It would take ~5000 years at the current annual rate of animal cases to match the number of human cases just 40 years ago.
That's The Great Pyramid of Giza ago time... PLUS the amount of time since Michelangelo, Leonardo da Vinci, and Raphael roamed the earth.
The cool thing is that at a few hundred, one could theoretically* round up all (known) animal cases left. That's truly incredible work getting to this point if you think about it.
* Yes, geopolitical issues, geography, and plenty of other reasons might make this somewhat impossible... but the fact that we can actively picture a few hundred animals in our brains means that it's a very attainable goal.