Each version of the Gastrea virus is representative of a different type of animal, and that dictates the 'model' of that particular Gastrea. For example, the first human we see succumb to the virus in episode one transforms into a spider, and as such is a spider model:
"The yellow and black spotted pattern of his body would certainy raise a visceral aversion in any human. It was a huge spider.
But the little girl neither ran away, not screamed - she just calmly got ready. Suddenly, she heard a voice coming from out of nowhere.
'Gastrea confirmed - model: spider, stage I. Engaging in battle!'"
Black Bullet Light Novel, Volume 1
As all Initiators are cursed children, by definition they carry a particular strain of the Gastrea virus with it's own animal DNA, providing them with an animal model. While each model is named solely from the animal DNA their version of the Gastrea virus contains, that DNA often affects the abilities of the initiator, providing unique bonus affects alongside the usual cursed children abilities of extreme agility and regeneration. These bonus affects are in line with the animal of their particular model.
- Enju Aihara - Rabbit model:
Much like a rabbit, the majority of her strength is concentrated in her legs, and she fights with mostly kicks.
- Yuzuki Katagiri - Spider model:
She has the ability to release a very thin spider web string from her fingertip, invisible to the naked eye. These webs can stick to several surfaces.
- Tina Sprout - Owl model:
She can see incredibly well, both at long distances and in the dark, shown in both her fight with Rentaro and her assassination attempt on Seitenshi.
- Midori Fuse - Cat model:
Midori has the ability to extend her nails to form prominent claws, which are keen enough to slice though solid objects, including the metal in rifles.
As for Midori's cat ears, this is explained as an unusual reaction where the Gastrea virus affects the host body more readily, causing a partial transformation.