Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-vtfg7 Total loading time: 0.338 Render date: 2022-05-29T08:41:19.483Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

A New Mathematical Model of Syphilis

Published online by Cambridge University Press:  08 April 2010

F. A. Milner*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University P.O. Box 871804, Tempe, AZ 85287-1804, USA
R. Zhao
Affiliation:
Department of Computer Science, Purdue University, West Lafayette, IN 47907-2107, USA
*
* Corresponding author. E-mail: milner@asu.edu
Get access

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.

Type
Research Article
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baughn, R. E. Musher, D. M.. Secondary syphilitic lesions . Clin. Microbiol. Rev., 18 (2005), 205-216.CrossRefGoogle ScholarPubMed
Breban, R., Supervie, V., Okano, J. T., Vardavas, R., and Blower, S.. The transmission dynamics of syphilis and the CDC’s elimination plan . Available from Nature Proceedings 〈 http://dx.doi.org/0.1038/npre.2007.1373.1 ⟩ (2007).
Breban, R., Supervie, V., Okano, J. T., Vardavas, R., and Blower, S.. Is there any evidence that syphilis epidemics cycle? Lancet Infect. Dis. 8 (2008), 577-581. CrossRefGoogle ScholarPubMed
Centers for Disease Control and Prevention. The National Plan to Eliminate Syphilis from the United States, 2006, http://www.cdc.gov/stopsyphilis/plan.htm.
Diekmann, O., Heesterbeek, J. A. P. Metz, J. A. J.. On the definition and the computation of the basic reproduction ratio R 0 in models for infectionus diseases in heterogeneous populations . J. Math. Biol. 28 (1990), 365-382.CrossRefGoogle Scholar
Doherty, L., Fenton, K. A., Jones, J., Paine, T. C., Higgins, S. P., Williams, D. Palfreeman., A. Syphilis: old problem, new strategy . BMJ, 325 (2002), 153-156.CrossRefGoogle ScholarPubMed
Dushoff, J., Huang, W. Castillo-Chavez, C.. Backwards bifurcations and catastrophe in simple models of fatal diseases . J. Math. Biol., 36 (1998), 227-248.CrossRefGoogle ScholarPubMed
Garnett, G. P., Aral, S. O., Hoyle, D. V., Cates, W. Anderson, R. M.. The natural history of syphilis: implications for the trasmission dynamics and control of infection . Sex. Transm. Dis., 24 (1997), 185-200.CrossRefGoogle Scholar
Gomes, M. G. M., Franco, A. O., Gomes, M. C. Medley, G. F.. The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy . Proc. Biol. Sci., 271 (2004), 617-623.CrossRefGoogle ScholarPubMed
Gomes, M. G. M., Margheri, A., Medley, G. F. Rebelo, C.. Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence . J. Math. Biol., 51 (2005), 414-430.CrossRefGoogle ScholarPubMed
Gomes, M. G. M., White, L. J. Medley, G. F.. Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives . Journal of Theoretical Biology, 228 (2004), 539-549.CrossRefGoogle ScholarPubMed
Gökaydin, D., Oliveira-Martins, J. B., Gordo, I. Gomes, M. G. M.. The reinfection threshold regulates pathogen diversity: the case of influenza . J. R. Soc. Interface, 4 (2007), 137-142.CrossRefGoogle ScholarPubMed
Grassly, N. C., Fraser, C. Garnett, G. P.. Host immunity and synchronized epidemics of syphilis across the United States . Nature, 433 (2005), 417-421.CrossRefGoogle ScholarPubMed
Hadeler, K.P. Van den Driessche, P.. Backward bifurcation in epidemic control . Mathematical Biosciences, 146 (1997), 15-35.CrossRefGoogle ScholarPubMed
Hurtig, A. K., Nicoll, A., Carne, C., Lissauer, T., Connor, N., Webster, J. P. Ratcliffe, L.. Syphilis in pregnant women and their children in the United Kingdom: results from national clinician reporting surveys 1994-7 . BMJ, 317 (1998), 1617-1619.CrossRefGoogle ScholarPubMed
LaFond, R. E. Lukehart, S. A.. Biological basis for syphilis . Clin. Microbiol. Rev., 19 (2006), 29-49.CrossRefGoogle ScholarPubMed
Morgan, C. A., Lukehart, S. A. Van Voorhis, W. C.. Protection against syphilis correlates with specificity of antibodies to the variable regions of Treponema pallidum repeat protein K . Infect. Immun. 71 (2003), 5605-5612.CrossRefGoogle ScholarPubMed
Myint, M., Bashiri, H., Harrington, R. D. Marra, C. M.. Relapse of secondary syphilis after Benzathine Penicillin G: molecular analysis . Sex. Transm. Dis., 31 (2004), 196-199.CrossRefGoogle ScholarPubMed
Oxman, G. L., Smolkowski, K. Noell, J.. Mathematical modeling of epidemic syphilis transmission: implications for syphilis control programs . Sex. Transm. Dis., 23 (1996), 30-39.CrossRefGoogle ScholarPubMed
Parran, T.. Syphilis: a public health problem . Science, 87 (1938), 147-152.CrossRefGoogle ScholarPubMed
Pourbohloul, B., Rekart, M. L. Brunham, R. C.. Impact of mass treatment on syphilis transmission: a mathematical modeling approach . Sex. Transm. Dis., 30 (2003), 297-305.CrossRefGoogle ScholarPubMed
Reluga, T. C. Medlock, J.. Resistance mechanisms matter in SIR models . Math Biosci Eng., 4 (2007), 553-563.CrossRefGoogle ScholarPubMed
van den Driessche, P. Watmough, J.. Reproduction numbers and sub-shreshold endemic equilibria for compartmental models of disease transmission . Mathematical Biosciences, 180 (2002), 29-48.CrossRefGoogle ScholarPubMed

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A New Mathematical Model of Syphilis
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A New Mathematical Model of Syphilis
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A New Mathematical Model of Syphilis
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *