Abstract:

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The negative impact of HIV/AIDS in our society cannot be over-emphasized. Many industries are faced with decrease in manpower leading to low productivity and revenue generation as a result of their staffs being afflicted with HIV related diseases. Hence, developing mathematical models which determine the level at which the virus will pose a risk to humans and at what rate the HIV- infected adults and children finally develop AIDS then die is very crucial. In this research, we extend existing models by applying the concept of inverse probabilities to construct HIV transmission pattern in the past in order to predict future infectious cases. Secondly, Kolmogorov differential equations involving probability generating function is applied to derive the mean and variance of the HIV virus persons infected in a given population. The mathematical models presented in this paper have advantage over existing ones because if the relevant data are available, the models can be used to determine epidemiological parameters such as the expectation and variance of the HIV transmission and its subsequent progression to AIDS. Also, the research identifies what data is needed so that predictions of future infection can be more precise. This will make the relevant agencies to predict HIV/AIDS transmission patterns for many decades ahead and formulate future policies meant to curb the epidemic

Keyward(s): HIV/AIDS, transmission, patients, infection, population.

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