On April 10, 2017, The Minnesota Department of Health received notice about a suspected measles case in an unvaccinated child. On April 11th, there was a second report of the measles. On April 13th, a third case was confirmed. By May 31, 2017, 65 cases of the measles, an infectious disease thought to be eliminated in the United States, were confirmed. This outbreak occurred in an area with a low vaccination rate. Improvements in medical care have far removed many in the United States from risks of such infectious diseases. Consequently, this removal of illness has given way to the anti-vaccination movements as well as the idea of spacing out vaccinations. In this research we investigate a system of ordinary differential equations that model the effect of anti-vaccination groups on the spread of infectious diseases, such as the measles, in a society as well as quantify the cost that avoiding vaccination and disease impose on a society.