Computing Transition Intensity Using Time-Homogeneous Markov Jump Process: Case of South African HIV/AIDS Disposition

This research provides a technical account of
estimating Transition Probability using Time-homogeneous Markov
Jump Process applying by South African HIV/AIDS data from the
Statistics South Africa. It employs Maximum Likelihood Estimator
(MLE) model to explore the possible influence of Transition
Probability of mortality cases in which case the data was based on
actual Statistics South Africa. This was conducted via an integrated
demographic and epidemiological model of South African HIV/AIDS
epidemic. The model was fitted to age-specific HIV prevalence data
and recorded death data using MLE model. Though the previous
model results suggest HIV in South Africa has declined and AIDS
mortality rates have declined since 2002 – 2013, in contrast, our
results differ evidently with the generally accepted HIV models
(Spectrum/EPP and ASSA2008) in South Africa. However, there is
the need for supplementary research to be conducted to enhance the
demographic parameters in the model and as well apply it to each of
the nine (9) provinces of South Africa.


Authors:



References:
[1] S. W. Duffy, N. E. Day, L. Tarbar, H. H. Chen, “Models of breast
tumour progression: Some age-specific results,” Journal of the National
Cancer Institute, vol 22, no. 93, pp. 94-97, 1997.
[2] J. Bergenthum, L. Rüschendorf, “Comparison of semimartingales and
Lévy processes,” Annals of Probability, vol, 35, pp. 228–254, 2007a.
[3] S. Lee, J. Ko, X. Tan,. I. Patel, R. Balkrishnan, J., Chang, “Markov
chain modelling analysis of HIV/AIDS progression: A race-based
forecast in the United States,” Indian J Pharm Sci (serial online), vol 76,
pp. 107-15, 2014. Available
from: http://www.ijpsonline.com/text.asp?2014/76/2/107/131519.
[4] Stats SA Statistics South Africa. Mortality and causes of death in South
Africa, 2010: Findings from death notification. Available:
http://www.statssa.gov.za/publications2/P03093/P030932010.pdf.
Accessed 12 Dec 2013.
[5] R. E. Dorrington, “The ASSA2000 suite of models. Actuarial Society of
South Africa Convention, 2000. Somerset West, South Africa,”
Available: www.assa.org.za/default.asp?id=1000000086, 2004.
Accessed 25 February 2015.
[6] Department of Health. “Concordat and moratorium on genetics and
insurance.” Available online at http://www.dh.gov.uk., 2005. Accessed
January 2015.
[7] R. E. Dorrington, D. Bourne, D.,. Bradshaw, R. Laubscher, I. M
Timæus,. “The impact of HIV/AIDS on adult mortality in South Africa.
Burden of Disease Research Unit, Medical Research Council,”
Available: http://www.mrc.ac.za/bod/complete.pdf, 2001. Accessed 30
July 2012.
[8] R. E. Dorrington, “Alternative South African mid-year estimates, 2013,”
Centre for Actuarial Research. Available:
commerce.uct.ac.za/Research_Units/CARE/Monographs/Monographs/
Mono13.pdf, 2013. Accessed 19 Nov 2013.
[9] Stats SA. “Statistician General’s results launch presentation – Census
2011,” Available: www.
statssa.gov.za/Census2011/Products/SG_Presentation.pdf, 2011.
Accessed January 2015.
[10] O. Shisana, T, Rehle L. C. Simbayi, “South African national HIV
prevalence, incidence, behaviour and communication survey, 2008: A
turning tide among teenagers?” Human Sciences Research Council.
Available: http://www.hsrcpress.ac.za, 2009. Accessed 9 January 2015.
[11] H. Daduna, R. Szekli, “Dependence ordering for Markov processes on
partially ordered spaces,” Journal of Applied Probability, vol 43,
pp.793–814, 2006.
[12] A. S. Macdonald, “Genetics and insurance: What we have learned so
far?” Scandinavian Actuarial Journal, vol 324, no, 348, pp. 27 – 28,
2003b.
[13] A. S. Macdonald, H. R. Waters, and C. T. Wekwete “A model for
coronary heart disease and stroke, with applications to critical illness
insurance underwriting I: The model,” North American Actuarial
Journal, vol 13, no, 40, pp. 40-48, 2005a.
[14] B. Maughan-Brown, A. S. Venkataramani N, Nattrass J. Seekings A.
W. Whiteside, “A cut above the rest: traditional male circumcision and
HIV risk among Xhosa men in 134. Cape Town, South Africa,” Journal
of Acquired Immune Deficiency Syndromes, vol. 58, pp. 499-505, 2011.
[15] F. Nyabadza Z. Mukandavire, S. D. Hove-Musekwa, “Modelling the
HIV/AIDS epidemic trends in South Africa: Insights from a simple
mathematical model. Nonlinear Analysis,” Real World Applications, vol
12, pp. 2091-2104, 2011.
[16] R. S. McClelland, S. M. Graham, B. A. Richardson, “Treatment with
antiretroviral therapy is not associated with increased sexual risk
behavior in Kenyan female sex workers,” AIDS, vol 24, pp. 891-7,
2010.
[17] D. J. McQuoid-Mason, “Is the mass circumcision drive in KwaZulu-
Natal involving neonates and children less than 16 years of age legal?
What should doctors do?” South African Medical Journal, vol 103, pp.
283-4, 2013.
[18] N. McGrath, L. Richter, and M. L. Newell, “Sexual risk after HIV
diagnosis: a comparison of pre-ART individuals with CD4>500 cells/μl
and ART-eligible individuals in a HIV treatment and care programme in
rural KwaZulu-Natal, South Africa,” Journal of the International AIDS
Society, vol 16, pp. 18048- 1809, 2013.
[19] J. McNeil, “A history of official government HIV/AIDS policy in South
Africa,” Available: www.sahistory.org.za/topic/history-officialgovernment-
hivaids-policy-south-africa, 2012. Accessed January 2015.
[20] Actuarial Society of South Africa, “ASSA2008 AIDS and Demographic
Model,” Available: http://aids.actuarialsociety.org.za, 2008. Accessed 5
April 2011.
[21] L. A. Shafer, R. N. Nsubuga, R White,. “Antiretroviral therapy and
sexual behaviour in Uganda: a cohort study,” AIDS, vol, 25, pp. 671-8,
2011.
[22] J. Kimani, R. Kaul N. J. Nagelkerke “Reduced rates of HIV acquisition
during unprotected sex by Kenyan female sex workers predating
population declines in HIV prevalence,” AIDS vol 22, pp. 131-7, 2008.
[23] R. Kaul, C. R. Cohen, D. Chege, “Biological factors that may contribute
to regional and racial disparities in HIV prevalence,” American Journal
of Reproductive Immunology, vol 65, pp. 317-24, 2011.
[24] W, He S. Neil, H. Kulkarni Duffy, “Antigen receptor for chemokines
mediates trans-infection of HIV-1 from red blood cells to target cells and
affects HIV-AIDS susceptibility,” Cell Host and Microbe vol, 4, pp. 52-
62, 2008.
[25] J. Lajoie, J. Hargrove L. S. Zijenah, J. H. Humphrey, B. J. Ward. and M.
Roger, “Genetic variants in nonclassical major histocompatibility
complex class I human leukocyte antigen (HLA)-E and HLA-G
molecules are associated with susceptibility to heterosexual acquisition
of HIV-1,” Journal of Infectious Diseases. Vol, 193, pp. 298-301, 2006.