Research article Special Issues

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

The effect of the needle exchange program on the spread of some sexually transmitted diseases

1 Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., H-6720 Szeged, Hungary
2 Department of Mathematics, Institute of Environmental Engineering Systems, Szent István University, Páter Károly utca 1., H-2100 Gödöllõ, Hungary

Special Issues: Differential Equations in Mathematical Biology

## Abstract    Full Text(HTML)    Figure/Table    Related pages

In this paper we consider a model for the spread of a sexually transmitted disease considering sexual transmission and spread via infected needles among intravenous drug users. Besides the transmission among drug users, we also consider sexual contacts between intravenous drug users and non-drug users. Furthermore, the needles are considered as a vector population. For several European countries, a sharp increase of sexually transmitted diseases was reported and several others are rated as endangered based on the number of syringes given out per intravenous drug users per year. The main purpose of the paper is to investigate the dynamics of this model including the effect of needle exchange and study the risk of an increased transmission among non-drug users, induced by the reduction of the needle exchange program. Following the determination of the basic reproduction number $\mathcal{R}_0$ it is shown that all solutions tend to the unique disease-free equilibrium if $\mathcal{R}_0$ < 1. We also prove that the disease persists in the human population if $\mathcal{R}_0$ > 1. Our numerical simulations, based on real life and hypothetical data for HIV, suggest that a decrease in the rate of the distribution and discharge rate of new needles might imply that the considered disease is becoming endemic in the considered human population of drug users and non-drug users. A variant of our model with time- variable needle distribition parameter is fitted to recent HIV data from Hungary to give a forecast for the number of infected in the following years.
Figure/Table
Supplementary
Article Metrics

Citation: Eliza Bánhegyi, Attila Dénes, János Karsai, László Székely. The effect of the needle exchange program on the spread of some sexually transmitted diseases. Mathematical Biosciences and Engineering, 2019, 16(5): 4506-4525. doi: 10.3934/mbe.2019225

References

• 1. W. Atkinson, J. Hamborsky, L. McIntyre, et al., Hepatitis B, in: J. E. Bennett, R. Dolin, M. J. Blaser (Eds.), Epidemiology and prevention of vaccine-preventable diseases (The Pink Book), pp. 211–234. Public Health Foundation, Washington DC, 2009.
• 2. N. Scherbaum, B. T. Baune, R. Mikolajczyk, et al., Prevalence and risk factors of syphilis infection among drug addicts, BMC Infect. Dis. 5 (2005), 6.
• 3. Centers for Disease Control and Prevention, HIV Basics, available at: https://www.cdc.gov/hiv/basics/index.html.
• 4. N. Loimer, R. Schmid and A. Springer (eds), Drug addiction and AIDS, Springer, 1991.
• 5. A. J. Saxon, D. A. Calsyn, S. Whittaker, et al., Sexual behaviors of intravenous drug users in treatment, J. Acquir. Immune Defic. Syndr., 4 (1991), 938–944.
• 6. Y. Yao, K. Smith, J. Chu, et al., Sexual behavior and risks for HIV infection and transmission among male injecting drug users in Yunnan, China, Int. J. Infect. Dis., 13 (2009), 154-–161.
• 7. D. Hedrich, E. Kalamara, O. Sfetcu, et al., Human immunodeficiency virus among people who inject drugs: Is risk increasing in Europe?, Euro Surveill., 48 (2013).
• 8. S. Mushayabasa and C. P. Bhunu, Hepatitis C virus and intravenous drug misuse: a modeling approach, Int. J. Biomath., 7 (2014), 22 pp.
• 9. C. P. Bhunu and S. Mushayabasa, Assessing the effects of intravenous drug use on Hepatitis C transmission dynamics, J. Biol. Syst., 19 (2011), 447–460.
• 10. J. Gani, Needle sharing infections among heterogeneous IVDUS, Monatsh. Math., 135 (2002), 25–36.
• 11. Y. Ji, S. Kumar and S. Sethi, Needle exchange for controlling HIV spread under endogenous infectivity, INFOR Inf. Syst. Oper. Res., 55 (2017), 93–117.
• 12. E. H. Kaplan and R. Heimer, HIV prevalence among intravenous drug users: model-based estimates from New Haven's legal needle exchange, J. Acquir. Immune Defic. Syndr., (1992), 163–169.
• 13. E. H. Kaplan and E. O'Keefe, Let the needles do the talking! Evaluating the New Haven needle exchange, Interfaces, 23 (1993), 7–26.
• 14. E. H. Kaplan and R. Heimer, A model based estimate of HIV infectivity via needle sharing, J. Acquir. Immune Defic. Syndr., 5 (1992), 1116–1118.
• 15. D. Greenhalgh and W. Al-Fwzan, An improved optimistic three stage model for the spread of HIV amongst injecting intravenous drug users, Discrete Contin. Dyn. Syst., Supplement 2009, 286–299.
• 16. D. Greenhalgh and F. Lewis, The general mixing of addicts and needles in a variable-infectivity needle-sharing environment, J. Math. Biol., 44 (2002), 561–598.
• 17. F. Lewis and D. Greenhalgh, Three stage AIDS incubation period: a worst case scenario using addict–needle interaction assumptions, Math. Biosci., 169 (2001), 53–87.
• 18. E. H. Kaplan, Needles that kill: modeling human immunodeficiency virus transmission via shared drug injection equipment in shooting galleries, Rev. Infect. Dis., 11 (1989), 289–298.
• 19. R. F. Baggaley, M-C. Boily, R. G. White, et al., Risk of HIV-1 transmission for parental exposure and blood transfusion: a systematic review and meta-analysis, AIDS, 20 (2006), 805–812.
• 20. Centers for Disease Control and Prevention, HIV in the United States, 2017, available from: https://www.cdc.gov/hiv/statistics/overview/ataglance.html.
• 21. Centers for Disease Control and Prevention, HIV risk behaviors. Estimated per-act probability of acquiring HIV from an infected source, by exposure act, available from: https://www.cdc.gov/hiv/risk/estimates/riskbehaviors.html
• 22. O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7 (2010), 873–885.
• 23. L. Farina and S. Rinaldi, Positive linear systems. Theory and applications, John Wiley AND Sons, 2000.
• 24. Hungarian AIDS foundation, HIV/AIDS statistics for Hungary (in Hungarian), available from: http://www.aidsinfo.hu/statisztika_magyar_t.
• 25. Hungarian National Focal Point, Facts and figures about the needle exchange programs, available from: http://drogfokuszpont.hu/szakteruleteink/artalomcsokkentes/artalomcsokkentes-tenyek-es-szamok/?lang=en
• 26. J. P. LaSalle, Stability by Liapunov's direct method, with applications, Mathematics in Science and Engineering, Academic Press, New York, 1961.
• 27. Z. Shuai and P. van den Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM J. Appl. Math., 73 (2013), 1513–1532.
• 28. H. Smith, An introduction to delay differential equations with applications to the life sciences, Springer, New York, 2011.
• 29. H. L. Smith and H. R. Thieme, Dynamical systems and population persistence, Graduate Studies in Mathematics, Vol. 118, AMS, Providence, 2011.
• 30. Hungarian National Focal Point, 2018 National Report to the EMCDDA by the Reitox National Focal Point, available from: http://drogfokuszpont.hu/wp-content/uploads/HU_EMCDDA_jelentes_HUNGARY_2018_EN.pdf