Let's use math to test a theory in real time.

The last two weeks appears to have witnessed an explosion of Measles cases in Southwestern Wisconsin. Except they did not explode, they just went unreported and unmeasured for a period of time before someone took notice. Once the alarm was sound, public health officials went into the field, and quickly found more cases.

This outbreak is unusual in another sense: it is earlier than expected. Historically, before we began to reap the benefit of the MMR vaccine, measles would stay dormant in the summer and then slowly build over the fall and winter as the school year and weather brought children (who lacked immunity from never having had the disease) together.

First a Theory

What does this pattern suggest? This looks like a close knit religious community with low vaccination rates had an outbreak and were dealing with it themselves, until such time as they could not.

Iowa county Wisconsin has a growing Amish population, and vaccination rates in Amish communities vary widely based upon local beliefs, leadership, and customs. This outbreak would fit a pattern.

Measles Outbreaks in Anabaptist Communities, 2013–Present

2013: Southern Alberta, Canada:Hutterite and Mennonite communities with 42 confirmed cases.

2014: Ohio, USA: Amish community with 383 confirmed cases across nine counties.

2024–2025: Southwestern Ontario, Canada: Mennonite community, traced to a New Brunswick gathering with over 177 confirmed cases.

2025: Gaines County, Texas, USA:Old Colony Mennonite community with over 762 confirmed cases and 3 deaths.

2025: Taber, Alberta, Canada: Low German Mennonite community and other low vaccination communities with over 2,000 cases.

My purpose is not to single out a particular community, I was a member of an Anabaptist community and I am very sympathetic to their goals and reading of Christian Scripture. My purpose is to show how we can apply math to what we know about a phenomenon to extrapolate evidence for what is not yet known. I won't lie; I would consider it a bonus if it highlighted the dangers of vaccine skepticism.

From Theory to Forecast (aka “Mathing the Math)

Measles has a reproduction number of 15. Vaccination rates do not change how effectively measles spreads, it reduces the population susceptible to infection. So, assuming the general population of 6 year olds in Wisconsin has a vaccination rate of .79 our adjusted R value is 15(1-.79)=3.15.

Estimates of vaccine rates among Amish communities vary widely, but let’s take the largest estimate I could find with a vaccination rate of .41 (but trending downwards). 15(1-.41)=8.85.

Measles can incubate for 7-21 days but the generally accepted average is 12 days for each new generation of infections. So it find k for each community we take ln(R)/days. Our general population comes out at k=.09562. The Amish community would have a value of k=.1817.

So our exponential growth functions look like this:

General Population: (n)e^.09562t
Amish Community: (n)e^.1817t

Two Forecasts

If the measles outbreak is focused in the Amish Community and social distancing measures were not undertaken the moment the infection went public, we would expect to see cases rise to ~125 in the next seven days. This number could be larger if we over-estimated the vaccine rate in the Amish community or the current number of cases continues to be understated.

If the cases are centered in the General Community, that number should be significantly lower, ~68 or less, given that school has yet to begin in the general population and we live less social lives and have smaller families with fewer children than our Amish neighbors.

If the cases are somewhere in-between, we would be led to believe that the infection is spreading in both communities.

Measles outbreaks strain medical resources in the area impacted, created unnecessary suffering for the individuals infected, and result in needless deaths. These facts are not in dispute. This is real life, it is not a math game. But we can use math to test theories. We can use it to discern details of a narrative that are not reported in the news media. It can help confirm or deny a hypothesis.

With another week’s of reporting, we should be able to discern if this outbreak is concentrated in one community or the other. Let’s find out.


Addendum:

The math also works backwards. With the 35 known cases we can estimate ln(35)/.1817 that if the infection is in the Amish community, the first person would have been infectious around July 22, 2026. If it was in the general community, (ln(35)/.09562) the first person would have been infectious around July 5, 2026. I would posit it is more likely that the measles infection worked its way through an Amish Community for 11 days without be noticed than existing in the general community for 28 days without being reported.