Covid-19: Has South Dakota Reached Herd Immunity?

Summary

• The high-intensity fall outbreak in the US is moving south and east as some plains and western states have finally seen new cases roll over.
• The governor in South Dakota has refused to implement a mask mandate and has focused on livelihoods more than lives.
• I consider whether South Dakota and some other states may have reached local herd immunity.
• The evidence for mask mandates does not seem compelling to me.

The covid-19 pandemic continues to evolve geographically in the United States. I have argued repeatedly in this space that the geographic story is a major part of the national numbers. 

Here is the national map of covid hot spots from October 1. It shows the average daily cases over the most recent week. This is from the New York Times website, as is anything else herein not otherwise sourced.

Notice that the colors in the plains states (the Dakotas, Nebraska, and Kansas) are almost entirely red. The unfortunate display used at the time did not effectively present how intense the outbreak already was in those places.

The Times later changed the display by filling in every county, and has changed the color scale as well. Here are the maps from November 21 and December 4. These have the same display type and color scale.

November 21: 

December 4: 

There are several things worth noticing about this set of three maps:

1. Across the states one can see well, from the tier connecting Minnesota to Louisiana eastward, there are intense infections over a far larger area in recent weeks than in early October.
2. Over the past two weeks cases have grown more intense in Michigan, Ohio, Pennsylvania, Kentucky, and Tennessee. They have generally been spreading southward and eastward during the past two months.
3. Over the past two weeks cases have been on the decline in Wisconsin, Illinois, Iowa, the Dakotas, and other western states.

What I find significant is that before the governors in some states gave into pressure to impose a mask mandate, cases had flattened (North Dakota) or were dropping (Iowa).

In North Dakota, the governor only initiated a statewide mask mandate on November 13. This was after the hospitals reached 100% capacity. Notably, it was also after the rate of new active cases had flattened.

Then there is South Dakota.

South Dakota

The governor in South Dakota did impose some restrictions and declare a state of emergency in March. She lifted that order on May 11. Some localities have imposed local restrictions since.

Subsequently, Governor Noem has refused to impose a mask mandate or other mandatory restrictions on her population. She has “remained fixated on livelihoods rather than lives.”

Here are the hospitalizations in South Dakota:

The South Dakota Department of Health reports, on December 4, that there is now significant hospital bed capacity available: 

It seems that, despite the usual media headlines about dire conditions in hospitals, South Dakota has not ended up pushed above capacity overall.

Here is the rate of new active cases in South Dakota. It peaked in mid-November. 

There are two reasons why the rate of active cases might have turned over. These are herd immunity and decreases in how effectively the virus spreads.

All indications are that colder weather makes respiratory diseases like covid and the flu spread more rapidly in cooler climates. Because of this, the minimum level of behavioral controls, and the culture of South Dakotans, I am unconvinced that recent changes in efficacy of spreading are likely.

To my mind it remains worth considering whether herd immunity might be the story.

The epidemiologists are unlikely to consider this even possible. They, like most left-leaning, university trained professionals can see themselves as Philosopher Kings. Many of them would like to restrict our behavior forever.

If you don’t know about Plato and his Philosopher Kings, look it up. It matters.

A Simple Stupid Pandemic Model

The population of South Dakota is 885,000, so they are approaching known cases of 10% of their population. If they are detecting 1 in 5 cases, then they are approaching 50% who have been infected and now (mostly) are immune. 

I decided to look a bit further at the plausibility of this hypothesis by doing a simple model.

Let me start by describing the model. I hope to be clear enough that a reader might get the main points even if math is not one of their languages.

As the disease spreads, the fraction of the population composed of infected people who are are potentially contagious increases. The infected people infect those that can be infected. These are people who are not infected and not immune.

The infected people become non-contagious and later immune at some rate, given by a parameter, M. To correspond to what I have read about how long people stay contagious, I used M = 1/7. This implies that half the newly contagious population becomes non-contagious in about 5 days.

The rate the disease spreads involves several elements. These include weighted average over the infected population of how contagious they are, the total number of people interacting, and some average over geographic variations. I used a parameter Q to represent the net effect of these.

Math speakers: The fraction infected and contagious is designated by the italic f with the subscript i.  The fraction no longer contagious or otherwise immune is designated by italic f with subscript m. The equations describing the evolution of these fractions are these:

The value of Q that gave some plausible approximation of what we have seen in South Dakota and other places corresponds to a doubling time of 3.5 days when the infected fraction is very small. 

This doubling time obtained is about 1.5 times what we saw in a lot of places last spring. It does not seem implausible to me. 

Evidently Q is related to the much-discussed Ro. But I chose to use a different symbol to avoid baggage.

In actuality several factors limit the utility of this kind of model. One of them is geographic. In places like Wisconsin, Ohio, or the US as a whole, where the growth of the pandemic involves spreading in space more than increasing uniformly everywhere, the model is less relevant.

An even bigger limitation is that Q is not constant in time. Changes in personal behavior, in governmental behavior, in the virus itself, and in the weather can lead Q to change. We mentioned this aspect above.

The model will be somewhat realistic if Q does not change much during the period when infections are most intense. If one starts this model with no immune people and with one in a million people infected, this is what it does:

The rate of new immunity (plus non-contagiousness), shown in black, will match the rate of new cases, with a delay of a week or so. Features of these results that matter are:

• It takes quite a few months to reach the peak
• The peak (at half its height) is about 50 days wide
• The maximum rate of new cases per day is 700 per 100k population
• At the end, 50% of the population has been infected and is immune 

The first two of these aspects are roughly consistent with what we see, but also reflect the choice of Q.   

