Browsing by Author "Rashid, Mohamed Amour"

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    A Markov chain model for the analysis of the spread of HIV-AIDS in Dar es Salaam.
    (University of Dar es Salaam, 2004) Rashid, Mohamed Amour
    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.
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    Modelling dynamics of HIVand aids in Tanzania: effects of complacency and geographic distribution Mohamed Amour Rashid
    (University of Dar es Salaam, 2015) Rashid, Mohamed Amour
    The dynamics of HIV and AIDS in Tanzania by incorporating the effects of complacency and geographic distribution were studied. Three different models were formulated and analysed. These were the deterministic model on complacency, the stochastic model on complacency, and the role of geographic distribution. The deterministic model was formulated by developing the standard SIR model by incorporating the effects of awareness campaigns on complacency; the stochastic model was formulated using the event-driven approach, while the geographic distribution model was formulated using meta-population approach. Parameter estimation was carried out by implementing a Simple Metropolis Algorithm (SMA). Qualitative analyses showed that the deterministic model possesses both a disease free equilibrium (DFE) and a unique endemic equilibrium (EE) if the basic reproduction ratio R0 > 1. The eigenvalues approach showed that the DFE is locally stable provided that R0 < 1. Further analyses using Routh-Hurwitz criteria showed that the EE is also locally stable. Numerical solutions of the deterministic and the stochastic models on complacency showed that awareness and retention of AIDS cases altogether reduce new HIV infection in the society. The geographic distribution model showed that in addition to awareness and retention, the reduction of sexual contact rates within and between the regions has a significant reduction in new HIV infection in the society. The model also suggests that awareness at regional levels are more effective than on national level. By incorporating awareness campaigns, retention of AIDS cases and reduction of sexual contacts, the models provide useful tools for prediction of sub-populations and control of new HIV infection in Tanzania.