Why is the Amazon permanently on fire?

[Water]

Playing as Inca, the Amazon has been on fire since turn 40, it's now turn 180.

The map keeps showing +/- 1 Food or Production when something burns or stops burning.

Half my cities are engulfed in flames for the majority of the game. Is there any way to stop this?

[Stormwinds]

If there is a contiguous patch of forest or rainforest, the fire will continue to spread. Thus, with a large enough section, the burnt-down portion will have regrown by the time the fire loops back. If you want it to stop, you need to cut the trees down so that the patches are small enough that there aren't enough trees in a contiguous area for the fire to spread to before it runs out.

To simplify, you need to chop the rainforest into smaller groups. The yields from the fires will still stay, so you don't have to worry about that.