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A nonlinear multi-population behavioral model to assess the roles of education campaigns, random supply of aids, and delayed ART treatment in HIV/AIDS epidemics

Department of Mathematical Sciences, Georgia Southern University, 65 Georgia Ave, Room 3309, Statesboro, Georgia, 30460, USA

Special Issues: HIV/AIDS: epidemiology, immunology and control

The successful reduction in prevalence rates of HIV in many countries is attributed to control measures such as information and education campaigns (IEC), antiretroviral therapy (ART), and national, multinational and multilateral support providing official developmental assistance (ODAs) to combat HIV. However, control of HIV epidemics can be interrupted by limited random supply of ODAs, high poverty rates and low living standards. This study presents a stochastic HIV/AIDS model with treatment assessing the roles of IEC, the supply of ODAs and early treatment in HIV epidemics. The supply of ODAs is assessed via the availability of medical and financial resources leading more people to get tested and begin early ART. The basic reproduction number ($\mathfrak{R}_{0}$) for the dynamics is obtained, and other results for HIV control are obtained by conducting stability analysis for the stochastic SITRZ disease dynamics. Moreover, the model is applied to Uganda HIV/AIDS data, wherein linear regression is applied to predict the $\mathfrak{R}_{0}$ over time, and to determine the importance of ART treatment in the dynamics.
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Keywords HIV/AIDS education campaigns; supply of HIV/AIDS aids; basic reproduction number; stochastic stability; linear regression; delayed ART treatment

Citation: Divine Wanduku. A nonlinear multi-population behavioral model to assess the roles of education campaigns, random supply of aids, and delayed ART treatment in HIV/AIDS epidemics. Mathematical Biosciences and Engineering, 2020, 17(6): 6791-6837. doi: 10.3934/mbe.2020354


