Darryl’s Analysis

The great thing about Caladiums is they are cyclical growers: their leaves stay nice for a few months (maybe up to a year) then they die off.  The bulbs are stored in a cool, dry place for 2 or 3 weeks, then they can be replanted to grow a new set of leaves (which will eventually die off again, and the cycle continues).

The point is, if one cycle is pest-ridden, I would simply cut off everything and remove as much of the old soil as possible.  Give the bulbs a thorough washing with water, store them as mentioned above and re-start them after 2-3 weeks in new soil.  This would be the fastest and most effective way to eradicate the aphids.

Alternatively, you could try treating it with insecticidal soap (link here) on a regular basis.  I repeat: *treat on a regular basis* – they will not all die in one treatment.  Each time you kill everything you see, there will be a small percentage that aren’t completely killed by the spray or they were missed entirely.  This means you should expect to be treating the plant every few days as you see new aphids emerging.  If you don’t mind these regular treatments, then you could enjoy this round of leaves for the remainder of the season.  I would also be careful about keeping any other plants nearby as the aphids can easily spread to other plants.