Abstract and Applied Analysis

A Computational Study of HSV-2 with Poor Treatment Adherence

A. Mhlanga, C. P. Bhunu, and S. Mushayabasa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Herpes simplex virus type 2 (HSV-2) is the most prevalent sexually transmitted disease worldwide, despite the availability of highly effective antiviral treatments. In this paper, a basic mathematical model for the spread of HSV-2 incorporating all the relevant biological details and poor treatment adherence is proposed and analysed. Equilibrium states of the model are determined and their stability has been investigated. The basic model is then extended to incorporate a time dependent intervention strategy. The aim of the control is tied to reducing the rate at which HSV-2 patients in treatment quit therapy before completion. Practically, this control can be implemented through monitoring and counselling all HSV-2 patients in treatment. The Pontryagin’s maximum principle is used to characterize the optimal level of the control, and the resulting optimality system is solved numerically. Overall, the study demonstrates that though time dependent control will be effective on controlling new HSV-2 cases it may not be sustainable for certain time intervals.

Article information

Source
Abstr. Appl. Anal., Volume 2015 (2015), Article ID 850670, 15 pages.

Dates
First available in Project Euclid: 11 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1449867421

Digital Object Identifier
doi:10.1155/2015/850670

Mathematical Reviews number (MathSciNet)
MR3429182

Zentralblatt MATH identifier
1344.92175

Citation

Mhlanga, A.; Bhunu, C. P.; Mushayabasa, S. A Computational Study of HSV-2 with Poor Treatment Adherence. Abstr. Appl. Anal. 2015 (2015), Article ID 850670, 15 pages. doi:10.1155/2015/850670. https://projecteuclid.org/euclid.aaa/1449867421


