How soon is that gonna be a thing? Asking for my feline overlords…
Just a single data point here - it may not be a serious disease for your overlords.
In March 2020, a family member was ill with COVID-19. The family cat shared a room with him and for several days it was lethargic and unable to jump up on the counter to feed. Back to normal rather quickly.
(However another family member who interacted with cat and not the COVID patient tested positive - asymptomatic.)