Vaccine effectiveness 66% against Delta infection

"The COVID-19 vaccines are extremely effective at preventing serious illness, hospitalization, and death."

The article starts out with a hopeful tone. Then they go on to show that being vaccinated reduces your risk of hospitalization by 3.7x and risk of infection by 2.9x (no controls for differing behavior, of course). That's 73% effectiveness against hospitalization and 66% against infection. Historical data on the site show those numbers have been dropping.

I am very happy to have that level of protection, but it is nowhere near the 98-99% effectiveness repeated (without data) in other places. And it is no excuse for relaxing your behavior because you think your vaccine will protect you. We are in the biggest wave yet, everyone should be masking, social distancing, avoiding school as hard as we EVER have.

https://www.dhs.wisconsin.gov/covid-19/vaccine-status.htm

Dear Florida

Germany on the Mend

Good news out of Germany, seeing two consecutive days of significant improvement in the number of active cases. Additionally, the number of new cases is trending downward as well (after accounting for the regular weekly ebb and flow). Switzerland also continues a slow and steady improvement. In addition, Spain and Italy are very close to halting their growth. Overall, very good news in Europe. Canada, UK, and US numbers are all continuing on a 7-9% growth rate. In the Mideast, Iran's numbers are encouraging, but we must take their reports with a grain of salt. Conflicting numbers continue to surface, particularly around the reported number of deaths.

Unfortunately, there are no new stay-at-home orders in the US. In fact, Kansas Republican lawmakers weakened the order in their state, deciding that their governor's order does not apply to religious gatherings. I'm pretty sure that viruses are functionally atheists, however. Religious gatherings in South Korea were one of the biggest transmission vectors and the hardest to get under control.

Today I am adding a couple of new columns to show the linear and quadratic model predictions for each state. This will help show which states are breaking their trend lines, and hopefully help identify new trends and improvements. Today, Georgia, Texas, Maryland, and Rhode Island are the outlier performers, coming high on both the linear and quadratic models. Montana and Wyoming has shocking reversals in their active cases, seeing significant drops. Maybe the sparse, rural nature of these states enforces a de facto social distancing. It's also possible that their testing is uneven and we will see an equal jump in cases tomorrow.

One thing that I am noticing is that the regular weekly variation is affecting the growth models. This is enough to make linear models seem accurate for early in the week, while quadratic models are better later in the week. In looking into this phenomenon with more long-term models and regularization of the variation over the week, it seems that the weak quadratic model is a better overall fit for many of the states right now. This is interesting, since it would be more consistent with Kiskowski and Chowell's local saturation model. More data over the next few days will help validate or refute some of my suspicions.

Predictions

Some of our readers are understandably having a hard time understanding the numbers and where the analysis is coming from. I thought I would try something a little different by making a few predictions - well, extrapolations really - and showing where they are coming from. I will focus for the moment on the United States, since it's a little more like comparing apples to apples than, say, showing models for Italy and Turkey side-by-side.
First up, New York (State). New York was hit early and hit hard. It still has 1/3 of the active cases in the US right now. Also, a highly cited model keeps predicting that NY is about to peak in the next few days. Let's take a look at the past two weeks, and see how things are looking right now. The blue line is the active confirmed cases in NY over the past, while the purple and red lines extrapolate (predict) those numbers into the next few days. The purple line is a straight line estimate (linear growth). This estimate has been pretty good at predictions over the past week, though it tends to be a little conservative. The red line is an N-squared model, assuming some curvature to the data. This has more flexibility, so it can easily overfit the data, and in fact does a slightly worse job of prediction over the past week, typically overshooting the real numbers. The reality will probably be somewhere between these two lines, but hugging much closer to the linear (purple) line. That means by the end of the day today, we expect the number of active cases to be between 127k-131k. By April 12, the expectation is between 155k-167k.

The next chart shows the behavior of some of the states with the most active infections. Each of these is transitioning from exponential growth to linear, and the N-squared model has been a good fit so far. Extrapolating out, we see that each of these are behaving very similarly, with only Michigan break from the pack and growing slightly faster than the rest.

Finally, a few of the other states, including both states with linear growth and transitional models. These states are chosen specifically because they are stable over the past ten days, so states with new events with a sudden impact on the model, or very noisy data are not show, as they aren't good examples for our explanations. However, the same principles apply.

Wuhan Lockdown Lifted

China has lifted the lockdown in Wuhan province today after 11 weeks. It could be a great symbol of how pandemics can be controlled by strong measures, or it could be too early and lead to a new flare-up. I am very curious to see what happens there.

In Europe, Germany posted their first drop in active cases, and Switzerland continues to improve. There are early signs in the numbers that we may begin to see sublinear growth in Europe in the near future, but the data is not conclusive yet. We may be seeing noise, or simply a realignment to a lower linear growth rate.

In the US, Wisconsin held primary elections today despite strong protests from the Democrats. Results will not be reported until the 13th. It remains to be seen how this affected turnout. In South Carolina, Governor McMaster finally made an official stay at home order yesterday, after many in the state had already begun. The state had already shifted to a linear growth model over the past week, but it is still good to have the leadership on board.

