Technically, we’re
talking about the
second plague pandemic.
Second bubonic plague outbreak, but there were other pandemics. The first was the
Antonine Plague, believed to be smallpox, which broke out in the late 2nd century. It, with retrospect, ended the golden age to the empire and likely helped precipitate Crisis of the 3rd Century. From then through to the early Medieval, the empire would be rocked by periodic plagues. Each time impacted the state's ability to collect taxes and maintain order.
The first, known as the Justinian Plague, broke out about 541 CE and quickly spread across Asia, North Africa, the Middle East, and Europe. (The Eastern Roman Emperor Justinian I, for whom the pandemic is named, actually survived the disease.)
There was no western Roman emperor at the time, so you can drop the directional indicator. He was augustus and basileus; Roman emperor.
The western imperial office was abolished by emperor Zeno in 476 and the imperial regalia was sent to Constantinople by Odoacer. Theodoric the Great is kind of an iffy case. Emperor Anastasius sent the regalia west with Theo (who dressed like an emperor), and was referred to by Anastasius as an "imperial colleague." He was western emperor-in-all-but-name, but he died in 526. None of his successors had that level of clout with the east.
Note that Belisarius reconquered the city of Rome ~3 years before the plague hit, so you don't even have that awkward "Roman Empire without Rome" aspect you get with most of Byzantine history.