As many of you know I am a huge proponent of the COVID vaccine. Not only does it reduce your risk of catching COVID, and getting severely ill from COVID, it also is the only legitimate path to normalcy.

One of the most common counterpoints I hear to the vaccine is that it doesn’t actually prevent you from getting COVID. I believe this narrative gained momentum because several of the vaccine trials focused on infection rate in individuals that had received the vaccine and "severe infection/death" from COVID in vaccinated individuals. The severe infection and death results were most commonly reported by the mainstream media.

Logistically, executing a trial with transmitted infections as the primary endpoint would be very difficult. You would have to test all of the participants contacts on a regular basis to see if they contracted covid and prove it came from the vaccinated individual.

Because of this I commonly hear, “What’s the point? I can still spread COVID if I get it. It's only 90% effective. I’ll take my chances.”

Hmmm...Can you really spread COVID after being vaccinated? Let's look at some data.

**Design**

The study of interest in this post is a simple observation study. It was conducted in a large network of nursing homes. These patients are the most vulnerable not only to the disastrous effects of the virus, but were at the mercy of their environment, which is usually restricted to a confined indoor space.

The researchers simply looked at infection rates pre and post vaccination in vaccinated and unvaccinated individuals. The residents were tested every 3 to 7 days during the vaccination campaign. There was no control group. They did not attempt to compare to infection rates prior to vaccine. This significantly weakens the power of the data. But I highlighted this study because the results were remarkable.

**Results Summary**

There were 18,242 residents that received the vaccine. Roughly 4000 residents elected not to have the vaccine. They received either the Pfizer of Moderna vaccine. After the first dose of the vaccine there were only 822 reported cases out of 18,242 (4.5% failure rate). Two weeks after the 2nd dose there were only 38 reported cases in vaccinated individuals (0.3% failure rate).

The data from unvaccinated individuals was very impressive. There were only 12 cases in 4000 unvaccinated individuals (0.3% infection rate) after day 42.

**My Take**

The vaccine has decimated COVID. The stark change in infection rates is real world evidence of how powerful this technology is. Prior to the vaccine nursing homes were facing 25 infections per 1000 residents per week. This was during the thick of the pandemic with significant restrictions in place. Eating alone in your room, no visitors, no events, couldn’t leave without permission, could only be outside the facility for a short number of hours and this required permission. The network above was likely dealing with 750-1000 infections per week based on an infection rate of 25 infections per 1000 resident (September – December 2020). All the way down to 50 total infections 42 days after completing their vaccine campaign.

I find this 90% effective argument to be a misunderstanding of how infectious diseases spread.

This 90% effective rate is just for you. It is not for the population. When you have 10 people with a 90% reduction in risk, then the true risk of infection for an unvaccinated individual engaging with these 10 individuals is extremely low. If you have 100 people with a 90% reduction in risk, then the true risk of infection for an unvaccinated individual engaging with these 100 individuals is even lower.

You may recognize this phenomenon. My bringing it up may induce flashbacks and PTSD from calculus class. It’s known as exponential decay. I'm sure you remember the equation.

(y=a(1-b)^x).

AHHHHHHHHHH!!!!

This is why you see the 0.3% failure rate in this observational study instead of a 10% failure rate everyone keeps quoting, even though 4000 individuals passed on the vaccine. As more individuals get vaccinated, there are fewer and fewer hosts, which leads to fewer and fewer infections, and further down the exponential decay tail you go.

It looks something like this.

So, let’s say you have an infection rate of 25 per 1000 "resident weeks" to begin. You have a 90% effective rate. It takes 4 weeks to complete an entire vaccine cycle. What is your rate at 8, 12, 16, and 32 weeks.

8 weeks = 4.0 per 1,000 resident weeks

12 weeks = 1.6 per 1,000 resident weeks

16 weeks = 0.7 per 1,000 resident weeks

32 weeks = 0.1 per 1,000 resident weeks

Does this look familiar to the numbers in the red rectangles above? Math is fun.

So, can you spread COVID after getting the vaccine? The answer is yes but it is highly unlikely.

Can we really get rid of COVID if the vaccine is only 90% effective? YES! We can exponentially decay it to smithereens.

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