Pilate's Head of the Secret Police, Afranius appears usually as "the
man in the hood." He is a master of disguise and deception.
Bulgakov may have found the name in Renan, who writes of the noble Afranius
Burr, Praetorian Prefect of Rome. He was the apostle Paul's jailer, but
treated him humanely (Renan, Antichrist, 4 see Sokolov, 549). According
to Book 14 of Tacitus' Annals,
Afranius may have been poisoned by the emperor Nero:
Burrus died, whether from illness or from poison was a question. It was
supposed to be illness from the fact that from the gradual swelling of his
throat inwardly and the closing up of the passage he ceased to breathe.
Many positively asserted that by Nero's order his throat was smeared with
some poisonous drug under the pretence of the application of a remedy, and
that Burrus, who saw through the crime, when the emperor paid him a visit,
recoiled with horror from his gaze, and merely replied to his question,
"I indeed am well."
(translated by Alfred John Church and William Jackson Brodribb)
The full text is available at the Internet Classics Archive.