Epidemic Models for SARS and Measles
Author(s): Edward Rozema
The College Mathematics Journal, Vol. 38, No. 4 (Sep., 2007), pp. 246-259
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/27646499
Tag: First order equations
Abstract: Severe acute respiratory syndrome or SARS is a respiratory disease caused by the SARS coronavirus. In late 2002 and early 2003, Between November 2002 and July, an outbreak of SARS in southern China nearly became a pandemic. In the matter of a few weeks, SARS spread to 37 countries. Over 8000 cases were reported, and the fatality rate was over 9%. Models of epidemics usually involve systems of differential equations; however, the author has chosen to model the epidemic using a single differential equation in order to make the paper accessible to second-year calculus students. The author begins by examining the SARS data and modeling the epidemic using logistic growth and then a more generalized model of logistic growth proposed by Pearl and Reed in 1923. This model fits the data much better. The author goes on to use a model proposed by Richards (1959) to explore the SARS epidemic. Using this model, he compares the SARS epidemic to an outbreak of measles in the Netherlands in 1999–2000.
Review by Thomas W. Judson, Stephen F. Austin State University, March 16, 2013.