Luther College senior Doorenbos selected to complete summer research on mathematical models for vaccinations

When a large enough portion of a community becomes vaccinated and eliminates the risk of a disease outbreak, that community gains herd immunity. John Doorenbos, Luther College senior from Grinnell, Iowa, has been selected to do collaborative research over the summer to formulate a mathematical model to understand what proportion of individuals in a community need to be vaccinated in order to gain herd immunity. His research focuses on how the particular structure of the community affects the proportion of immune individuals required.

Doorenbos, the son of Roy and Darlene Doorenbos of Grinnell, is majoring in mathematics and computer science at Luther. He is a 2012 graduate of Grinnell Community High School.

According to Doorenbos, vaccinations bring benefits to all members of a community, even those who are unvaccinated. Community members who get vaccinated cannot contract the disease, which benefits those who are not vaccinated by lowering their chances of contracting the disease. When enough members have been vaccinated, the community gains herd immunity.

Doorenbos will build off work that has already been done in the simplest case of a well-mixed population and expand on the simpler model to accommodate more realistic situations. Using linear algebra, differential equations, probability and statistics, he will continue to analyze and modify the model to improve its accuracy.  

The results of this research will provide information about vaccination thresholds for herd immunity for a variety of diseases. Once complete, Doorenbos's research will be presented at Luther and other off-campus opportunities.

"With the measles outbreak early this year, this research is timely and important. Being able to work on a project that can contribute in a unique way to an already large area of study is an exciting prospect. Using skills learned in both of my majors, this interdisciplinary research is allowing me to get a taste of what I might be doing in the future," Doorenbos said.

Doorenbos is working with Kyle Fey, Luther assistant professor of mathematics, and Erin Ellefsen, Luther junior, on "A mathematical model for vaccinations" over the course of the summer.

Doorenbos's research is funded by the Tomson Family Faculty Fellowship. This program is one of a wide selection of experiential learning opportunities at Luther intended to deepen the learning process and that are part of Luther's academic core.

A national liberal arts college with an enrollment of 2,400, Luther offers an academic curriculum that leads to the Bachelor of Arts degree in more than 60 majors and pre-professional programs. For more information about Luther visit the college's website:

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