Modelling dynamics of HIVand aids in Tanzania: effects of complacency and geographic distribution Mohamed Amour Rashid
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Date
2015
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Publisher
University of Dar es Salaam
Abstract
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.
Description
Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark
(THS EAF RA643.86.T34R37)
Keywords
HIV infections, Aids (Disease), Geographical distribution, Tanzania
Citation
Rashid, M.A. (2015) Modelling dynamics of HIVand aids in Tanzania: effects of complacency and geographic distribution Mohamed Amour Rashid, Doctoral dissertation, University of Dar es Salaam, Dar es Salaam