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An HIV/AIDS model is formulated with variable force of infection for the adult population. Its actions are reduced to a prevalence equation that is a non-logistic equation whose explicit solution is derived. The implications of applying the solution to the evolution of the HIV/AIDS epidemic are discussed with respect to the positive boundedness of the coefficients. Prevalence projections are presented for various initial prevalences and behavior change parameters. The main finding is that indoi:10.3844/ajassp.2005.1274.1278 fatcat:exoy27enhvfuniykgzqjx3u5eq