From the looks of it, the movie isn't as far fetched as I had thought, if a doctor could get it (accidentally I'm guessing, but he was a bit too close and over gracious towards the victims).
The doctor was dealing with infected patients. The virus literally makes you bleed out of everywhere / vomit / etc.. Literally, every bit of you is sending out bodily fluids which even will infect you if they even touch your skin. Of course a doctor is going to be infected eventually.