For one thing, I don't know that a virus that would be lethal to a human would affect a half-saiyan. But... who knows?

For a second, yeah, there are contrivable scenarios that could work against him, no doubt, buuuuuuut the same can be said, and even more so, for many, many other heroes. In addition, Trunks isn't a DC/Marvel superhero. He doesn't hang out fighting petty crime, doesn't listen to the police radio to find things to stop, doesn't know other people around who would call him up and ask for help. He would probably ONLY get involved in something city-threatening or bigger: he simply wouldn't know about other stuff going on. Teenage Gohan, he of Great Saiyaman dance-party fame, would be another story: he actively pursued the superhero game.

I mean, maybe Trunks would eventually get involved like that, but it wouldn't be automatic for him. And if he DID get involved like that, it would take time and be a process, and Trunks, pragmatic and realistic as he is, would surely learn about the threats that exist for that kind of life. He'd almost surely take the time to track down a Batman, a Superman, a Wonder Woman, a Captain America, a Spider Man, and ask them how this thing works. And they would certainly say "cool, we welcome the help, especially someone as badass as you, by the way, there are some sick f&*ks around, so pay attention to your surroundings and don't shake disease-ridden hands."

Well, Batman likely would not do that, but the others, definitely.