The purpose of this note is to explain some simple math that is very relevant to current events.

Every disease has a basic reproduction number, R. It is the average number of secondary infections created by an infectious individual (in an otherwise susceptible population). Early in covid R was 2.5 but it grew to 5 or more as the disease evolves. Measles has an R that is much higher. According to Google’s AI overview “it is widely cited as being between 12 and 18.”

The other number we need is u, the fraction of the population that is unvaccinated. If Ru < 1 herd immunity has been achieved and the disease cannot spread. If we suppose R = 14.28 then this means 93% of the population has to be successfully vaccinated. The word successful refers to the fact that sometimes vaccinations do not produce the desired immunity. My wife Susan was vaccinated against whooping cough but caught it from her Christian Scientist neighbors.

As usual reality is more complicated than math. Even if Ru < 1 there can be groups of people who for religious, political, or other reasons do not believe in vaccination. This creates areas in which the disease can spread.  The 2025 Texas measles outbreak was centered in a close-knit and under-vaccinated Mennonite community in West Texas’ Gaines County, where low vaccination rates were a key factor in the rapid spread of the highly contagious virus. The outbreak started within this community but eventually spread beyond it to other Texas counties and into New Mexico. 

Florida has recently made a dangerous decision to no longer require children be vaccinated for measles and other diseases in order to attend school. While it will take several years until herd immunity is lost, the fact that school populations are stratified by age it will almost immediately create subpopulations in which diseases can spread. The problem will grow worse over time. When it gets bad it will be very hard to raise vaccination levels in the population to stop it. .

Vaccine policy needs to be informed by science. It is not enough for RFKJr to say “I am not taking away anyone’s vaccines.” It is important to have people in HHS and CDC who advocate for vaccination, and educate the public about the need for them and their safety and effectiveness. Last but not least we need to remove barriers to getting vaccinations such as the current need for a prescription to get a covid vaccination. Fortunately that virus has evolved to be less deadly but it can still cause serious disease in people with “high risk health conditions.” These people can get vaccinated but they will be much less safe if there is a significant amount of  covid infection  in the population as a whole.