A quick diversion to talk about viral spread

 Before I get too much farther into the government and pharma responses to the coronavirus, I want to further flesh out some details about how viral spread has been measured and reported.

When talking about a virus, most people would be concerned about getting it, but they'd be really concerned about needing hospitalization or even dying from it.  Depending on one's state of life and attitude towards hospitals, the concerns may not even be in that order.

But they are obviously related.  You have to catch the virus before you can die from it. The non-pharmaceutical interventions (NPIs) were mostly concerned with limiting the number of people that get infected, though some claims were made that some or all of them would result in a smaller viral load so you might get less sick even if you got infected.  But I've seen no evidence that this is true.

So let's start getting some numbers.  Early on in the virus, about twenty percent of people with the virus ended up in the hospital and one-two percent of them died.  The fatalities almost always were in the hospital, so that implies that if you needed to go to the hospital you had a 10% chance of dying.  Pretty grim.

Lately those numbers seem to be closer to ten to fifteen percent for needing hospitalization and one percent or less for fatality.  It mostly depends on how old or frail you are.

However, to measure the number of people catching the virus, we have the R number.

disclaimer: I'm writing this mostly as a retrospective so I myself can look at it in the future to remind myself about what happened.  Of all things that I'm writing, this is the subject I know the least about.  It's not merely my experiences, but it's speculation on the virology itself.

My understanding is that a virus has an intrinsic measure of how easily it spreads (the reproduction constant), which is denoted R0.  A value of 2 would indicate that every infected person will infect 2 more people while he's infectious.  At any time, it will likely reproduce more slowly that that due to availability of infection targets and barriers to viral transmission.  So the R number at any given time will likely be lower than R0 because it's an all-in number.  As a simple example, measles has a very high R0 of around 10, but if someone gets sick but everyone he comes into contact with is immune, the R number will be 0.

Since I'm in Texas, I'll focus on Texas.  The State health department did not estimate R on a state-wide basis.  However, the Tarrant County (Fort Worth) health department did and Texas Medical Center in Houston (the largest hospital in the world, so likely a good proxy for the county as a whole) did.  In both cases, the R value varied between 0.6 and 1.4 during the ebb and flow of the pandemic.  An R value of 1.4 was actually pretty high and I'm not sure it was real.  Usually it popped up during "catch-up" days (like when the health departments were closed for a holiday weekend and all the cases were entered at once the following Monday and Tuesday).  During periods of undeniable growth, an R value of 1.2 was more normal.

The reason I started all of this nonsense with the Physical Activity Guidelines for Adults and the Dietary Guidelines was a set the expectations for your typical no-cost or low-cost intervention.  In those cases, adherence to either guideline would typically lead to a 10-20% reduction in whatever bad thing you were worried about (like risk of heart attack).  I took some pains to depict this as a real benefit, but a modest impact.  If everyone did it, the population as a whole would see great reductions in the amount of suffering that life entails.  But if a single person did it, he could hardly consider himself immune to whatever bad thing he was worried about.  By placing those as the first point of discussion, I was leading up to the point that I assume that the various NPIs put in place around the rona fall into the same category.

However, things are clearly different with a virus.  If you don't exercise and eat crap and get a heart attack, that's bad on you.  Your family and coworkers won't "catch" a heart attack from you (though family members can "inherit" a poor lifestyle from each other that increases their risk, but that's different).   However, if you catch a virus you most certainly can pass it on. So a "modest" improvement might still lead to viral spread.  It will spread slower than otherwise but eventually will still overwhelm the system.  That doesn't mean it isn't worth doing by the previous arguments, but it also means that perfect adherence to public health orders can still result in a health care crisis.  Real benefits, but not a cure.

So let's see some numbers.  To start with, here are the impacts of various reductions on various R numbers.

