Base of a tree? Welp, yep, you try the soap and smother methods first. But if for whatever reason that fails (user error, soap works if done right) your best bet is a bifenthrin based insecticide. It's something you want to avoid near food gardens and any well /drinking water, but if you use it in isolated instances, it will basically kill a good chunk of pests within inches of spraying for about a week or two.
It's mostly harmless in small amounts, but still carcinogenic IIRC. Some people use diluted bifenthrin as personal bug spray as an alternative to... other... carcinogenic compounds, so yeah, managed risk, use common sense. And I have no idea if it's safe as a bug spray, but I'd imagine the people who do use it, have a pretty nasty situation and are desperate, Places with heavy west nile carriers.
