Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 104819, 17 pages
http://dx.doi.org/10.1155/2014/104819
Research Article

HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling

Department of Mathematics, University of Zimbabwe, P.O. Box MP 167 Mount Pleasant, Harare, Zimbabwe

Received 5 July 2014; Accepted 5 October 2014; Published 13 November 2014

Academic Editor: Peter G. L. Leach

Copyright © 2014 A. Mhlanga et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. J. Looker, G. P. Garnett, and G. P. Schmid, “An estimate of the global prevalence and incidence of herpes simplex virus type 2 infection,” Bulletin of the World Health Organization, vol. 86, no. 10, pp. 805A–812A, 2008. View at Publisher · View at Google Scholar · View at Scopus
  2. K. J. Looker, G. P. Garnett, and G. P. Schmid, “An estimate of the global prevalence and incidence of herpes simplex virus type 2 infection,” Bulletin of the World Health Organization, vol. 86, no. 10, pp. 805–812, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. CDC [Centers for Disease Control and Prevention], Division of Sexually Transmitted Disease Surveillance 1999. Atlanta: Department of Health and Human Services, Centers for Disease Control and Prevention (CDC), 2000.
  4. K. Owusu-Edusei Jr., H. W. Chesson, T. L. Gift et al., “The estimated direct medical cost of selected sexually transmitted infections in the United States, 2008,” Sexually Transmitted Diseases, vol. 40, no. 3, pp. 197–201, 2013. View at Publisher · View at Google Scholar · View at Scopus
  5. WHO [World Health Organisation], The Second Decade: Improving Adolescent Health and Development, WHO Adolescent and Development Programme (WHO/FRH/ADH/98.19), Geneva, Switzerland, 1998.
  6. K. L. Dehne and G. Riedner, Sexually Transmitted Infections among Adolescents: The Need for Adequate Health Care, WHO, Geneva, Switzerland, 2005.
  7. Y. L. Hill and F. M. Biro, Adolescents and Sexually Transmitted Infections, CME Feature, 2009.
  8. CDC [Centers for Disease Control and Prevention] Division of STD Prevention, Sexually Transmitted Disease Surveillance 1999, Department of Health and Human Services, Centers for Disease Control and Prevention (CDC), Atlanta, Ga, USA, 2000.
  9. W. Cates and M. C. Pheeters, “Adolescents and sexually transmitted diseases: current risks and future consequences,” in Proceedings of the Workshop on Adolescent Sexuality and Reproductive Health in Developing Countries: Trends and Interventions, National Research Council, Washington, DC, USA, March 1997.
  10. K. C. Chinsembu, “Sexually transmitted infections in adolescents,” The Open Infectious Diseases Journal, vol. 3, pp. 107–117, 2009. View at Google Scholar
  11. S. Y. Cheng and K. K. Lo, “Sexually transmitted infections in adolescents,” Hong Kong Journal of Paediatrics, vol. 7, no. 2, pp. 76–84, 2002. View at Google Scholar
  12. S. L. Rosenthal, L. R. Stanberry, F. M. Biro et al., “Seroprevalence of herpes simplex virus types 1 and 2 and cytomegalovirus in adolescents,” Clinical Infectious Diseases, vol. 24, no. 2, pp. 135–139, 1997. View at Publisher · View at Google Scholar · View at Scopus
  13. G. Sucato, C. Celum, D. Dithmer, R. Ashley, and A. Wald, “Demographic rather than behavioral risk factors predict herpes simplex virus type 2 infection in sexually active adolescents,” Pediatric Infectious Disease Journal, vol. 20, no. 4, pp. 422–426, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Noell, P. Rohde, L. Ochs et al., “Incidence and prevalence of Chlamydia, herpes, and viral hepatitis in a homeless adolescent population,” Sexually Transmitted Diseases, vol. 28, no. 1, pp. 4–10, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. R. L. Cook, N. K. Pollock, A. K. Rao, and D. B. Clark, “Increased prevalence of herpes simplex virus type 2 among adolescent women with alcohol use disorders,” Journal of Adolescent Health, vol. 30, no. 3, pp. 169–174, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. C. D. Abraham, C. J. Conde-Glez, A. Cruz-Valdez, L. Sánchez-Zamorano, C. Hernández-Márquez, and E. Lazcano-Ponce, “Sexual and demographic risk factors for herpes simplex virus type 2 according to schooling level among mexican youths,” Sexually Transmitted Diseases, vol. 30, no. 7, pp. 549–555, 2003. View at Google Scholar · View at Scopus
  17. I. J. Birdthistle, S. Floyd, A. MacHingura, N. Mudziwapasi, S. Gregson, and J. R. Glynn, “From affected to infected? Orphanhood and HIV risk among female adolescents in urban Zimbabwe,” AIDS, vol. 22, no. 6, pp. 759–766, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. P. N. Amornkul, H. Vandenhoudt, P. Nasokho et al., “HIV prevalence and associated risk factors among individuals aged 13–34 years in rural Western Kenya,” PLoS ONE, vol. 4, no. 7, Article ID e6470, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. Centers for Disease Control and Prevention, “Youth risk behaviour surveillance—United States,” Morbidity and Mortality Weekly Report, vol. 53, pp. 1–100, 2004. View at Google Scholar