Export citation

References

  • M. Laga, M. O. Diallo, and A. Buvé, “Interrelationship of sexually transmitted diseases and HIV: where are we now?” AIDS, vol. 8, no. 1, pp. S119–S124, 1994.
  • S. O. Aral and J. N. Wasserheit, “STD-related health care seeking and health service delivery,” in Sexually Transmitted Diseases, K. K. Holmes, P. F. Sparling, P. A. Mardh et al., Eds., pp. 1295–1306, McGraw-Hill, New York, NY, USA, 3rd edition, 1999.
  • S. Kalichman and D. Rompa, “HIV treatment adherence and unprotected sex practices in people receiving antiretroviral therapy,” Sexually Transmitted Infections, vol. 79, no. 1, pp. 59–61, 2003.
  • S. Mushayabasa and C. P. Bhunu, “Modeling the impact of early therapy for latent tuberculosis patients and its optimal control analysis,” The Journal of Biological Physics, vol. 39, no. 4, pp. 723–747, 2013.
  • A. J. Christensen, Patience Adherence to Medical Treatment Regimens: Bridging the Gap between Behavioral Science and Biomedicine, Yale University Press, New Haven, Conn, USA, 2004.
  • P. J. McDonnell and M. R. Jacobs, “Hospital admissions resulting from preventable adverse drug reactions,” Annals of Pharmacotherapy, vol. 36, no. 9, pp. 1331–1336, 2002.
  • B. L. Senst, L. E. Achusim, R. P. Genest et al., “Practical approach to determining costs and frequency of adverse drug events in a health care network,” American Journal of Health-System Pharmacy, vol. 58, no. 12, pp. 1126–1132, 2001.
  • D. Watson-Jones, H. A. Weiss, M. Rusizoka et al., “Risk factors for herpes simplex virus type 2 and HIV among women at high risk in northwestern Tanzania: peparing for an HSV-2 intervention trial,” Journal of Acquired Immune Deficiency Syndromes, vol. 46, no. 5, pp. 631–642, 2007.
  • Z. Feng, Z. Qiu, Z. Sang, C. Lorenzo, and J. Glasser, “Modeling the synergy between HSV-2 and HIV and potential impact of HSV-2 therapy,” Mathematical Biosciences, vol. 245, no. 2, pp. 171–187, 2013.
  • A. P. Fiddian, A. M. Halsos, B. R. Kinge, A. E. Nilsen, and K. Wikstrom, “Oral acyclovir in the treatment of genital herpes. Preliminary report of a multicenter trial,” The American Journal of Medicine, vol. 73, no. 1, pp. 335–337, 1982.
  • C. Celum, R. Levine, M. Weaver, and A. Wald, “Genital herpes and human immunodeficiency virus: double trouble,” Bulletin of the World Health Organization, vol. 82, no. 6, pp. 447–453, 2004.
  • H. B. Bosworth, Improving Patient Treatment Adherence. A Clinician's Guide, Springer, New York, NY, USA, 2010.
  • M. L. Plummer, D. Watson-Jones, S. Lees et al., “A qualitative study of participant adherence in a randomized controlled trial of herpes suppressive therapy for HIV prevention in Tanzania,” AIDS Care: Psychological and Socio-Medical Aspects of AIDS/HIV, vol. 22, no. 4, pp. 499–508, 2010.
  • S. M. Blower, T. C. Porco, and G. Darby, “Predicting and preventing the emergence of antiviral drug resistance in HSV-2,” Nature Medicine, vol. 4, no. 6, pp. 673–678, 1998.
  • A. Mhlanga, C. P. Bhunu, and S. Mushayabasa, “HSV-2 and substance abuse amongst adolescents: insights through mathematical modelling,” Journal of Applied Mathematics, vol. 2014, Article ID 104819, 17 pages, 2014.
  • C. N. Podder and A. B. Gumel, “Transmission dynamics of a two-sex model for herpes simplex virus type-2,” Canadian Applied Mathematics Quarterly, vol. 7, no. 2, pp. 339–386, 2009.
  • S. Blower and P. Volberding, “What can modeling tell us about the threat of antiviral drug resistance?” Current Opinion in Infectious Diseases, vol. 15, no. 6, pp. 609–614, 2002.
  • 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 uncertaintyčommentComment on ref. [16?]: We deleted reference [19] in the original manuscript, which was a repetition of [16?]. Consequently we will replace all the citations of [19] within text with those of [16?]. Please check all highlighted cases throughout.,” Bulletin of Mathematical Biology, vol. 71, no. 3, pp. 720–749, 2009.
  • L. J. Abu-Raddad, A. S. Magaret, C. Celum et al., “Genital herpes has played a more important role than any other sexually transmitted infection in driving HIV prevalence in Africa,” PLoS ONE, vol. 3, no. 5, Article ID e2230, 2008.
  • D. R. Bangsberg, S. Perry, E. D. Charlebois et al., “Non-adherence to highly active antiretroviral therapy predicts progression to AIDS,” AIDS, vol. 15, no. 9, pp. 1181–1183, 2001.
  • C. E. Golin, H. Liu, R. D. Hays et al., “A prospective study of predictors of adherence to combination antiretroviral medication,” Journal of General Internal Medicine, vol. 17, no. 10, pp. 756–765, 2002.
  • 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.
  • R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
  • H. L. Smith and P. Waltman, The Theory of the Chemostat, Cambridge University Press, 1995.
  • H. R. Thieme, “Persistence under relaxed point-dissipativity (with application to an endemic model),” SIAM Journal on Mathematical Analysis, vol. 24, no. 2, pp. 407–435, 1993.
  • J. Li, Y. Yang, and Y. Zhou, “Global stability of an epidemic model with latent stage and vaccination,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2163–2173, 2011.
  • H.-F. Huo and R. Chen, “Stability of an HIV/AIDS treatment model with different stages,” Discrete Dynamics in Nature and Society, vol. 2015, Article ID 630503, 9 pages, 2015.
  • D. R. Powell, J. Fair, R. J. Le Claire, L. M. Moore, and D. Thompson, “Sensitivity analysis of an infectious disease model,” in Proceedings of the International System Dynamics Conference, Boston, Mass, USA, July 2005.
  • L. M. Arriola and J. M. Hyman, “Being sensitive to uncertainty,” Computing in Science and Engineering, vol. 9, no. 2, pp. 10–20, 2007.
  • J. M. Wright, Y. Htun, M. G. Leong, P. Forman, and R. C. Ballard, “Evaluation of the use of calendar blister packaging on patient compliance with STD syndromic treatment regimens,” Sexually Transmitted Diseases, vol. 26, no. 10, pp. 556–563, 1999.
  • K. Beaucage, H. Lachance-Demers, T. T.-T. Ngo et al., “Telephone follow-up of patients receiving antibiotic prescriptions from community pharmacies,” American Journal of Health-System Pharmacy, vol. 63, no. 6, pp. 557–563, 2006.
  • H. Reyes, H. Guiscafre, O. Muñoz, R. Perez-Cuevas, H. Martinez, and G. Gutierrez, “Antibiotic noncompliance and waste in upper respiratory infections and acute diarrhea,” Journal of Clinical Epidemiology, vol. 50, no. 11, pp. 1297–1304, 1997.
  • P. Kardas, “Patient compliance with antibiotic treatment for respiratory tract infections,” Journal of Antimicrobial Chemotherapy, vol. 49, no. 6, pp. 897–903, 2002.
  • H. R. Joshi, “Optimal control of an HIV immunology model,” Optimal control applications and methods, vol. 23, no. 4, pp. 199–213, 2002.
  • D. Kirschner, S. Lenhart, and S. Serbin, “Optimal control of the chemotherapy of HIV,” Journal of Mathematical Biology, vol. 35, no. 7, pp. 775–792, 1997.
  • 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.
  • W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, NY, USA, 1975.
  • M. Reitano, S. Tyring, W. Lang et al., “Valaciclovir for the suppression of recurrent genital herpes simplex virus infection: a large-scale dose range-finding study,” Journal of Infectious Diseases, vol. 178, no. 3, pp. 603–610, 1998.
  • D. Watson-Jones, K. Baisley, M. Rusizoka et al., “Measurement and predictors of adherence in a trial of HSV suppressive therapy in Tanzania,” Contemporary Clinical Trials, vol. 30, no. 6, pp. 504–512, 2009. \endinput