Population Immunity vs COVID-19 Spread Rate, Cont’d

In my previous post I demonstrated a strong negative correlation between cumulative COVID cases and the Rt (current rate of reproduction of the virus) on a countywide basis in the US. I mentioned, though, that my quick and dirty data analysis was incomplete – a univariate analysis can be misleading if there are confounding factors. In this post, I expand the data to a multivariate model to examine possibly correlated factors.

For those who think the hypothesis I expressed in my previous posts (that population immunity is the primary factor determining Rt) is wrong, there are two likely counterarguments:

  • People in regions more strongly impacted by COVID take it more seriously, leading to more social distancing and mask wearing.
  • Mask mandates have generally been introduced in places with high case loads, and its those mandates that are mostly responsible for the reduction in spread.

The multivariate model I present here includes 3 new factors:

The base dataset and date ranges remain the same as in my previous post. Each datapoint corresponds to one major county in America every 4th Tuesday. Here are the results from an OLS:

Multiple linear regression results predicting Rt by county. High Cumulative case /capita and mask mandates both show strong statistical significance in lowering Rt. Current cases and social mobility fail to pass the significance test (p=0.197,0.225).

The R2 value isn’t terribly high, so we need to be careful about making strong conclusions (lower R2 indicates a lot is left unexplained). But the results do suggest some meaningful takeaways:

  • My view remains unchallenged. Even after accounting for social mobility and mask wearing (mandates), the cumulative case rate (which is associated with population-level immunity) is by far the best predictor of Rt.
  • Surprisingly, the coefficient for mobility is negative – which would imply that higher mobility leads to reduced virus spread if the coefficient was statistically significant (p<0.05). It is not. This could suggest that Stay at Home/Shelter in Place orders may have been worthless for containing the spread in America, though I suspect it might instead mean that the mobility data doesn’t accurately measure what’s meaningful in spreading the virus. I think weather may play a major role here – if people are going places, but staying outside during the summer, that would be effectively quite different from traveling places in the winter, when gathering must occur indoors in much of the nation.
  • Mask mandates do appear to contribute to reducing the spread, though they don’t guarantee anything.
  • Current Case /Capita does not seem to matter (another indication that people in current hot spots don’t adjust their behavior, thereby causing a reduction in Rt).

Some notes and caveats:

  • I normalized all input variables to have zero mean and stdev=1
  • I smoothed the Apple mobility indexes with a 14-day moving average, then computed a single score by averaging the walking/driving/transit scores. This score may not give the best predictor of Rt, but I wanted to keep it as simple as possible.
  • Ideally, the mobility data would’ve been measured year-over-year, instead of indexed in January. But this is the data I have.
  • I should’ve smoothed the Current Cases /Capita with a moving average, but I got lazy.
  • The statistical significance numbers are likely to be modestly overstated, as the data is likely not all 100% independent (bordering counties, repeated points from same location 4 weeks apart).
  • I got most of the dates for the beginning of statewide mask mandates here, though I had to Google 2 or 3 missing dates. Some counties/cities had mask mandates before their states implemented them, but I’m not sure I’m willing to put in the time/effort to collect that data.

Immune, But For How Long?

I believe we can now be confident that immunity from COVID-19 lasts for at least 6 months, whether an infection becomes symptomatic or not.

During much of the pandemic, all kinds of doomsayers and worry-warts have cried about COVID immunity disappearing. Here’s a paper that shows recovered patients that never developed symptoms were far more likely to lose their antibodies within 3 months than patients that got sick. With asymptomatic infections currently estimated at 40% of all infections, that could be a real concern.

We’ve also now seen several documented cases of legitimate reinfections:

Recently, though, a team of Chinese scientists published a paper that studied symptomatic COVID patients, showing that antibodies were still detectable 6 months after infection. But that still didn’t answer the question of lasting immunity in asymptomatic patients.

I believe we can safely say immunity will last for 6 months or longer in almost all people who are infected by SARS-CoV-2. Here’s why.

Back in April/May, I had a series of python scripts I ran daily which generated charts from curated COVID data in the U.S. One major phenomenon I noticed was that the trends in deaths/cases in New York were diverging greatly with the rest of the nation. New York deaths steadily dropped, while deaths in the rest of the nation continued to increase for quite a while before they finally peaked.

Given everything we knew at the time, I found this surprising at first. How was it that New York was able to get control of this, given all their inherent disadvantages, while the virus continued to spread around the rest of the country? Were people in NYC social distancing more? Was Andrew Cuomo some kind of hero?

No. Andrew Cuomo is neither a hero nor a competent governor. My hypothesis at the time, which I now believe has shown to be true, was that NYC had reached a level of public immunity necessary to keep the Rt of the virus below 1.0 (update: some more evidence on this). This is not to say they actually reached true herd immunity (which is what I originally thought before any of the seroprevalence studies were published). If NYC were to go back to completely normal, they would almost certainly see a surge in cases. But with some levels of social distancing, they have enough immunity to keep cases from surging.

Here’s a chart of NYC cases over time, smoothed by applying a 7-day moving average:

Now, some people will continue to argue that the real reason cases were brought down and remain low is that NYC is still locked down and citizens are still exercising extreme social distancing. What does the mobility data for NYC, provided by Apple, say about that?

Note that mobility in NYC hit bottom about a month before cases peaked. After the peak, as cases continued to decline, mobility continued to increase. (A couple of caveats: it would be better if the mobility were measured as year-over-year, instead of indexed to Jan 1. Also, the cases shown are impacted by testing availability).

What’s especially important is that even 6 full months after the mobility trough, we haven’t seen any real surge in COVID cases in NYC. If a significant percentage of people infected with COVID were to lose their immunity after 6 months or less, symptomatic or not, we’d almost certainly see some surge in NYC by now.

Given that the number of genuine reinfections worldwide has been limited so far, I’m now guessing that immunity will last a year or more. Of course, that’s less certain at this time.