Does Vaccinations Plus Cases Equals Population Immunity in Arizona?

 

On Monday I did a post worrying about Arizona's falling vaccination rate.  I showed a curve suggesting that if things keep going the way they are now, the percent fully vaccinated might level-off well before we get to 50% of the population.

In a conversation about that with some public health people I know, it was pointed out that we also have to take previous cases into account when considering the percent who make have some level of immunity.  Having had and recovered from COVID-19 give you some immunity, but not as much as if you're fully vaccinated.  The thinking seems to be that having a case is somewhat similar to one dose of a two-vaccine regimen.

But there are problems with rolling infection-based immunity together with vaccinations to estimate what percent of the population is protected.  For one thing, many people who have had COVID-19 have also gotten vaccinated.  Some researchers I know who recently completed a nationwide study told me that about 35% of people who had or thought they COVID-19 reported also having vaccinated.

Another problem is that not every case of COVID-19 is reported.  Some researchers I know who have been looking at serology studies (looking for evidence of infection in blood samples taken for other reasons) estimate there are 4.5 unreported infections for every reported infection.

So based on this, we can do some back-of-the-envelope calculations of the percent of Arizonans who have some level of immunity. The ADHS website says that 812,742 cases have been confirmed in the state.  Based on the serology numbers, there are probably an additional 3,657,338 unreported cases, for a total of 4,470,081 suspected/reported cases.  

As I reported on Sunday, 45.65% of the Arizona population, or 5,718,183 people, have received a dose. But according to the survey results described above, 35% of those represent people who have already been infected.  Subtracting those from the vax doses leaves 3,716,818 people who have not been infected but have received a dose.  

That means 8,186,899 Arizonans have some level of protection.  What's the problem with that number?  The state population is only 7,424,805. So much for back-of-the-envelope calculations!  

But the point is, a lot more people in the state have some level of protection than the pure vaccination numbers would indicate. One public health person I know estimates the number at 60%-70%.  

So maybe I was over-worried in Monday's post. This would explain why our infection rates are so low, and continuing to fall, even though we're only around 35% fully vaccinated.

Header image by Gerd Altmann from Pixabay 

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