Mathematical analysis of the effect of screening and vaccination on the dynamics of HIV/AIDS

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University of Dar es Salaam
In this dissertation, deterministic compartmental mathematical models are for- mulated and analyzed to assess the effects of screening and vaccination on thedynamics of HIV/AIDS. In modelling the dynamics of HIV/AIDS, the population is divided into six subclasses of susceptibles, unaware infective, aware infectives. preventive vaccinated population, therapeutic vaccinated population and AIDS population. The model has been analyzed for the existence of disease free and endemic points and their stability. It has been shown that the disease free equi- librium point is asymptotically stable when the effective reproduction number is less than unity and unstable when an effective reproduction number is greater than unity. The threshold quantity for therapeutic vaccination, ηc has been de termined and is shown that the disease can be eradicated in the population when η > ηc The model analysis shows that screening and vaccination, in the form of pre-ventive and therapeutic, have substantial effect on eradication HIV/AIDS. It is noted that endemicity increases in the absence of interventions and reduces after implementing interventions. In order to reduce the spread of disease, preventive vaccination efficacy rate (σ), should be sufficiently large while its waning rate (ϴ) kept at minimal point. Numerical simulations and sensitivity analysis are carried out to support the analytical results and to determine the parameters influencing the dynamics of the disease.
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screening, Mathematical models
Michael, J.(2010) Mathematical analysis of the effect of screening and vaccination on the dynamics of HIV/AIDS. Master dissertation, University of Dar es Salaam. Dar es Salaam.