The third aspect has some interest. It also is not very dependent on the model. If you are to have a peak in infections lasting a couple months and end up with about half the population having been infected, then the height of that peak will be somewhere around 700 per 100k people per day. We will return to this below.

The fourth bullet point above also deserves comment. The population modeled remains vulnerable to local outbreaks if the virus keeps being reintroduced from outside it.

Such outbreaks will not be sustained, but might become large if some local area has an insufficient number of infected people. I fear that such circumstances are exactly what the governor of Michigan is creating in my own, northern part of the state.

If one starts with some multiple of 10% initially immune, the fraction of newly infected necessary for herd immunity does come down, but not by huge amounts.

The Total Fraction Infected

That peak rate in the model of 700 new active cases per 100k people is an interesting number. In scanning the counties over many weeks now, the most intense regions of activity have a known rate of new active cases above 100 and often reaching 250 or more.

The largest such number I have ever noticed is the current rate in Lincoln County, Colorado, at 1,042 per 100k (after Dec. 4 reporting). They would seem nearly certain to come out of this with local herd immunity. The largest this week in South Dakota is Dewy county, at 747.

We know that a large fraction of cases are not detected in most places. It looks quite plausible to me that large fractions of the middle of the US are or soon will be reaching immune fractions near 50%.

The Times also has a map of known per capita infections:

Every place that is bright orange or darker has above 5% of the population with known cases and may well be within spitting distance of having herd immunity. It is very plausible that the two darkest colors show places that have it locally.

In many of the other places, showing yellow or dim orange, the local government is imposing massive collateral damage on their population trying to fight what seems now inevitable. The progress on the vaccine has been a spectacular achievement. But it comes too late.

This outcome for the pandemic may not have been inevitable. Widespread fast testing might have made the story very different.

But maybe not. Culturally the West is not Asia.

Do Masks Matter?

I don’t mind mask mandates. Based on the initial story about the virus, that it was spread mostly by droplets before they could fall to earth, they made a lot of sense.

But the scientific evidence has evolved. From what I read, it has now long been quite clear that a small fraction of those infected shed massive amounts of the virus, in ways that can infect many people in the same room in a relatively short amount of time. 

If the virus particles these people shed are able to float around the room and do that, they will escape common masks in large numbers. Some fraction will end up stopped by the mask. But that won’t be enough to stop the spread.

One thing that was remarkable to me was that it was weeks if not months after there was clear evidence of airborne spread of the virus before the WHO and the CDC admitted it was occurring. This seems to me to be bureaucratic ossification at its best.

With the virus so widespread, it may matter even more that people in the US will not stop gathering in small private groups. Everybody feels OK at the time and all have been “being careful.” Governments cannot stop this.

If the virus is widespread enough, as it seems to be, then it will keep spreading this way. Governor Newsom in California is inflicting massive damage on his population in what may well prove to be a quixotic quest. Governor Whitmer in Michigan is going the same direction.

Sweden has not instituted a mask mandate. They have also been comparatively light-handed in restrictions on human activity.

Here is the rate of new active daily cases in Sweden, from their public health department:

This looks much like most everywhere else in the West, doesn’t it? Sweden is a country of about 10 million people. Their overall rate of known infections per capita is about 2.5% now.

My state of Michigan, of population 9 million people, is at 4.3%. California, population 39 million, it at 3.3%.

Of course there are differences among these places. This likely includes a difference in the fraction of cases they detect. Sweden is near the upper end of countries in per capita testing, and in the middle of the pack for positivity rate.

These comparisons don’t convince me that mask mandates make much of a difference. The public health authorities seem to me to have been fooling themselves, and us.

This makes sense to me. If a masked person ends up in a room with an active shedder of the virus for an extended period, the mask probably does not protect them. 

It makes a lot of sense for a vulnerable person to wear a mask, as protection from droplets and from their own hands. But as a public health measure I do not find the evidence for mask mandates compelling.

What to Do?

If the hypothesis discussed above about herd immunity in South Dakota is correct, then they will see vastly reduced cases within a few weeks. If not, they are likely to have a next outburst.

Whether or not the hypothesis is correct, I am with the South Dakota governor that livelihoods matter more than lives. Especially the lives of those most likely to die in this particular pandemic.

I even go a bit further. Even with full financial support (at whatever long-term societal cost), the psychological damage of the pandemic and also of the restrictions imposed in many places is enormous and will have enduring negative consequences.

I know this is brutal. It is not what I would wish for. But it is the hand we have been dealt.

The psychological welfare of a child and the economic welfare of their parent are, in my view, more important than the continued life and quality of life of anybody over 65. Including me.

South Dakota is enduring two miserable months of peak pandemic. Matters were worse in North Dakota, where hospitals did briefly overflow but cases are now rapidly plummeting.

In contrast, California and other states are enduring month after month of economic destruction, psychological devastation, and stress to health care workers. To my mind this was not worth it. 

The right answer, even now, is to open up the economies and open up field hospitals. And to accept that the cost of reducing the collateral damage is that more people, mostly older, will die or suffer from enduring aftereffects.

Implement simplified treatment protocols that can be followed by people with minimal training. Train those in the national guard not working in health care already and new hires as necessary to follow those protocols. Taking temperatures, giving oxygen, putting people on today’s CPAP machines, and even providing intravenous drugs can be done by people with little training. Accept that fatality rates in such field hospitals will be higher than those achieved in regular hospitals with more highly trained staff.

This is tough business. But it is not rocket science. Alas, it will not be embraced by the would-be Philosopher Kings, who are the cause of massive unnecessary suffering.

They have good company. Plato failed at being a Philosopher King too.