  20. K. Buchacz, W. McFarland, M. Hernandez et al., “Prevalence and correlates of herpes simplex virus type 2 infection in a population-based survey of young women in low-income neighborhoods of Northern California,” Sexually Transmitted Diseases, vol. 27, no. 7, pp. 393–400, 2000. View at Publisher · View at Google Scholar · View at Scopus
  21. L. Corey, A. Wald, C. L. Celum, and T. C. Quinn, “The effects of herpes simplex virus-2 on HIV-1 acquisition and transmission: a review of two overlapping epidemics,” Journal of Acquired Immune Deficiency Syndromes, vol. 35, no. 5, pp. 435–445, 2004. View at Publisher · View at Google Scholar · View at Scopus
  22. E. E. Freeman, H. A. Weiss, J. R. Glynn, P. L. Cross, J. A. Whitworth, and R. J. Hayes, “Herpes simplex virus 2 infection increases HIV acquisition in men and women: systematic review and meta-analysis of longitudinal studies,” AIDS, vol. 20, no. 1, pp. 73–83, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. S. Stagno and R. J. Whitley, “Herpes virus infections in neonates and children: cytomegalovirus and herpes simplex virus,” in Sexually Transmitted Diseases, K. K. Holmes, P. F. Sparling, P. M. Mardh et al., Eds., pp. 1191–1212, McGraw-Hill, New York, NY, USA, 3rd edition, 1999. View at Google Scholar
  24. A. Nahmias, W. E. Josey, Z. M. Naib, M. G. Freeman, R. J. Fernandez, and J. H. Wheeler, “Perinatal risk associated with maternal genital herpes simplex virus infection,” The American Journal of Obstetrics and Gynecology, vol. 110, no. 6, pp. 825–837, 1971. View at Google Scholar · View at Scopus
  25. C. Johnston, D. M. Koelle, and A. Wald, “Current status and prospects for development of an HSV vaccine,” Vaccine, vol. 32, no. 14, pp. 1553–1560, 2014. View at Publisher · View at Google Scholar · View at Scopus
  26. S. D. Moretlwe and C. Celum, “HSV-2 treatment interventions to control HIV: hope for the future,” HIV Prevention, Counselling and Testing, pp. 649–658, 2004. View at Google Scholar
  27. C. P. Bhunu and S. Mushayabasa, “Assessing the effects of intravenous drug use on hepatitis C transmission dynamics,” Journal of Biological Systems, vol. 19, no. 3, pp. 447–460, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. C. P. Bhunu and S. Mushayabasa, “Prostitution and drug (alcohol) misuse: the menacing combination,” Journal of Biological Systems, vol. 20, no. 2, pp. 177–193, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. Y. J. Bryson, M. Dillon, D. I. Bernstein, J. Radolf, P. Zakowski, and E. Garratty, “Risk of acquisition of genital herpes simplex virus type 2 in sex partners of persons with genital herpes: a prospective couple study,” Journal of Infectious Diseases, vol. 167, no. 4, pp. 942–946, 1993. View at Publisher · View at Google Scholar · View at Scopus
  30. L. Corey, A. Wald, R. Patel et al., “Once-daily valacyclovir to reduce the risk of transmission of genital herpes,” The New England Journal of Medicine, vol. 350, no. 1, pp. 11–20, 2004. View at Publisher · View at Google Scholar · View at Scopus
  31. G. J. Mertz, R. W. Coombs, R. Ashley et al., “Transmission of genital herpes in couples with one symptomatic and one asymptomatic partner: a prospective study,” The Journal of Infectious Diseases, vol. 157, no. 6, pp. 1169–1177, 1988. View at Publisher · View at Google Scholar · View at Scopus
  32. A. Wald, A. G. Langenberg, K. Link et al., “Effect of condoms on reducing the transmission of herpes simplex virus type 2 from men to women,” Journal of the American Medical Association, vol. 285, no. 24, pp. 3100–3106, 2001. View at Publisher · View at Google Scholar · View at Scopus
  33. A. H. Mokdad, J. S. Marks, D. F. Stroup, and J. L. Gerberding, “Actual causes of death in the United States, 2000,” The Journal of the American Medical Association, vol. 291, no. 10, pp. 1238–1245, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Wald, A. G. Langenberg, K. Link et al., “Effect of condoms on reducing the transmission of herpes simplex virus type 2 from men to women,” Journal of the American Medical Association, vol. 285, no. 24, pp. 3100–3106, 2001. View at Publisher · View at Google Scholar · View at Scopus
  35. E. T. Martin, E. Krantz, S. L. Gottlieb et al., “A pooled analysis of the effect of condoms in preventing HSV-2 acquisition,” Archives of Internal Medicine, vol. 169, no. 13, pp. 1233–1240, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. A. C. Ghani and S. O. Aral, “Patterns of sex worker-client contacts and their implications for the persistence of sexually transmitted infections,” Journal of Infectious Diseases, vol. 191, no. 1, pp. S34–S41, 2005. View at Publisher · View at Google Scholar · View at Scopus
  37. G. P. Garnett, G. Dubin, M. Slaoui, and T. Darcis, “The potential epidemiological impact of a genital herpes vaccine for women,” Sexually Transmitted Infections, vol. 80, no. 1, pp. 24–29, 2004. View at Publisher · View at Google Scholar · View at Scopus
