  The interference model has been widely used and studied in block experiments
where the treatment for a particular plot has effects on its neighbor plots. In
this paper, we study optimal circular designs for the proportional interference
model, in which the neighbor effects of a treatment are proportional to its
direct effect. Kiefer's equivalence theorems for estimating both the direct and
total treatment effects are developed with respect to the criteria of A, D, E
and T. Parallel studies are carried out for the undirectional model, where the
neighbor effects do not depend on whether they are from the left or right.
Moreover, the connection between optimal designs for the directional and
undiretional models is built. Importantly, one can easily develop a computer
program for finding optimal designs based on these theorems.
