Modeling the Transmission and Survival Rate of HIV/AIDS in Ghana

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A comprehensive deterministic HIV/AIDS transmission model incorporating treatment strategies is presented and rigorously analyzed. Two structures of the model are considered with preliminary one consisting of eight differential equations of the state variables and the expanded one also consisting of twenty differential equations involving parameters which determine the transmission rate and treatment HIV/AIDS of the model. A compartment model that tracks the spread of HIV in multiple two-sex populations over time in the presence of limited treatment was investigated. In this study we investigate the effects of treatment and the future spread of HIV in all populations. Treatment simulations shows that when the probability of transmission is high, it is harder to prevent the future spread of HIV, even with treatment .ART-distribution methods are introduce to prevent the largest number of future HIV infections. The model has been fit to represent the HIV epidemic in rural and urban areas in Ghana. With the model, the spread of HIV among urban and rural regions were examined and observed the effects of preferential treatment to rural areas on the spread of HIV in the country as a whole. The researcher investigated the effects of preferentially treating women on the spread of HIV. It was observed that, preferentially treating urban women produces the most dramatic effect in reducing the number of infected male and females in rural and urban areas.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Science in Industrial Mathematics,