As you can gather from other answers already given here:
- Your "virus" wouldn't be a biological construct;
- It would be orders of magnitude smaller than a proper virus.
I should mention then something called a strangelet. Now there is a lot of physics to this beast, but TL;DR:
- This is a thing made of quarks, just like protons and neutrons;
- Protons and neutrons are nuclear matter. Strangelets, on the other hand, are strange matter (particle physicists come up with the best terms ever);
- A strangelet should be at least as big as an atom, but here's the cool thing: if the current model for them is right, they grow like katamaris!
From the wiki:
If the strange matter hypothesis is correct and its surface tension is larger than the aforementioned critical value, then a larger strangelet would be more stable than a smaller one. One speculation that has resulted from the idea is that a strangelet coming into contact with a lump of ordinary matter could convert the ordinary matter to strange matter. This "ice-nine"-like disaster scenario is as follows: one strangelet hits a nucleus, catalyzing its immediate conversion to strange matter. This liberates energy, producing a larger, more stable strangelet, which in turn hits another nucleus, catalyzing its conversion to strange matter. In the end, all the nuclei of all the atoms of Earth are converted, and Earth is reduced to a hot, large lump of strange matter.
What I could not find anywhere is the rate at which a strangelet would grow and convert nuclear matter.
Since this is all hypothetical and you are going into sci-fi, you could use strangelets for inspiration. It goes like this: someone touches a strangelet somehow, and now their body is slowly but surely coming apart. Let's say that it would take ten years for the whole body of an adult to be converted into a strangelet... This is so slow, that the body may somehow "excrete" or otherwise get rid of part of the strangelets, and rebuild some parts of it somehow... But the person would be afflicted by symptoms not unlike those of cancer/acute radiation syndrome and leprosy, with the body destroying itself from inside out.
As a bonus: a strangelet will affect any nuclear matter, not just living matter... So your patients would have a more extreme version of the midas touch. Anything that comes in contact with them, even the very air they breath, is doomed to slow destruction. Just imagine. Someone afflicted with strangeletitis sets foot on a planet. That planet may last for millenia or even millions of years, but everything in it will be converted to plasma as the eons pass as surely as two plus two equals four.
This also makes this "disease" the most contagious thing in the universe. It is the very matter of the cosmos that is getting sick. The only way to prevent spread is throwing whatever planet is showing any case of this into a black hole.