This paper presents models for repeat HIV screening under conditions of con
stant low HIV incidence. The models reveal a direct link between the preval
ence of undetected HIV infection and the screening interval between repeat
HIV tests. We show how to select screening intervals that either achieve a
given HIV prevalence level, or optimally balance the cost of repeat HIV tes
ting against the cost of HIV infection. Alternatively, given an existing re
peat screening program, the model implies that cost of infection for which
the given screening interval is optimal. The method also suggests how to se
lect an HIV testing technology. The models are applied to existing repeat t
esting programs in the U.S. Army and among legal commercial sex workers in
the state of Nevada in the Far West of the United States.