Abstract
We develop and use mathematical models that describe changes in the South African population over the last decades, brought on by HIV and AIDS. We do not model all the phases in HIV progression but rather, we show that a relatively simple model is sufficient to represent the data and allows us to investigate important aspects of HIV infection: firstly, we are able to investigate the effect of awareness on the prevalence of HIV and secondly, it enables us to make a comparison between South Africa and Botswana. A comparison is made between two models: a model that does not reflect awareness of the devastating impact of HIV and AIDS, and a model with an added psychological awareness factor. Both models are fitted to data that reflects the incidence of HIV and AIDS within South Africa. This allows us to examine the impact of psychological awareness. We show that inclusion of the effect of awareness is absolutely necessary to arrive at a model description that satisfactorily fits the available HIV and AIDS data for South Africa. We also show that a relatively simple modelling of awareness (as opposed to more complex mathematical techniques that have been used in past studies) is sufficient to accurately describe the observed patterns in the data. Even though awareness alone is not sufficient to eradicate any disease and other control strategies should be explored and implemented concurrently with educational campaigns, we are able to conclude (through thorough model analyses procedures) that the current level of awareness in South Africa is far below the level that is effectively required to eradicate HIV from the South African population. The awareness model is also fitted to HIV-related data for Botswana and we compare the results with the South African case. Though the effect of awareness is currently estimated at a much higher level in Botswana, other factors such as poorer health care and cultural differences may play a role in limiting the ability of awareness to combat HIV in Botswana.
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References
Baryarama F, Mugisha J, Livingstone S (2006) An HIV/AIDS model with variable force of infection and its application to the epidemic in Uganda. Am J Appl Sci 2(9):1274–1278
Bhunu CP, Mushayabasa S, Kojouharov H, Tchuenche JM (2011) Mathematical analysis of a HIV/AIDS model: Impact of educational programs and abstinence in sub-Saharan Africa. J Math Model Algorithm 10(1):31–55
Centre for Disease Control (2001) Morbidity and Mortality Weekly Report. http://www.cdc.gov/mmwr/pdf/wk/mm5021. 50(1). Accessed 10 April 2012
Chen FH (2004) Rational behavioural response and the transmission of STD’s. Theor Popul Biol 66:307–316
Chen FH (2006) On the transmission of HIV with self-protective behaviour and preferred mixing. Math Biosci 199:141–159
Dennis JE, Schnabel RB (1983) Numerical methods for unconstrained optimization and non-linear equations. Prentice Hall, Englewood Cliffs, NJ
Doctors Without Borders (2009) Top ten humanitarian crises: aid blocked and diseases neglected. http://doctorswithoutborders.org/publications/topten/2009/article.cfm?id=4127. Accessed 25 May 2012
Eaton JW, Johnson LF, Salomon JA, BArnighausen T, Bendavid E, Bershteyn A, Bloom DE, Cambiano V, Fraser C, Hontelez JAC, Humair S, Klein DJ, Long EF, Phillips AN, Pretorius C, Stover J, Wenger EA, Williams BG, Hallett TB (2012) HIV Treatment as Prevention: Systematic Comparison of Mathematical Models of the Potential Impact of Antiretroviral Therapy on HIV Incidence in South Africa, PLoS Med 9(7): e1001245. doi:10.1371/journal.pmed.1001245
Galvani AP, Slatkin M (2003) Evaluating plague and smallpox as historical selective pressures for the CCR5 Delta 32 HIV resistance allele. Proc Natl Acad. doi:10.1073/pnas.2435085100
Ghani AC, Garnett GP (2000) Risks of acquiring and transmitting sexually transmitted diseases in sexual partner networks. Sex Transm Dis 27(10):579–587
Heuveline P (2003) HIV and population dynamics: a general model and maximum-likelihood standards for east Africa. PubMed 40(2):217–45
Hilborn R, Mangel M (1997) The ecological detective—confronting models with data. Princeton University Press, New Jersey
Hussaini N, Winter M, Gumel AB (2011) Qualitative assessment of the role of public health education program on HIV transmission dynamics. Math Med Biol A J IMA 28(3):245–270
Hyman JM, Li JIA (1997) Behaviour changes in SIS STD models with selective mixing. SIAM J. Appl. Math. 57(4):1082–1094
Johnson L, Dorrington R, Bradshaw D, van Wyk V, Rehle T (2009) Sexual behaviour patterns in South Africa and their association with the spread of HIV: insights from a mathematical model. Demogr Res 21(11):289–340
Kassa SM, Ouhinou A (2011) Epidemiological models with prevalence dependent endogenous self-protection measure. Math Bio Sci 229:41–49
Keesman KJ (2011) System identification: an introduction. Springer. pp 61–74
Mathworks documentation R2011b (2011) http://www.mathworks.com/help/toolbox/optim/toolbox/lsqnonlin.html. Accessed 12 Feb 2012
McGregor L (2002) Botswana battles against ‘extinction’. www.gaurdian.co.uk. Accessed 30 Oct 2013
Misra AK, Sharma A, Singh V (2011) Effect of awareness programs in controlling the prevalence of an epidemic with time delay. J Biol Syst 19(2):389–402
Mookodi LG, Ntshebe O, Taylor I (2003) Botswana. http://www2.hu-berlin.de/sexology/IES/botswana.html. Accessed 30 Oct 2013
Morris M, Kretzschmar M (1997) Concurrent partnerships and the spread of HIV. AIDS 11(5):641–648
Mosinger J, Deumie M, Lang KMIV (1999) Infected long-term nonprogressors: epidemiology, mechanisms of delayed progression, and clinical and research implications. Microbes infect 1(13):1113–1120
Mukandavire Z, Garira W (2007) Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals. Theor Popul Biol 72(3):346–365
Mukandavire Z, Garira W, Tchuenche JM (2009) Modelling effects of educational campaigns on HIV/AIDS transmission dynamics. Appl Math Model 33:2084–2095
Simon C, Yosinao N (2011) A mathematical model to distinguish sociological and biological susceptibility factors in disease transmission in the context of H1N1/09 influenza. J Theor Biol 286:50–56
SSA (Statistics South Africa) (2006) Adult mortality (Age 15–64) based on death notification data in South Africa: 1997–2004. Pretoria. http://www.statssa.gov.za/publications/Reports/Report-03-09-052004. Accessed 15 Jan 2012
Tchuenche JM, Bauch CT (2012) Dynamics of an infectious disease where media coverage influences transmission. ISRN Biomathematics. doi:10.5402/2012/581274
UNAIDS/WHO (2008) Report on the global AIDS epidemic. http://www.who.int/hiv/HIVCPBWA. Accessed 25 Jan 2012
Van Groesen E, Molenaar J (2007) Continuum modeling in the physical sciences. SIAM, USA
Verhulst PF (1838) Notice sur la loi que la population suit dans son accroissement. Corr Mat et Phys 10:113–121
Acknowledgements
The authors would like to thank Dr. Hans Stigter, (Biometris, Wageningen University, The Netherlands) for his contributions to certain aspects of the model analyses. We would also like to thank Prof. Dr. Mart de Jong (Quantitative Veterinary Epidemiology Group, Wageningen University, The Netherlands) for his comments on an earlier version of the manuscript.
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Viljoen, T., Spoelstra, J., Hemerik, L. et al. Modelling the Impact of HIV on the Populations of South Africa and Botswana. Acta Biotheor 62, 91–108 (2014). https://doi.org/10.1007/s10441-014-9210-3
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DOI: https://doi.org/10.1007/s10441-014-9210-3