A Markov chain model for the analysis of the spread of HIV-AIDS in Dar es Salaam.
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Date
2004
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Publisher
University of Dar es Salaam
Abstract
In this study, we analysed the spread of HIV/AIDS in Dar es Salaam. We were able to estimate the cumulative HIV/AIDS cases in the year 2000 since 1980, also by the end of the 2004 and 2020. The progression of HIV/AIDS was described using six discrete states of disease infection. These states were 1. Un-infected; 2. Infected; 3. Seropositive; 4. Pre-AIDS conditions; 5. Full Blown AIDS; and 6. Death due to AIDS. The matrix approach of Markov chain model was used whereby the transition probabilities per year for all possible transitions were calculated and put in the transition probability matrix. These probabilities were; 0.0033, 1.000, 0.0070, 0.0254, 0.0702, and 0.4727 for transitions of the states 1 - 2, 2 - 3, 3 - 4, 4 - 5, 4 - 6, and 5 - 6 respectively. The analysis obtained the following results; there were 87,137 cases of HIV/AIDS in 2000, 118,804 cases by the end the year 2004. Finally, it was estimated that these cumulative cases of HIV/AIDS would become 349,393 when it reaches the year 2020, if the rate of new infections will remain constant. The reported cases were 16,053 by the end of the 2000. So the results reflect the real situation of reporting HIV/AIDS cases. It is known that only one out of five to six cases in Dar es Salaam or Tanzania in general, is reported to the National AIDS Control Programme (NACP). However, these results should be used with care as a number of parameters in our model need to be measured more accurately.
Description
Keywords
Marcov processes, AIDS (Diseases)
Citation
Rashid, M. A. (2004). A Markov chain model for the analysis of the spread of HIV-AIDS in Dar es Salaam. Masters dissertation, University of Dar es Salaam. Available at (http://41.86.178.3/internetserver3.1.2/detail.aspx?parentpriref=)