Eur. Phys. J. B (2015) 88: 107
https://doi.org/10.1140/epjb/e2015-50621-9

Regular Article

A simple model to quantitatively account for periodic outbreaks of the measles in the Dutch Bible Belt

¹ Department of Physics, East Carolina University, Greenville, NC 27858, USA
² M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
³ School of Agriculture, Policy, and Development, The University of Reading, Whiteknights, P.O. Box 217, Reading, RG6 6AH, UK

^a e-mail: bierm@ecu.edu

Received: 11 September 2014
Received in final form: 13 December 2014
Published online: 22 April 2015

Abstract

In the Netherlands there has been nationwide vaccination against the measles since 1976. However, in small clustered communities of orthodox Protestants there is widespread refusal of the vaccine. After 1976, three large outbreaks with about 3000 reported cases of the measles have occurred among these orthodox Protestants. The outbreaks appear to occur about every twelve years. We show how a simple Kermack-McKendrick-like model can quantitatively account for the periodic outbreaks. Approximate analytic formulae to connect the period, size, and outbreak duration are derived. With an enhanced model we take the latency period in account. We also expand the model to follow how different age groups are affected. Like other researchers using other methods, we conclude that large scale underreporting of the disease must occur.