Can you give the coronavirus to your pet? Can your pet give it to you?

Yes, a tiger at the Bronx Zoo tested positive for the novel coronavirus. And yes, a cat in Belgium had traces of the virus’s genome in its stool and vomit.

But to be perfectly clear: There is no evidence that pets can spread COVID-19 to people. One study, from a veterinary diagnostic lab, tested thousands of samples from dogs and cats, and found no cases of the disease. And an early version of a report on a small experiment testing whether the virus could spread between cats found that it can—but it does not suggest that cats are an important vector in spreading disease among humans. With more than 1.4 million cases of COVID-19 globally, experts say that if pets were a significant vector, we’d know by now.

“This is almost exclusively a human-to-human transmitted disease,” Michael San Filippo, a spokesman for the American Veterinary Medicine Association, told NBC affiliates. “The risk to pets is very low, with only a handful of cases of the virus appearing in companion animals, and no cases of people getting sick from their pets.”

There is a small chance that a sick person could give the virus to certain animals. We now know tigers (and probably lions) are susceptible to it, and cats and dogs as well. But the number of reported human-to-animal cases is very small. Still, to be extra safe, if you’ve been diagnosed with COVID-19, experts say you should restrict your contact with pets and other animals, just as you should with people.

At least until we know more. Scientists are rushing to figure out what other species the virus might be able to infect, but there are so many factors to consider, it’ll be awhile before we know for sure.

In the meantime, washing your hands before and after interacting with a pet—same as you would with a fellow human—is the safest thing to do.