Recent events have led to an increased interest in emerging infectious diseases. This article applies various deterministic models to the SARS epidemic of 2003 and a measles outbreak in the Netherlands in 1999-2000. We take a historical approach beginning with the well-known logistic curve and a lesser-known extension popularized by Pearl and Reed in the 1920s. We then considered Richards generalization in 1959 using a shape parameter. This method remains popular today in the biological literature but is often neglected in mathematical texts. The paper is accessible to students finishing the second year of calculus.