		R values
		1.0	1.1	1.2	1.3
Reduction	1%	0.99	1.09	1.19	1.29
	5%	0.95	1.05	1.14	1.24
	10%	0.90	0.99	1.08	1.17
	15%	0.85	0.94	1.02	1.10
	20%	0.8	0.88	0.96	1.05

That's not as helpful as it could be, so let's look at it from another perspective.  If the virus is increasing with an R value of 1.1, that means that if 10 people are infected, they will infect 11 people.  And those 11 people will infect 12 people and so on.  So let's look at how many are infected given a number of replications

	R
Replication	1.1	1.2	1.3	1.4
0	10	10	10	10
1	11	12	13	14
2	12	14	17	20
3	13	17	22	27
4	15	21	29	38
5	16	25	37	54
6	18	30	48	75
7	19	36	63	105
8	21	43	82	148
9	24	52	106	207
10	26	62	138	289
11	29	74	179	405
12	31	89	233	567
13	35	107	303	794
14	38	128	394	1111
15	42	154	512	1556
16	46	185	665	2178
17	51	222	865	3049
18	56	266	1125	4269
19	61	319	1462	5976
20	67	383	1900	8367

Those are huge differences.  Moving from an R of 1.2 to 1.1 or 1.3 to 1.2 would completely change the nature of the pandemic.

Of course, the virus doesn't spread exponentially forever.  Eventually it runs out of people to infect.  And that doesn't mean that EVERYONE gets infected, but just that people that the infected would interact with mostly get infected or are already immune.  Even in 2020-2021 in our connected global digital village, there are many people who live in an insular community.  Even more so when people that could were told to work from home.  Perhaps the virus spreads like wildfire through an ethnic community but mostly stops at the borders, depending on how self-sufficient that neighborhood is.

So when looking at that table, the question is not how many people will get infected, but how quickly the same number of people will get infected.  If a theoretical maximum of 1000 people will get infected, it's plain that that number will be reached much quicker if the R value is 1.4 vs 1.1.  And the faster spread will put more pressure on society, including and especially doctors and hospitals.

Early on the in pandemic, people noticed that the viral outbreaks in various places seemed to drop off after about 20% of the population were infected.  This is a very low number.  The purported infection rate required for so-called "herd immunity" is 70%.  Yet NYC and other places suffered persistently high new cases which dropped dramatically when about 20% of the people were infected.  Even accounting for a large number of infected people who never got tested and thus weren't counted, that was very unusual.  Is there that much natural immunity, including people who'd recently had a common cold caused by coronaviruses?  Alas, at some point as people tried to get back to normal cases picked up again.  So why the 20%?

I had a theory, which I have no way of proving, that the reason went something like this.  Supposed in a given city you break people into different cohorts:

1. Essential Workers who can't work from home and who were never locked down.
2. Non-essential workers who are working from home with with school aged children who are going to school at home.
3. Non-essential workers who are working from home with no school-aged children in the house
4. Retired people

I'm not counting people in nursing  homes or prisons because those are unique situations.  Let's assume that the numbers on those cohorts are like this:

Cohort 1: 25%

Cohort 2: 40%

Cohort 3: 10%

Cohort 4: 25%

Early on in the pandemic, everyone but cohort 1 were in their houses.  So they are out bumping into infected people and they get sick.  But they can't efficiently spread that disease to everyone else. Even if a plumber brought to the virus to someone in a different cohort, those people are mostly staying home so they won't spread it around further.  Let's say that 80% of cohort 1 gets the virus, at which point the virus stops spreading rapidly in that group.  That's about 20% of the entire population.

Now cases are down, so schools open back up.  And people in cohort 2 start mingling with each other at their kids school functions.  And the virus starts spreading in that group.  Again, when about 70%-80% of the people get it, the virus stops spreading rapidly. That's 28% to 32% of the population which added to cohort 1 is now around 50%.

The people in cohort 3 were the ones probably the most consistently locked down.  As of when I'm writing this in December 2021, most work-from-home types are still working from home, as least part of the time.  It's likely a lot of them will never return to the office as companies have realized they can work productively without worrying about the expense of office space.

