by Bingley
The term plague (pestis) was not used as precisely by Roman writers as it is by medical writers today. It is not certain what the plague was that repeatedly swept across the empire from 251 to 266, carrying off the emperors Hostilian (251), v. Gibbon X.III, Famine and pestilence and Claudius II (268-270), v. Gibbon XI, March. Death of the emperor, who recommends Aurelian for his successor.
St. Cyprian, Tascius Caecilius Cyprianus, who was alive at the time, wrote a treatise about the plague (De Mortalite):
XIV. This trial, that now the bowels, relaxed into a constant flux, discharge the bodily strength; that a fire originated in the marrow ferments into wounds of the fauces; that the intestines are shaken with a continual vomiting; that the eyes are on fire with the injected blood; that in some cases the feet or some parts of the limbs are taken off by the contagion of diseased putrefaction; that from the weakness arising by the maiming and loss of the body, either the gait is enfeebled, or the hearing is obstructed, or the sight darkened;--is profitable as a proof of faith. (IntraText Digital Library)
Unfortunately, this doesn't really give us enough to make any certain diagnosis about what the disease actually was.
Plague in the Ancient World: A Study from Thucydides to Justinian mainly focuses on the Athenian plague described by Thucydides (430 BC) and the plague under Justinian (542 AD), but does has a brief paragraph on this plague.
For more on plagues in antiquity, see N.S. Gill's Ancient Plagues at About.com.