The important thing is to keep the dead canes well pruned out, as the cane borer is one of the worst insect pests.
"Three Acres and Liberty" by Bolton Hall
I never was troubled with the currant worm cane borer.
"Trees, Fruits and Flowers of Minnesota, 1916" by Various
For borers, cut out and burn the affected canes.
"The Practical Garden-Book" by C. E. Hunn