The screwworm fly, Cochliomyia hominvorax, (Calliphoridae) is a livestock pest and human health hazard that was eradicated from the US, Mexico and Central America to the Panama Canal by the sterile insect release method (SIRM). Sterilized screwworm flies were liberated into the environment from aircraft, thereby inhibiting reproduction of the native screwworm population and causing its eradication. USDA APHIS currently maintains a 300 km wide barrier zone of continuous sterile fly release in eastern Panama to prevent screwworm reintroduction to Central America and the US. A reaction-diffusion model of this barrier zone will be presented. The goal of this model is to investigate how wide the barrier should be to prevent the spread of the fertile screwworm population from the extant side of the barrier to the zone of eradication. An analytical expression for the spatial distribution of sterile flies within the barrier zone will be presented. The spatial distribution of the fertile fly population has been investigated numerically using the method of lines. The model predicts that the screwworm population should expand into an empty environment as a traveling wave. If a sterile fly barrier is erected in front of this traveling wave, the barrier causes the wave to stall when sterile fly density exceeds a threshold value. Analytical predictions of the distance the fertile fly population penetrates into the barrier, the effect of sterile flies on the speed of the traveling wave and approximate formulas for the fertile fly population will also be presented.