  38. E. J. Schwartz and S. Blower, “Predicting the potential individual- and population-level effects of imperfect herpes simplex virus type 2 vaccines,” The Journal of Infectious Diseases, vol. 191, no. 10, pp. 1734–1746, 2005. View at Publisher · View at Google Scholar · View at Scopus
  39. C. N. Podder and A. B. Gumel, “Qualitative dynamics of a vaccination model for HSV-2,” IMA Journal of Applied Mathematics, vol. 75, no. 1, pp. 75–107, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. R. M. Alsallaq, J. T. Schiffer, I. M. Longini, A. Wald, L. Corey, and L. J. Abu-Raddad, “Population level impact of an imperfect prophylactic vaccine,” Sexually Transmitted Diseases, vol. 37, no. 5, pp. 290–297, 2010. View at Publisher · View at Google Scholar
  41. Y. Lou, R. Qesmi, Q. Wang, M. Steben, J. Wu, and J. M. Heffernan, “Epidemiological impact of a genital herpes type 2 vaccine for young females,” PLoS ONE, vol. 7, no. 10, Article ID e46027, 2012. View at Publisher · View at Google Scholar · View at Scopus
  42. A. M. Foss, P. T. Vickerman, Z. Chalabi, P. Mayaud, M. Alary, and C. H. Watts, “Dynamic modeling of herpes simplex virus type-2 (HSV-2) transmission: issues in structural uncertainty,” Bulletin of Mathematical Biology, vol. 71, no. 3, pp. 720–749, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. A. M. Geretti, “Genital herpes,” Sexually Transmitted Infections, vol. 82, no. 4, pp. iv31–iv34, 2006. View at Publisher · View at Google Scholar · View at Scopus
  44. R. Gupta, T. Warren, and A. Wald, “Genital herpes,” The Lancet, vol. 370, no. 9605, pp. 2127–2137, 2007. View at Publisher · View at Google Scholar · View at Scopus
  45. E. Kuntsche, R. Knibbe, G. Gmel, and R. Engels, “Why do young people drink? A review of drinking motives,” Clinical Psychology Review, vol. 25, no. 7, pp. 841–861, 2005. View at Publisher · View at Google Scholar · View at Scopus
  46. B. A. Auslander, F. M. Biro, and S. L. Rosenthal, “Genital herpes in adolescents,” Seminars in Pediatric Infectious Diseases, vol. 16, no. 1, pp. 24–30, 2005. View at Publisher · View at Google Scholar · View at Scopus
  47. H. W. Hethcote, “The mathematics of infectious diseases,” SIAM Review, vol. 42, no. 4, pp. 599–653, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  48. P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  49. J. Arino, F. Brauer, P. van den Driessche, J. Watmough, and J. Wu, “A model for influenza with vaccination and antiviral treatment,” Journal of Theoretical Biology, vol. 253, no. 1, pp. 118–130, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  50. V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, vol. 125 of Pure and Applied Mathematics: A Series of Monographs and Textbooks, Marcel Dekker, New York, NY, USA, 1989.
  51. L. Perko, Differential Equations and Dynamical Systems, vol. 7 of Texts in Applied Mathematics, Springer, Berlin, Germany, 2000.
  52. A. Korobeinikov and P. K. Maini, “A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence,” Mathematical Biosciences and Engineering. MBE, vol. 1, no. 1, pp. 57–60, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  53. A. Korobeinikov and G. C. Wake, “Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models,” Applied Mathematics Letters, vol. 15, no. 8, pp. 955–960, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  54. I. Barbalat, “Systéme d'équation différentielle d'oscillation nonlinéaires,” Revue Roumaine de Mathématique Pures et Appliquées, vol. 4, pp. 267–270, 1959. View at Google Scholar
  55. C. C. McCluskey, “Lyapunov functions for tuberculosis models with fast and slow progression,” Mathematical Biosciences and Engineering. MBE, vol. 3, no. 4, pp. 603–614, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  56. E. Jung, S. Lenhart, and Z. Feng, “Optimal control of treatments in a two-strain tuberculosis model,” Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, vol. 2, no. 4, pp. 473–482, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  57. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, NY, USA, 1975. View at MathSciNet
  58. D. L. Lukes, Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, vol. 162, Academic Press, New York, NY, USA, 1982.
  59. L. S. Pontryagin, V. T. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchevko, The Mathematical Theory of Optimal Processes, vol. 4, Gordon and Breach Science Publishers, 1985.
  60. G. Magombedze, W. Garira, E. Mwenje, and C. P. Bhunu, “Optimal control for HIV-1 multi-drug therapy,” International Journal of Computer Mathematics, vol. 88, no. 2, pp. 314–340, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  61. M. Fiedler, “Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices,” Czechoslovak Mathematical Journal, vol. 24(99), pp. 392–402, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet