is larger.

Again infections in both groups increase.

So these arguments can only work if somehow the transmission rates at other times are lower than they would have been.

I see 3 somewhat plausible scenarios (there may be more) that could do this. Then I'll point out why I think other strategies are better.

1) while it rips through the low-risk we dramatically decrease transmission in the high-risk group.

This could work, if we can do it. Can we?

Until some country has proven that it can dramatically decrease transmission in aged-care facilities and multi-generational families, the people arguing for this without specifying how to do it might as well be talking about non-magical unicorns.

2) we let it rip in the low-risk group and then introduce incredibly strict lock-down. Based on what I've seen in different countries, I cannot imagine this being less than a month of lockdown, probably 6-8 weeks, and very, very strict, after 4-6 weeks of let-it-rip hedonism.

If you're aware that heterogeneity reduces the herd immunity threshold, you should realize this will dramatically increase the overshoot past that threshold, negating much of that benefit.

3) Transmission rates from L to H or within H will increase in the future. [perhaps b/c of winter or intervention fatigue]. This may hold, but now we're dealing with a lot of uncertainty about two effects, both of which increase deaths.

Wrapping up - if you say "let the low-risk people get infected to protect the high-risk", you have to realize that this only helps hit the herd immunity threshold sooner.

That does not equate to fewer deaths. Indeed all else being equal it would cause more deaths.

What do I think?

We now know ways to reduce transmission more efficiently than we knew 6 months ago. In a few months we'll be even better.

We are also developing better treatments. Survival rates will continue to rise.

There is a good chance we will have an effective vaccine which will be wide-spread enough in 6 months to start having an impact on deaths.

Why would we implement a strategy that accelerates infections?

Certainly effort should focus on protecting high risk people, but the idea that letting or even encouraging infections in low risk individuals to happen inherently protects high-risk individuals is wrong.

[and if you're thinking about scenario 3 where you expect transmission to increase in the future]:

we need to be confident we can increase transmission and get it back down otherwise peak infectiousness might correspond to the epidemic peak, which is the worst possible outcome.