A simple subset of an epidemic population model for HIV-AIDS can be split into the following: Susceptible, HIV-Infected, AIDS-infected, and Removed subsets (SHAR). We consider that the rate at which susceptible people become infected is proportional to the number of encounters between susceptible and infected individuals, which is proportional to the product of the two populations. A non-linear model is developed and its solution is produced with an Excel numerical approach using difference

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... tions. Some solutions also are produced using MAPLE (CAS). Further research analysis, refining the model and qualitative analysis is the goal of this research.