It was by a well-known author. Harlan Ellison, perhaps, or maybe one of Bradbury's darker stories? I remember it being a short story in a collection, but searching the Internet has come up empty thus far.
The story starts when a guy enters a bar and starts talking to bartender about how he's being hauled around the country by some MiB-types against his will. Somehow the Feds found that he, and his entire group of friends, were totally free of all diseases and determined that being exposed to him was the same as immunizations to everything. The MiB are trying to surreptitiously expose him to a wide swath of the general public. Barkeep is skeptical in a "sure buddy" kind of way. As he's trying to convince the barkeep, the MiB show up and whisk him away.
Eventually it's discovered he's actually an asymptomatic carrier, not a cure, and whatever he's carrying first kills of all the viruses and such in a host, then starts killing the host itself. All his old friends are now dead or dying, as are masses of people in a trail of all the places they've been. The agents decide to cut and run with one of them saying he was going to get his wife and kids and just disappear into the wilderness.