"Turn off logging. Then you won't see anything in the logs and you can stop worrying and get on with life."
It would be unwise to condone such an idea !
Talk about a "hear no evil, see no evil,speak no evil" approach !
No, I'm not saying spend your life reporting ever single event you see in the logs. But once in a while, you should go through them and report to the relevant ISPs. Just as you would expect, and hope that some kind soul would make a report to your ISP if they found your network appeared to be originating attacks (whether due to viruses or otherwise).