  • 1. CDC, About HIV, 2020. Available from: https://www.cdc.gov/hiv/basics/whatishiv.html.
  • 2. WHO, HIV/AIDS, 2020. Available from: https://www.who.int/news-room/fact-sheets/detail/hivaids.
  • 3. S. D. Lawn, M. E. Török, R. Wood, Optimum time to start antiretroviral therapy during hiv-associated opportunistic infections, Curr. Opin. Infect. Dis., 24 (2011), 34-42.
  • 4. H. Joshi, S. Lenhart, K. Albright, K. Gipson, Modeling the effect of information campaigns on the hiv epidemic in uganda, Math. Biosci. Eng., 5 (2008), 757-770.
  • 5. S. Singh, J. E. Darroch, A. Bankole, A, b and c in uganda: the roles of abstinence, monogamy and condom use in hiv decline, Reprod. Health Matters, 12 (2004), 129-135.    
  • 6. E. C. Green, D. T. Halperin, V. Nantulya, J. A. Hogle, Uganda's hiv prevention success: the role of sexual behavior change and the national response, AIDS Behav., 10 (2006), 335-346.
  • 7. Z. Mukandavire, W. Garira, J. Tchuenche, Modelling effects of public health educational campaigns on hiv/aids transmission dynamics, Appl. Math. Model., 33 (2009), 2084-2095.
  • 8. S. Del Valle, E. A. Morales, M. C. Velasco, C. M. Kribs-Zaleta, S. H. Schmitz, Effects of education, vaccination and treatment on hiv transmission in homosexuals with genetic heterogeneity, Math. Biosci., 187 (2004), 111-133.
  • 9. The Global Fund, 2020. Available from: https://www.theglobalfund.org/en/.
  • 10. Presidendent's Emergency Plan for AIDS Relief, 2020. Available from: https://www.hiv.gov/federal-response/pepfar-global-aids/pepfar.
  • 11. P. Nunnenkamp, H. Öhler, Throwing foreign aid at hiv/aids in developing countries: Missing the target?, World Dev., 39 (2011), 1704-1723.
  • 12. J. N. Fobil, I. N. Soyiri, An assessment of government policy response to hiv/aids in ghana, SAHARA J J. Soc. Asp. H., 3 (2006), 457-465.
  • 13. Cuts in foreign aid for HIV place millions at risk, October 2017. Available from: https://www.healio.com/news/infectious-disease/20171010/cuts-in-foreign-aid-for-hiv-placemillions-at-risk.
  • 14. R. P. Walensky, E. D. Borre, L. Bekker, E. P. Hyle, G. S. Gonsalves, R. Wood, et. al., Do less harm: evaluating hiv programmatic alternatives in response to cutbacks in foreign aid, Ann. Intern. Med., 167 (2017), 618-629.
  • 15. ILOAIDS, ILO programme on HIV/AIDS and the World of Work, HIV/AIDS and poverty: the critical connection, Brief October 2005, Available from: www.ilo.org/aids.
  • 16. M. Munoz-Laboy, N. Severson, S. Bannan, Occupations, social vulnerability and HIV/STI risk: The case of bisexual Latino men in the New York City metropolitan area, Glob. Public Health, 9 (2014), 1167-1183.
  • 17. S. Gillespie, S. Kadiyala, R. Greener, Is poverty or wealth driving HIV transmission?, Glob. Public Health, 21 (2007), S5-S16.
  • 18. H. Huo, R. Chen, X. Wang, Modelling and stability of hiv/aids epidemic model with treatment, Appl. Math. Model., 40 (2016), 6550-6559.
  • 19. H. Liu, J. Zhang, Dynamics of two time delays differential equation model to hiv latent infection, Phys. A., 514 (2019), 384-395.
  • 20. D. Wanduku, B. Oluyede, Some asymptotic properties of SEIRS models with nonlinear incidence and random delays, Nonlinear Anal. Model., 25 (2020), 461-481.
  • 21. S. Ma, H. Huo, Global dynamics for a multi-group alcoholism model with public health education and alcoholism age, Math. Biosci. Eng., 16 (2019), 1683-1708.
  • 22. A. Kumar, P. K. Srivastava, Y. Takeuchi, Modeling the role of information and limited optimal treatment on disease prevalence, J. Theoret. Biol., 414 (2017), 103-119.
  • 23. S. Okware, J. Kinsman, S. Onyango, A. Opio, P. Kaggwa, Revisiting the ABC strategy: HIV prevention in Uganda in the era of antiretroviral therapy, Postgrad Med. J., 81 (2005), 625-628.
  • 24. CDC, HIV, PrEP, 2020. Available from: https://www.cdc.gov/hiv/basics/prep.html.
  • 25. WHO, HIV/AIDS, Pre-exposure prophylaxis, 2020. Available from: https://www.who.int/hiv/topics/prep/en/.
  • 26. WHO, WHO Expands Recommendation on Oral Pre-exposure Prophylaxis of HIV Infection (PrEP), Policy Brief, WHO reference number: WHO/HIV/2015.48, 1-2.
