It would depend on the amount of potential the infectious disease has to kill and how clear it was the other person would get infected through his efforts.
Before the infection you would be allowed to potentially kill someone on the way to potentially kill someone else with an infectious disease if there is no other way to prevent him from doing so. (Rambam Hilchos Rotzeach 1:8)
Normally Beis Din would only give the death penalty if the infectious disease was given through lethal injection that had the normal ability to kill and if there were witnesses and warning . Potential to kill or indirect infection would not suffice. After the infection it would have to seem like the person IS (not may) going to die (Sanhedrin 78a-b). It would not have to be instant death though . It would be similar to locking someone into a smoke filled room where they will suffocate to death. (see Sanhedrin 77B and Rambam ibid 3:9)
Even without the death penalty the guy causing the infection would be considered to be a murderer if the victim dies (Rambam Hilchos Rotzeach 2:3) Sanhedrin would have the right to kill such a person and if they don’t he would still be severely punished (ibid 2:4-5)
If the infectious disease only has the potential to kill or the infection was caused indirectly then it would be like sending a rabid dog or poisonous snake at someone. (see Sanhedrin 76B) The Halacha is that the one who sent the snake or rabid dog would not by killed by Beis Din but the goel hadam (redeemer of the blood)would be allowed to kill him (ibid 3:10) The Gemora Sanhedrin 78A explains that the reason sending a snake on someone doesn’t carry the death penalty is because it is only the causing as opposed to directly killing someone.