Starting to see some disinformation in here.
Ich, even if it is not present, is not always in the system. This is a myth that a thread over in the "Fish Disease Treatment" forum has debunked.
UV can be effective in killing off ich. However, there are certain flow rates that have to be run through the UV unit as the amount of contact a certain organism is in with UV determines if it will kill it. I believe ich requires one of the longest contact times.
There are three stages of ich:
1. Obviously when YOU first notice it in the system as the white spots (yes, I know out of chronological order, sue me). This is the parasite in the host that is boring out of the fish to reprodude.
2. When the fish goes to sleep, the ich parasite exits the body (the white dots you see) in the area the fish sleeps in. So, even if the fish appears to be fine because most fish return to the same spot to sleep, ich will reinfect them. (Ich is active at night.)
3. The free-swimming ich. This is the stage where ich can spread to other fish and infect the entire system.
The above is not 100% correct on everything or in the way that it occurs, but this is the general life cycle of ich.
To completely destroy ich you would have to remove EVERY fish from the system and let it go fishless for a minimum of two months as this is the life cycle of ich with no host.
If there is a fish in the system, ich can infect it and it can be a carrier to spread to other fish. Even if the fish shows NO signs of infection, assume ich is still present.
The only way to make sure no ich sees the DT is proper QT, inspection, and treatment of new fish before introduction into the DT.
HTH (and ich experts correct anything I messed up or post a link please).