Periodic orbits in a seasonally-forced SEIR epidemic model

Infectious diseases affect millions of people every year. In fact, more than 17 million deaths worldwide each year are attributed to infectious diseases [6]. An endemic disease is a disease which persists over time in a given population or geographic region [4]. For example, prior to the development of the measles vaccine in the 1960’s and eradication of measles from the United States in 2000, measles was endemic, exhibiting biennial cycles with alternating years of high and low incidence [1, 2, 5] (Figure 1).