Adding discrete stacks of velocity instead of a continuous force to move is interesting--I think it actually works for a space game where momentum is conserved in zero-gravity!
It felt pretty easy to dodge all of the kittehs, and even when I hit one it didn't typically spread the disease to anyone else. Perhaps there could be a scaling difficulty or something, where more cats spawn if there are a lot of healthy cats, and some cats die if there's too much plague?