^It's not about sustenance, it's about passing the virus to a healthy host.
Actually, that is
about sustenance. Viruses eat, it's just that what they eat is incredibly small (DNA strands). A healthy body will have healthy cells and therefore intact DNA strands. A body with a disease caused by a virus or some degenerative disorder will have unhealthy cells and broken or perverted DNA strands, which to the zombie virus is pretty much the equivalent of spoiled meat. (Actually, not the equivalent. That pretty much is spoiled meat.)
That's a strained analogy. There are a 100 trillion cells in the human body. The worst of illnesses isn't going to make the slightest dent in that.
The most important thing for a virus is that the host is susceptible to it and that they're alive