A non-linear mathematical model is proposed to study the vertical transmission dynamics of HIV/AIDS in a growing population. The population is compartmentalized into four classes namely: susceptibles, infectives, pre-AIDS and AIDS. The model equations are transformed into proportions in order to make more biological meaning. The transformed equations are used for numerical experiments while quantitative analysis is carried out using the original model equations. The existence and stability of the disease-free equilibrium state of the new model equations is analyzed. Through the determination of the steady states solutions, stability analysis and calculation of basic reproduction number, R_0
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