I was thinking about creating a thread about this as tips, but i post here anyway.
Pestilence is supposedly dropped at Dark Zones only, the drop rate is very low, but i can personally confirm that it is obtainable in non-occupied (Normalization ON) zones, but i cannot confirm if it applies to ALL 3 zones. I never go to zones when they are occupied, but the drop rate is allegedly higher when the zone is occupied (Normalization OFF). All you have to do is take out any named enemy for the weapon to drop. You dont have to clear Landmarks, as some ppl have hinted that clearing higher level Landmarks will give better chances. I actually got my 3rd Pestilence from busting a DZ Drop, it was kinda surprising because i would not expect named enemies to show up at DZ Drops.
It is pretty worth reminding this again and again, that simply picking up Pestilence is not "done", "over", or "permanent", as it is still contaminated, so you must extract it via Extraction Zone. If you go down for whatever reason while the Pestilence is in your BACKPACK, other players can steal it, same thing for extraction as Rogue players can cut the rope and hijack the weapon. Leaving the Dark Zone will instantly "erase" all contaminated items in your backpack, same thing with Fast Traveling to ANY place.