Breaking the chain of transmission through vaccination

Like any other human vaccine, coronavirus vaccines aren't only meant to protect individuals from developing symptomatic COVID-19, but to break chains of transmission throughout the population, insulating vulnerable people through multiple layers of protection. Let me explain how this works. Say that the older of two unvaccinated child siblings, E.L., is exposed to a classmate with COVID-19 in the school cafeteria. What's the chance that she brings the infection home to her younger sibling, G.L., and what's the chance that younger sibling inadvertently gives the infection to Grandpa when he visits? Grandpa is vaccinated and boosted, of course, but since he has cancer and is immune compromised, he is only 60 percent less likely to catch the virus than an unvaccinated person. Let's say that due to the vagaries of distance and air circulation, the unvaccinated older sibling has a 50 percent chance of developing COVID-19 from her school exposure. Since she shares a bed with her younger sibling and doesn't go into quarantine until she has been infectious for two days, let's say that there is an 80 percent chance that if infected, she infects her sister also. This then becomes a straightforward math problem.

Probability E.L. catches COVID-19 from classmate: 0.50

Probability G.L. catches COVID-19 from E.L: 0.50 X 0.80 = 0.40

Probability Grandpa catches COVID-19 from G.L.: 0.40 X (1 - 0.60) = 0.16

So, there is about a 1 in 6 chance of an intact chain of transmission from E.L.'s classmate to E.L.'s Grandpa, via G.L. Not tremendously high, but outcomes with 1 in 6 odds happen all the time, as any sports fan can attest, and given the high risk of severe illness in immune compromised adults over age 65, most people would probably call this an unacceptable risk for Grandpa.

What if E.L. and G.L. were both fully vaccinated, though? The Pfizer-BioNTech vaccine had a reported efficacy of 90.7 percent against symptomatic disease in a randomized clinical trial of 5 to 11 year-old children; efficacy against asymptomatic transmission is uncertain, but for the sake of this scenario I will assume it's 80 percent. Let's run these calculations again, with the vaccine actions in bold.

Probability E.L. catches COVID-19 from classmate: 0.50 X (1 - 0.80)

Probability G.L. catches COVID-19 from E.L: 0.10 X 0.80 X (1 - 0.80) = 0.016

Probability Grandpa catches COVID-19 from G.L.: 0.016 X (1 - 0.60) = 0.0064

In this scenario, there is about a 1 in 156 chance of an intact chain of transmission from E.L.'s classmate to E.L.'s Grandpa, via G.L. 1 in 156 is better odds than winning the big prize in the lottery, but most people would feel pretty comfortable that an event this unlikely would not happen on any given day.

In summary, people who suggest that once Grandpa (or Grandma, or Great-Aunt Amy or other older people who are important to you or somebody else) is vaccinated and boosted, it's a "personal choice" for them and their children to get vaccinated too, are demonstrating ignorance of math and public health. We will only get through this pandemic by breaking the transmission chain together, not with 1 in 5 American adults declining vaccinations for themselves and their children because they don't think they will get very sick or that their inaction could quite possibly lead to someone else's disability or death - maybe even someone they love. I wish that every person with access to vaccination would just do the right thing and mandates wouldn't be necessary, but the declaration "I'm pro-vaccine but anti-mandate" is a non sequitur. If you're really pro-vaccine, you want everyone to get vaccinated whether they like it or not, for the good of your community and country and the whole human race.