An SIA Model of HIV Transmission in Ghana

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In this thesis an SIA compartment model of the transmission dynamics of HIV/AIDS is developed using Ghana Data. The resulting system of three non-linear differential equations was analyzed in respect of stability of the three equilibrium points namely the disease free which was found to be unstable and two endemic equilibrium points which were found to be stable. Further analysis to determine the conditions for the breakout of epidemic were done using the basic reproductive number of the infection. Simulations of solutions of the model in various scenarios were also performed. It was found that the rate of transition from HIV infected to AIDS relative to the rate of transition from susceptible to HIV infected state would need to be increased in order to effectively control the spread of the disease.
A thesis submitted to the School of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the award of the Degree of Master of Philosophy in Mathematics