Abstract: In this study, we studied the Susceptible-Exposed-Infectious-Aids, (SEIA) Epidemic model for vertical transmission of HIV/AIDS, along the line of Michael et al. assumptions with other additional considerations and employed the Routh-Hurwitz stability conditions and the threshold parameter, to examine the equilibrium states, (disease-freeequilibrium, DFE and the endemic equilibrium, EE states,). The threshold conditions for the stability of the disease-fee equilibrium and endemic equilibrium states are obtained and the Biological interpretations are also provided.