A New Mathematical Model of Syphilis

F. A. Milner; R. Zhao

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 6, page 96-108
  • ISSN: 0973-5348

Abstract

top
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.

How to cite

top

Milner, F. A., and Zhao, R.. "A New Mathematical Model of Syphilis." Mathematical Modelling of Natural Phenomena 5.6 (2010): 96-108. <http://eudml.org/doc/197631>.

@article{Milner2010,
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. },
author = {Milner, F. A., Zhao, R.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {backward bifurcation; partial immunity; vaccination; syphilis; ordinary differential equations},
language = {eng},
month = {4},
number = {6},
pages = {96-108},
publisher = {EDP Sciences},
title = {A New Mathematical Model of Syphilis},
url = {http://eudml.org/doc/197631},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Milner, F. A.
AU - Zhao, R.
TI - A New Mathematical Model of Syphilis
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/4//
PB - EDP Sciences
VL - 5
IS - 6
SP - 96
EP - 108
AB - 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.
LA - eng
KW - backward bifurcation; partial immunity; vaccination; syphilis; ordinary differential equations
UR - http://eudml.org/doc/197631
ER -

References

top
  1. R. E. Baughn D. M. Musher. Secondary syphilitic lesions. Clin. Microbiol. Rev., 18 (2005), 205-216. 
  2. R. Breban, V. Supervie, J. T. Okano, R. Vardavas, and S. Blower. The transmission dynamics of syphilis and the CDC’s elimination plan. Available from Nature Proceedings 〈 ⟩ (2007).  URIhttp://dx.doi.org/0.1038/npre.2007.1373.1
  3. R. Breban, V. Supervie, J. T. Okano, R. Vardavas, and S. Blower. Is there any evidence that syphilis epidemics cycle?Lancet Infect. Dis.8 (2008), 577-581.  
  4. Centers for Disease Control and Prevention. The National Plan to Eliminate Syphilis from the United States, 2006, . URIhttp://www.cdc.gov/stopsyphilis/plan.htm
  5. O. Diekmann, J. A. P. Heesterbeek J. A. J. and Metz. On the definition and the computation of the basic reproduction ratio R0 in models for infectionus diseases in heterogeneous populations. J. Math. Biol.28 (1990), 365-382. 
  6. L. Doherty, K. A. Fenton, J. Jones, T. C. Paine, S. P. Higgins, D. Williams A. and Palfreeman.Syphilis: old problem, new strategy. BMJ, 325 (2002), 153-156. 
  7. J. Dushoff, W. Huang C. and Castillo-Chavez. Backwards bifurcations and catastrophe in simple models of fatal diseases. J. Math. Biol., 36 (1998), 227-248. 
  8. G. P. Garnett, S. O. Aral, D. V. Hoyle, W. Cates R. M. and Anderson. The natural history of syphilis: implications for the trasmission dynamics and control of infection. Sex. Transm. Dis., 24 (1997), 185-200. 
  9. M. G. M. Gomes, A. O. Franco, M. C. Gomes G. F. and Medley. The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy. Proc. Biol. Sci., 271 (2004), 617-623. 
  10. M. G. M. Gomes, A. Margheri, G. F. Medley C. and Rebelo. Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence. J. Math. Biol., 51 (2005), 414-430. 
  11. M. G. M. Gomes, L. J. White G. F. and Medley. Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives. Journal of Theoretical Biology, 228 (2004), 539-549. 
  12. D. Gökaydin, J. B. Oliveira-Martins, I. Gordo M. G. M. and Gomes. The reinfection threshold regulates pathogen diversity: the case of influenza. J. R. Soc. Interface, 4 (2007), 137-142. 
  13. N. C. Grassly, C. Fraser G. P. and Garnett. Host immunity and synchronized epidemics of syphilis across the United States. Nature, 433 (2005), 417-421. 
  14. K.P. Hadeler P. Van den Driessche. Backward bifurcation in epidemic control. Mathematical Biosciences, 146 (1997), 15-35. 
  15. A. K. Hurtig, A. Nicoll, C. Carne, T. Lissauer, N. Connor, J. P. Webster L. and Ratcliffe. Syphilis in pregnant women and their children in the United Kingdom: results from national clinician reporting surveys 1994-7. BMJ, 317 (1998), 1617-1619. 
  16. R. E. LaFond S. A. Lukehart. Biological basis for syphilis. Clin. Microbiol. Rev., 19 (2006), 29-49. 
  17. C. A. Morgan, S. A. Lukehart W. C. and Van Voorhis. Protection against syphilis correlates with specificity of antibodies to the variable regions of Treponema pallidum repeat protein K. Infect. Immun.71 (2003), 5605-5612. 
  18. M. Myint, H. Bashiri, R. D. Harrington C. M. and Marra. Relapse of secondary syphilis after Benzathine Penicillin G: molecular analysis. Sex. Transm. Dis., 31 (2004), 196-199. 
  19. G. L. Oxman, K. Smolkowski J. and Noell. Mathematical modeling of epidemic syphilis transmission: implications for syphilis control programs. Sex. Transm. Dis., 23 (1996), 30-39. 
  20. T. Parran. Syphilis: a public health problem. Science, 87 (1938), 147-152. 
  21. B. Pourbohloul, M. L. Rekart R. C. and Brunham. Impact of mass treatment on syphilis transmission: a mathematical modeling approach. Sex. Transm. Dis., 30 (2003), 297-305. 
  22. T. C. Reluga J. Medlock. Resistance mechanisms matter in SIR models. Math Biosci Eng., 4 (2007), 553-563. 
  23. P. van den Driessche J. Watmough. Reproduction numbers and sub-shreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180 (2002), 29-48. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.