It's not super-dangerous like in Africa, but it's disconcerting. One of Alexine's peccaries was killed a couple years ago. They take all types of intestinal parasites like tapeworms and amoebas and fly larvas that deposit under your skin. They're not harmful though. In terms of people getting sick, the Atlantic forest is disease-free.
Malaria is more prevalent in the Amazon region.
There's bacterial infections from bites and cuts that never heal. That's not common. In the Pantanal and the rainforest, it is quite safe. In the Amazon, you can get anything there. The birdlife of the Pantanal is absolutely breathtaking.