A New Mathematical Model of Syphilis

¹ School of Mathematical and Statistical Sciences, Arizona State University P.O. Box 871804, Tempe, AZ 85287-1804, USA
² Department of Computer Science, Purdue University, West Lafayette, IN 47907-2107, USA

^* Corresponding author. E-mail: milner@asu.edu

Abstract

The CDC launched the National Plan to Eliminate Syphilis from the USA in October 1999 [4]. In order to reach this goal, a good understanding of the transmission dynamics of the disease is necessary. Based on a SIRS model Breban et al. [3] provided some evidence that supports the feasibility of the plan proving that no recurring outbreaks should occur for syphilis. We study in this work a syphilis model that includes partial immunity and vaccination. This model suggests that a backward bifurcation very likely occurs for the real-life estimated epidemiological parameters for syphilis. This may explain the resurgence of syphilis after mass treatment [21]. Occurrence of backward bifurcation brings a new challenge for the plan of the CDC’s –striking a balance between treatment of early infection, vaccination development and health education. Our models suggest that the development of an effective vaccine, as well as health education that leads to enhanced biological and behavioral protection against infection in high-risk populations, are among the best ways to achieve the goal of elimination of syphilis in the USA.