Complex sentence: Within the last decade or so, greater attention has been paid to resistant infections in both livestock animals and household pets, and even more recently, to research that demonstrates antibiotic-resistant organisms can be transferred from humans to animals, and vice versa.
Split into simpler sentences: Within the last decade or so, greater attention has been paid to resistant infections in both livestock animals and household pets. Increasing research in the field continues to demonstrate that antibiotic-resistant organisms can be transferred from humans to animals, and vice versa.