Bane and area damage

Hi,
I'm wondering whether bane gains damage from the "increased area damage" mods coming either from the nodes in the passive tree or from support gems.
When I pick a talent with "increase area damage", there's no change in the bane tooltip, and pob doesn't show any change either.
This is weird since bane is supposed to be an aoe spell...
And what about support skills that boost area damage, like intensify?

Could someone please clarify?
Thanks in advance for your replies.

Bane deals damage over time. DoT does not scale with area damage.

https://pathofexile.gamepedia.com/Damage_over_time

Ok, thanks :)

Specifically, it applies a DoT to all things in an area.

Soulrend and Essence Drain work the same.