I don't really know how to score Cohort 4.  They probably are closer to cohort 2 than any other as they can be expected to meet with friends and attend some activities (but maybe not all) that their grandkids have at school, not to mention babysitting. On the other hand, a lot of the travel that retirees proverbially engage in would have been curtailed somewhat due to the rona restrictions.

The numbers don't really match up, but that's an attempt to explain the waves that were experienced.  Add in seasonal factors (as with the variations in cold and flu spread) and it starts to make sense. At least to me.  And it all worked until the variants started to appear.

Back to the discussion of R.  It's kind of hard to think about reducing R.  It's much easier to think about reducing the chances of infection.  Which is kind of related to R but not quite.  Here's an example.  Let's say that an infected person interacts with 1000 people and 10 of them get infected.  The R number is 10, but each person's chance of getting infected is 1% (10/1000).  Now let's say that given the same infection risk someone interacts with only 200 people.  Now only 2 people have been infected and the R number is 2.

It seems like R = (chance of being infected) * (number of people exposed).  But it's more complicated.  Let's say that in the first scenario of 1000 people exposed, 500 of them are immune.  Now only 5 will get infected and the R value will be 5, but each vulnerable person's risk is the same.

Now let's flip that around and say that a person has a 1% susceptibility of being infected.  A simple bit of algebra would say that if he interacts with 100 contagious people he's sure to get infected.  

Likelihood of infection = (number of contagious people contacted) * susceptability

It's more complicated than that. I'd probably need to do a binomial statistics analysis, but this is probably close enough for horseshoes or government work.  Regardless, we can see immediately that reducing the number of infected people the susceptible person is exposed to will reduce the likelihood of infection.  

Now let's take a look at the "susceptibility" part. This is where I'm really reaching, but I'd imagine that a number of things go into that. I speculated in the post about the flu that the flu is more prevalent in the winter because people's immune systems might be at a low point in the winter or the environment might be conducive to viral spread (ex, cold, dark dry days in the winter are more conducive to viral spread than warm, sunny humid days in the summer).  We might also be able to block or redirect the virus so it doesn't go straight into our noses.  Also one virus may inherently more likely to spread than another in the same environment. So let's add all of those together.

Likelihood of infection=(number of contagious people contacted) * 

(# of viruses we breath in) * 

(Environment) * (Immune system) * 

(innate infectiousness)

We can't do much about the innate infectiousness of the virus but maybe we can do something about the others.  And in the equation I am multiplying the factors together but there may be a more complicated function than that.   The number of viruses we breath in probably depends on the environment, for instance.

Mathematically that really should be written as

Likelihood=f(contagious contacts, viruses present, environment, immunity, innate infectiousness) 

Now, the million dollar question is this. Assuming my equation is correct or at least conceptually correct, how do the reduction of multiple factors interact?

For instance, if I cut the number of contagious people I come into contact with by 50% AND and I boost my immunity by 20% AND I reduce the number of viruses I breath in by 20% what is my new likelihood of infection?  Do the factors add, multiply or something more complicated?  Or maybe "Contagious Contact" is such a dominant factor that the effect of the other won't even be noticed?  It probably is the assumptions about these interactions that caused such controversy in some of the models that came out.  If you overweight "Number of people contacted", then lockdowns are essential. If you overweight "Reduce number of viruses" then masks are mandated. 

But if you do both, what happens?  What if you do masks and vitamins or vitamins and humidifiers? Well, what happens in nursing homes and prisons every year when the flu is running wild? There's no data, which consistently drove me bonkers.  Here we have an annual event that we can mark on the calendar 5 years in advance and these basic questions were never answered.  Or, if they were, the knowledge was thrown out the window.  Or, if it wasn't thrown out the window it was kept locked away and all we were told by the powers that be was "trust us".