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A New Mathematical Model of Syphilis

Published online by Cambridge University Press:  08 April 2010

F. A. Milner  and
R. Zhao
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:[email protected]
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Abstract

The CDC launched the National Plan to Eliminate Syphilis from the USA in October 1999[4]. In order to reach this goal, a goodunderstanding of the transmission dynamics of the disease is necessary. Based on a SIRSmodel Breban et al. [3] providedsome evidence that supports the feasibility of the plan proving that no recurringoutbreaks should occur for syphilis. We study in this work a syphilis model that includespartial immunity and vaccination. This model suggests that a backward bifurcation verylikely occurs for the real-life estimated epidemiological parameters for syphilis. Thismay explain the resurgence of syphilis after mass treatment [21]. Occurrence of backward bifurcation brings a new challenge for theplan of the CDC’s –striking a balance between treatment of early infection, vaccinationdevelopment and health education. Our models suggest that the development of an effectivevaccine, as well as health education that leads to enhanced biological and behavioralprotection against infection in high-risk populations, are among the best ways to achievethe goal of elimination of syphilis in the USA.

Keywords

backward bifurcationpartial immunityvaccinationsyphilis
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 6: Ecology (Part 2) , 2010 , pp. 96 - 108
Copyright
© EDP Sciences, 2010

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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