What is the meaning of the animal "models" of the Cursed Girls? In black bullet, the initiators are all cursed girls, and every one of them have an "animal model". Tina is an owl model, Enju is a rabbit model, and so on.

Is it just a classification to sum up the abilities? Doesn't seem so, since Yuzuki can spin webs (although maybe they are artificial webs) but definitely Midori's cat ears are not artificial.

The several gastrea are also referred to as animal models (spider, ant, etc). Is there any relation between gastrea and animal DNA in the source material?
The animal model the Cursed Girls is representing, what kind of animal gene the initiator possesses. 
As far as I have understood it by reading the wikia and reading the manga, a gastrea possesses DNA of animals, even though they are actually humans. They got infected with the Gastrea Virus which suddenly appeared around 2021. 
So, based on that I can assume that the animal factor is already inside the virus, even though I can not explain how exactly that happened.

So, to come back to your question, I do think that the model the Civil Security gave the initiator is a classification to sum up their abilities. Like the gastrea the cursed girls have the animal factor of the Gastrea Virus as well. But unlike becoming monsters in animal form, they just have the abilities and sometimes even the look of the animal, which would explain Midori's cat ears.

To read more about the gastrea, you should check out the wikia page about them by clicking right here.

I hope I helped you somehow. :)

Good day.