A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected) with vertical
transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the
world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained
countries are unable to meet the treatment needs of their infected populations. We consider a function
of number of AIDS cases in a community with an inverse relation. A stated theorem with proof
and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0 6 1 and unstable if R0 > 1. Finally, numerical simulations are presented to illustrate the results.