The picture gets clearer in the second chapter of the plague storyline, by Pasko, Swan and Springer, in Superman 312 (June 1977).
A recap of the events of the first issue is handled by Morgan Edge, chatting with Sam Tanner, the rival television executive who hired Lola Barnett away from WGBS.
Superman builds a wall around the resort, quarantining those within, and only then discovers that Linda Danvers is at the resort as well. She switches to Sueprgirl, and joins him as he heads to the Justice League satellite to check on the Flash, being tended to by Green Lantern. Hal informs them that a teleportation beam hit the resort just when Nam-Ek vanished, and they follow the trail to the West Indies.
They find Nam-Ek, as well as Amalak, who had come across the immortal Kryptonian floating around in space and joined forces with him. Amalak has let his hair grow out, and sprouted some facial hair as well, which makes him look much creepier than in his earlier appearances.
Superman encases Nam-Ek in crystal, leaving the horn exposed, intending to cure the people infected with the plague. But Amalak has managed to get the drop on Supergirl, temporarily blinding her, and holding her at gunpoint (with a star-cannon that will actually kill her).
Superman leaves, bringing Nam-Ek to the resort as Amalak prepares to kill Supergirl.
The story continues in the next issue.