We seek to discuss how the transmission of HIV infection, and hence AIDS disease, depends on various biological and social factors, which may be different within and between the different population groups. In this paper 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 locally asymptotically stable and two endemic equilibrium points which were found to be 96 Stephen Eduafo et al. stable. Further analysis to determine the conditions for the breakout of epidemic were done using the basic reproductive number of the infection. 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.
We use SIR model to predict the prevalence and incidence of Hepatitis B in Bosomtwe District of Ghana. The study is made up of two sections. An SIR model without vaccination is used to explain the spread of the HBV in the Bosomtwe district followed by the modeling HB with vaccination in the district. 3344 Isaac Kwasi Adu et al. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium states respectively. The stability condition of each equilibrium point is discussed. The basic reproductive number () of HB without vaccination is estimated to be 1.006 and the basic reproductive number () of HB with vaccination is estimated to be 0.9840. Our work shows that, the proportion of the population of Bosomtwe district that needs to be vaccinated in order to control HBV in the district is 871. According to the results of this study, whenever the transmission rate parameter value is increased, but when the transmission rate parameter value is reduced,. A combination of increased vaccination of newborns and immunization of susceptible adults appears to reduce HB prevalence in Bosomtwe District to the minimum.
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