Israel ๐ฎ๐ฑ, booster ๐๐๐, and herd immunity ๐.
A thread based on the Ministry of Health data with many graphs.
Let's dive!
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Many of you heard about the decline of vaccine effectiveness in Israel in the past few months. The MoH publishes now on a daily basis the rate of infection in unvaxxed, vaxxed (2nd dose), and boosted individuals per 100K, which is a real treasure! nature.com/articles/d4158โฆ
With this data, we can determine the **crude** VE of each group by dividing the rate of infection in second dosed individuals to unvaxxed. From Jan 2020 to now, this is the crude VE (crude = not adjusted to sex, age, and other demographic variables)
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The small increase from Feb to March? The most likely explanation is that the older population was vaccinated first followed by younger individuals, where VE is better.
By mid-Mar, we virtually vaccinated everyone who wanted. Below: daily vaxxed (green: 2nd dose)
We enjoyed great protection in Mar-May. But then with the advent of ฮ and waning immunity, the VE was in a free fall.
Why other countries don't see that?
1 ๐ฎ๐ฑ uses Pfizer, which wanes faster.
2 Everyone vaxxed in a short time period = easier to spot
3 3wk spacing between jabs.
I wondered about the avg. susceptibility of the ๐ฎ๐ฑpopulation over time.
If no one vaxxed, it's 100% (we assume everyone is susceptible)
If everyone is vaxxed with a perfect vaccine, it's 0% (no one is susceptible).
Mathematically:
1-(VE x vaxxed)/pop_size.
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Technical note: to calculate the susceptibility level above, I used the crude VE of the 2nd dose AND the 3rd dose (Aug 1st) from the MoH.
Let's overly Re (red) on the susceptibility level (black). Look how nicely Re traces the susceptibility!
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You probably ask what about the anomaly in Feb-March and June. Easy! On 2/15, ๐ฎ๐ฑ lifted the severe restrictions of the 3rd lockdown. R started to increase until hitting the immunity wall in Mar. On 6/15, ๐ฎ๐ฑ lifted nearly all covid19 restrictions and put some back in July 29th.
So what could we learn from the susceptible-R dual graph?
The data **suggests** that with the current restrictions, we need to maintain the avg. susceptibility level to ~60% to maintain R<1. If the VE for infection is 60% after 5 months, we need to vaccinated 70% of the pop.
Caveats
1 I didn't include in the analysis data on recovered individuals. It will probably reduce the level of vaccination to get R<1
2 Public data do not permit adjusting for demographic factors, so this is crude VE
3 smoothing => exp. window
4 data from: datadashboard.health.gov.il/COVID-19/generโฆ
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Due to โก๏ธ holiday season, it is hard to get a reliable estimator of R. Previously, I showed that the avg susceptiblity of ISR population (S) is nicely correlated with R. This estimator is not affected by # test but only by # vaxxed and VE.
As a reminder, S(t), the susceptiblity of day t is 1 - ฮฃf_i(t) โขVE_i(t). Where f_i(t) is the % of the population that already took the i-th dose and VE is the efficacy of the dose in day t. Both parameters can be in calculated from MoH public dashboard on a daily basis.
So...
So here is S as a func of time (black) versus smoothed R (red). Both are coorelated.
Now, we don't have good data for R in Sep, BUT due to booster, S is in levels similar to Mar 21 (60%)! At that time, it was enough for R=0.9, so I'm cautionally encouraged that we= heading out๐
Important data from Israel: the relative protection against contracting Covid19 at the 4th wave as a function of vax/prior reinfection status. The data is calibrated to RR=1 for people who received 2nd dose in Jan and no booster.
A few thoughts below on waning protection๐
One important take away is that a prior infection protects you but can wane without a vax. People who contracted covid during the 2nd wave (Sep-Oct 20; dark red) have 1.9x risk to get delta compared to people who contracted Covid during the 3d wave (Jan-Feb 21; light red).
Recall that Alpha (3rd wave) is not closer to Delta (4th wave) than the ancestral strain (2nd wave). So it is reasonable to assume that diff are due to waning immunity.
This means that a recovered person looses ~15% of the protection per month. After 2yrs =~ no protection.
The Israeli MoH released some results about the effectiveness of the booster to tame infection rate.
Behavior or immunity or both?
A short technical thread with interesting results.
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Israel does not conduct an RCT for the third dose. Thus, the main analysis for booster-VE is comparing the cases in boosted vs 2nd dosed as a proxy for increased protection. But boosted individuals might be โฌ๏ธcovid19-worried, leading to lower โฌ๏ธexposure.
To mitigate that, the MoH adjusted for basic demography and calendar day of infection and reported the graph below. Y-axis: Booster vs 2nd dose fold protection as a function of days from booster.
But there is something weird...๐ง
Interesting data about the performance of boosted as a function of time. Y: protection compared to 2 doses. X: days from booster.
There is an increase in protection with time after day 7. This reduces the chance of a behavioral effect (but not completely mitigate it)
These results are more puzzling. From right to left: days, # cases, # severe. Top line ๐๐. Bottom: ๐๐๐ >10days
Why puzzling? Because rate of (boosted severe/)(boosted cases) is ~5%. We saw a similar rate earlier in with only 2nd dose. Don't know how to explain that.