You can make animals immortal in sandbox mode. As someone who has accidentally allowed animals to starve to death, contract diseases, and sustain horrible injuries, let me tell you: it’s heartbreaking. If you play on sandbox mode you can turn all that off. Obviously it’s not realistic, but it might make you happier. And while your human staff members don’t age and die, they do sometimes quit. You can turn that off too, and force them to work for eternity in your immortal, undying zoo.