The presence of carriers usually complicates the dynamics and prevention of a disease. They are not recognized as disease cases themselves unless they are screened and they usually spread the infection without them being aware. We argue that this has been one of the major causes of the spread of human immunodeficiency virus (HIV). We propose, in this paper, a model for the heterogeneous transmission of HIV/acquired immunodeficiency syndrome in the presence of disease carriers. The model allows us to assess the role of screening, as an intervention program that can slow the epidemic. A threshold value ψ*, for the screening rate is obtained. It is shown numerically that if 80% or more of the carrier population is screened, the epidemic can be contained. The qualitative analysis is done in terms of the model reproduction number R. The model has two equilibria, the disease free equilibrium and a unique endemic equilibrium. The disease free equilibrium is globally stable of R < 1 and the endemic equilibrium is is locally stable for R > 1. A detailed discussion of the model reproduction number is given and numerical simulations are done to show the role of some of the important model parameters.