Rust on Silvan Blackberrys
First of all, you should ensure that you have correctly diagnosed the disease problem. Blackberry cultivars like Silvan are susceptible to yellow rust (Phragmidium), but also get cane and leaf rust (Kuehneola) and various other leaf fungal diseases (e.g. Septoria cane and leaf spot). You can access typical disease problems of blackberry and see pictures of these various diseases in the PNW Disease Management Handbook (http://pnwhandbooks.org/plantdisease/search/node/blackberry). If in doubt, take a sample to the OSU Extension Office for confirmation/further testing. For cane and leaf rust and Septoria leaf spot, the best control in the home garden is to quickly remove the spent fruiting canes (ones that fruited this season) so that the disease spores do not continue to rain down onto the new primocanes (next years canes). Once you remove the dead or dying floricanes remove them from the planting. Train the new primocanes up by the end of August to improve air flow for the new canes.