Move the medical bay-equipped ship to the planet with the plague. It will cure the plague if the lvl of the component is higher than or equal to the plague level.
Feel glad that plague random events are all lvl 1 and none of the AI AFAIK use plague bombs.
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"What do -you- want?" "I'd like to live -just- long enough to be there when they cut off your head and stick it on a pike as a warning to the next ten generations that some favors come with too high a price. I would look up into your lifeless eyes and wave like this..." *waggle* "...can you and your associates arrange that for me, Mr. Morden?"