{"title":"Computing Transition Intensity Using Time-Homogeneous Markov Jump Process: Case of South African HIV\/AIDS Disposition","authors":"A. Bayaga","volume":110,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":37,"pagesEnd":42,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10003500","abstract":"
This research provides a technical account of
\r\nestimating Transition Probability using Time-homogeneous Markov
\r\nJump Process applying by South African HIV\/AIDS data from the
\r\nStatistics South Africa. It employs Maximum Likelihood Estimator
\r\n(MLE) model to explore the possible influence of Transition
\r\nProbability of mortality cases in which case the data was based on
\r\nactual Statistics South Africa. This was conducted via an integrated
\r\ndemographic and epidemiological model of South African HIV\/AIDS
\r\nepidemic. The model was fitted to age-specific HIV prevalence data
\r\nand recorded death data using MLE model. Though the previous
\r\nmodel results suggest HIV in South Africa has declined and AIDS
\r\nmortality rates have declined since 2002 – 2013, in contrast, our
\r\nresults differ evidently with the generally accepted HIV models
\r\n(Spectrum\/EPP and ASSA2008) in South Africa. However, there is
\r\nthe need for supplementary research to be conducted to enhance the
\r\ndemographic parameters in the model and as well apply it to each of
\r\nthe nine (9) provinces of South Africa.<\/p>\r\n","references":"[1] S. W. Duffy, N. E. Day, L. Tarbar, H. H. Chen, \u201cModels of breast\r\ntumour progression: Some age-specific results,\u201d Journal of the National\r\nCancer Institute, vol 22, no. 93, pp. 94-97, 1997.\r\n[2] J. Bergenthum, L. R\u00fcschendorf, \u201cComparison of semimartingales and\r\nL\u00e9vy processes,\u201d Annals of Probability, vol, 35, pp. 228\u2013254, 2007a.\r\n[3] S. Lee, J. Ko, X. Tan,. I. Patel, R. Balkrishnan, J., Chang, \u201cMarkov\r\nchain modelling analysis of HIV\/AIDS progression: A race-based\r\nforecast in the United States,\u201d Indian J Pharm Sci (serial online), vol 76,\r\npp. 107-15, 2014. Available\r\nfrom: http:\/\/www.ijpsonline.com\/text.asp?2014\/76\/2\/107\/131519.\r\n[4] Stats SA Statistics South Africa. Mortality and causes of death in South\r\nAfrica, 2010: Findings from death notification. 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