I don't like sounding like an alarmist but the single strands you describe could very well be spider mites. They don't form webs like a tradition spider does. You can have strands of them here and there and not notice them.
They do form a small veil looking webs in key locations on the leaves - usually at junctures were the leaf stems form from the main stems or in the small part of the leaf say at the base where they all start out from.
The mite can be red, brownish, clear - newborns, or even black when dead.
Take a close look at the underside of the leaves - If they have small areas where looks kind of like off-white stuff in strange looking patches - not like ovals, but irregular.
If you see those they are more than likely the eggs.
If you happen to have spider mites, take it seriously, but don't spray the crap out of it with all kinds of mite killer (everything I've used burns the plants if mixed too strong or if they have to keep getting sprayed week after week).
There are many ways to get rid of them - Most ways don't kill the eggs so they keep coming back and become resistant to pestisides - It's like they are laughing at you by then. Try and avoid burning the plants - That's real easy to do with all the stuff on the market except releasing the bugs that eat spider mites - Real hard to do outdoors.
I used damn near everything - Ed Rosenthal's Zero Tollerance, Liquid Lady Bug (very expensive) Bang to help restore spider mite damage, Safer Soap, 2 Spider Mite fogger's done 5 days apart and a bunch of Live Lady Bugs.
After 7 months of that bull crap I got "No Spider Mites" It cost a lot like Liquid Lady Bug, but No Spider Mites kills the eggs too. I mixed as directed (shake a lot) and after two treatments within 6 days they have left the house garden! Thank God!