Most States Shifting to Linear Growth

Sorry I didn't post yesterday, but I needed a day off. Across the board, case counts came in lower than would be otherwise expected, but we're learning to expect that on Sundays.

Today, Spain's cases are looking especially good, with only about 3/4 of the new cases that my models predict, even accounting for Mondays being lower on average. Also, Spain, Italy, and Germany are all looking a little better than expected. Yesterday, Switzerland saw the total number of active cases grow by about 4%, but that's not enough to counteract Saturday's amazing drop of -5%. Today, they posted another encouraging drop of 8%, due to a slightly lower than average set of new cases combined with a large number of reported recoveries. France, and the Netherlands are all very well in line with the linear model. The UK, US, and Canada are all still not on the linear growth model yet, but appear to be slowly heading in that direction, as they come in under the exponential growth curve. If they continue at this rate, I expect Canada and UK to be linear within a week, and the US shortly after, but there are a lot of heterogeneous components to that actually happening. In the Mideast, Iran has fewer confirmed active cases, but that all comes from an increase in resolved cases, as new cases remains constant. Israel is doing slightly better today, and Turkey is still on track.

In the United States, most of the states with a large number of infections are switching over to the linear growth model. Maryland is still exponential, while Pennsylvania and Texas are still in a transition model. Louisiana and Tennessee are unpredictable right now, so no telling what will happen there, yet. Arizona and Alabama look like they are continuing with exponential growth. Connecticut had a bad day, with 1214 new confirmed cases (22% growth), but that looks like an outlier. The states with under 2000 cases are mostly unpredictable right now, with especially erratic behavior out of the Midwest. Many of these areas have limited resources and logistics for testing and reporting, contributing to the noise. Taken as a group, however, these states are showing distinct exponential growth.

I am still searching for an explanation to the linear growth effect we are seeing. While there are plenty of epidemiology papers describing late-stage linear (or at least sub-exponential) growth, these are all saturation effects that do not accurately describe the scale or duration of what we are observing. Admittedly, the stay-at-home behavior we are using to fight this epidemic is not something we have seen at this scale before, either, so I'm not too surprised. However, I am still hopeful that we can better understand the cause and model the core behavior so that we plan a better exit out of this situation we have found ourselves in, without having to wait for vaccines or cures for something as hard to defeat as the common cold.

Local Saturation Theory

France continues to adjust their numbers to align with international standards, leading to a significant jump in reported cases today. That is not an actual growth in cases, just continuing to move to a new baseline. The change from yesterday is left blank today while they sort things out. Iran is coming in a little low today, but that could be noise. The other countries are all coming in as expected.

Switzerland continues to see a decline in active cases. This is from a roughly constant number of new infections being overwhelmed by a higher rate of people recovering. If the linear model continues (i.e. the number of new infections stays more or less constant) their active cases should continue to decrease more quickly over the next week, before slowing down to asymptotically approach a steady level where people recovery just as fast as they are catching the disease. Which is about as weird as it sounds. To take this out to the extreme, if nothing changes, that means that about 1000 new Swiss will be infected every day. The population of Switzerland is about 8.6 million people. Even if we are undercounting the number of cases by a factor of 10, that means it will take 8,600,000/10,000 = 860 days = 2.35 years for the entire country to be infected. That assumes that it hasn't mutated enough by then, so that a previous infection from COVID-19 means that your body is still immune to COVID-21.

The US isn't quite at a linear growth model yet but with a majority of the states with the most infections all imposing comprehensive stay-at-home orders, things are getting closer.

So what is causing the linear growth? According to research on Ebola from Maria Kiskowski and Gerardo Chowell, the transition from exponential to linear growth is expected as the disease is "saturating" the local communities. The disease then passes through in a "wave" or a "bubble" through the community, infecting new people only along the leading edge of the "bubble" while the interior is fully saturated. This would imply one (or more) local areas of high infection that are slowly working their way through a region. Events could happen where a bubble hits a kind of connectivity dead-end, or a particular connectivity crossroads could split off a second bubble, but the basic linear behavior is maintained.

If we follow this theory for what we are seeing with COVID-19, you can't consider a city or a neighborhood as a bubble. One idea then is that stay-at-home orders are reducing the number of interactions enough that these bubbles can form a saturated area in a fairly small region. Perhaps a single household is only interacting with a very few number of other households now, and a bubble can form out of just a few such households. A full cut-off from the rest of the world would cause the bubble to collapse, with nowhere left to go. However, occasional forays into 'necessary services' such as a grocery store could provide just enough exposure to inadvertently cause one more temporary link.

My problem with this theory applied to COVID-19 is that there is not just one bubble. Most states do not have any significantly high saturation counties, and nearly all infected states have at least a few cases in more than half of the counties. So that would mean bubbles would have to be tiny, and saturation areas would be being created and dry up all the time. That they would continue to cancel each other out equally is awfully convenient. It also implies that the type of stay-at-home order doesn't truly matter to connectivity, since not all states and counties are implementing the same thing. While this seems plausible for some epidemics, it doesn't seem like the full story for this situation.

Let me know your thoughts and ideas in the comments below. I'm interested to see if we can crowdsource an answer to this. Because I don't know about you, but I don't have 2.35 years of pasta stockpiled.