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In this lesson, students explore the fundamental mathematical concepts underlying the spread of contagious diseases. Using a simple exponential model, students compare and contrast the effects of different transmission rates on a population and develop an understanding of the nature and characteristics of exponential growth. Students can then compare their projections with actual Ebola data from West Africa, to create context for analyzing the strengths and limitations of this simplified model.

The United States is now experiencing what promises to be one of the worst outbreaks of measles since the virus was declared eliminated from the country in 2000.  It began in early January at Disneyland Resort in Anaheim, California, and has since spread to 14 states and infected 84 people, according to the U.S. Centers for Disease Control and Prevention (CDC). Measles, caused by a paramyxovirus from the genus Morbillivirus, is one of the most contagious diseases in the world, infecting more than 90% of susceptible hosts that come in contact with an afflicted individual. In the absence of widespread vaccination, the average person with measles will infect an average of 12 to 18 other people; in contrast, Ebola is typically transmitted to 1.5 to 2.5 people.

15. That's all you need to know about the measles. OK, that's not true at all. There's no one weird trick that will give you a flat belly (besides lying face-down on something flat), and there's no one weird number that explains measles epidemiology. But the basic reproduction number, or R0, of a disease does shed some light on which diseases become epidemics and how we can keep them in check.