We know there are a lot of questions regarding your pets and the current situation with the COVID-19 virus.
The AVMA has posted answers to a lot of FAQ and will continue to update their website as more information is available: https://bit.ly/34bXBJg

One FAQ: Can pets spread COVID-19 to people?

It’s important to remember if you’re not ill with COVID-19, you can interact with your animals as you normally would, including feeding and otherwise caring for them. You should continue to practice good hygiene during those interactions. 

Another FAQ: “Are there special precautions I should take for caring for my animal should I become ill with COVID-19?”

There is no reason to remove pets from homes even if COVID-19 has been identified in members of the household, unless there is risk that the pet itself is not able to be cared for appropriately. Those ill with COVID-19 should restrict contact with pets and other animals, just as you would restrict your contact with other people