  • 27. D. Wanduku, The stochastic extinction and stability conditions for nonlinear malaria epidemics, Math. Biosci. Eng., 16 (2019), 3771-3806.
  • 28. D. Wanduku, Modeling highly handom dynamical infectious systems, in Applied Mathematical Analysis: Theory, Methods, and Applications, Springer, 2020, 509-578.
  • 29. D. Wanduku, Threshold conditions for a family of epidemic dynamic models for malaria with distributed delays in a non-random environment, Int. J. Biomath., 11 (2018), 1850085.
  • 30. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
  • 31. A. Korobeinikov, P. K. Maini, Non-linear incidence and stability of infectious disease models, Math. Med. Biol., 22 (2005), 113-128.
  • 32. Symptoms of HIV, How can you tell if you have HIV?, 2020. Available from: https://www.hiv.gov/hiv-basics/overview/about-hiv-and-aids/symptoms-of-hiv.
  • 33. D. Wanduku, Complete global analysis of a two-scale network sirs epidemic dynamic model with distributed delay and random perturbations, Appl. Math. Comput., 294 (2017), 49-76.
  • 34. D. Wanduku, G. Ladde, Fundamental properties of a two-scale network stochastic human epidemic dynamic model, Neural Parallel Sci. Comput., 19 (2011), 229-270.
  • 35. UNAIDS, AIDSinfo, 2020. Available from: http://aidsinfo.unaids.org/.
  • 36. World Data Atlas, Demograhics for Uganda, 2020. Available from: https://knoema.com/atlas/uganda/death-rate.
  • 37. UNAIDS, Making Condoms Work for HIV Prevention, Cutting-edge Perspectives, UNAIDS Best Practice Collection, 2004.
  • 38. M. Dorrucci, P. Pezzotti, B. Grisorio, C. Minardi, S. Muro, V. Vullo, et al., Time to discontinuation of the first highly active antiretroviral therapy regimen: a comparison between protease inhibitorand non-nucleoside reverse transcriptase inhibitor-containing regimens, AIDS, 15 (2001), 1733-1736.
  • 39. A. Monforte, A. Lepri, G. Rezza, P. Pezzotti, A. Antinori, A. Phillips, et al., Insights into the reasons for discontinuation of the first highly active antiretroviral therapy (HAART) regimen in a cohort of antiretroviral naive patients, AIDS, 14 (1999), 499-507.
  • 40. A. Monforte, L. Testa, F. Adorni, E. Chiesa, T. Bini, G. Moscatelli, et al., Clinical outcome and predictive factors of failure of highly active antiretroviral therapy in antiretroviral-experienced patients in advanced stages of HIV-1 infection, AIDS, 12 (1999), 1631-1637.
  • 41. Uganda National Antiretroviral Treatment and Care Guidelines for Adults, Adolescents and Children, Ministry of Health, Kampala, Uganda, 2nd edition, 2008. Available from: http://www.who.int/hiv/amds/uganda moh treatment guidelines.pdf.
  • 42. I. Kasamba, K. Baisley, B. N. Mayanja, D. Maher, H. Grosskurth, The impact of antiretroviral treatment on mortality trends of HIV-positive adults in rural Uganda: a longitudinal populationbased study, 1999-2009, Trop. Med. Int. Health, 17 (2012), e66-e73.
  • 43. T. S. Torres, S. W. Cardoso, L. S. Velasque, V. G. Veloso and B. Grinsztejna, Incidence rate of modifying or discontinuing first combined antiretroviral therapy regimen due to toxicity during the first year of treatment stratified by age, Braz. J. Infect. Dis., 18 (2014), 34-41.
  • 44. L. N. Azevedo, R. Arraes de Alencar Ximenes, P. Monteiro, U. R. Montarroyos, M. Democrito de Barros, Factors associated to modification of first-line antiretroviral therapy due to adverse events in people living with HIV/AIDS, Braz. J. Infect. Dis., 24 (2020), 65-72.
  • 45. S. Patrikar, G. C. S. Shankar, B. A. Kotwal, D. R. Basannar, C. V. Bhatti, B. R. Verma, et al., Predictors of first line antiretroviral therapy failure and burden of second line antiretroviral therapy, Med. J. Armed Forces India, 73 (2017), 5-11.
  • 46. E. J. Allen, Environmental variability and mean-reverting processes, Discret. Contin. Dynam. syst., 21 (2016), 2073-2089.
  • 47. E. J. Allen, L. Allen, A. Arciniega, P. Greenwood, Construction of equivalent stochastic differential equation models, Stoch. Anal. Appl., 26 (2008), 274-297.
  • 48. D. Wanduku, The stationary distribution and stochastic persistence for a class of disease models: Case study of malaria, Int. J. Biomath., 13 (2020), 2050024.


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