It is accurate to call Attila a truly formidable foe.
While the west was having issues, the impact on the east by the great migrations had so far, been comparatively miniscule. Beyond the migration, revolt, settlement, and revolt again of the Tervingi and Greuthungi (plus smaller groups) in the course of 375-401, the East was still in an advantageous position. The Sassanids were distracted with a large group of Huns (the Kidarites, and later the Hepthaltites who weren't actually Huns but I digress) on their northeast border, the economic centers of Syria and Egypt were untouched, and their major recruiting grounds in Thrace, Syria, and Isauria (as well as Dalmatia, after they gained much of that region and Pannonia from the west probably in 437/438) were intact.
If we do a simple estimate of the Notitia Dignitatum, an incomplete registrar of units that for the Eastern half dates to and was updated over the course of 398-405 AD, we'll find that the military strength of the empire in the Balkans numbered about 71,232 Comitatenses and 46,400 Limitanei along the Danube from the border of Noricum up to Novae (Shvishtov) in Moesia Secunda, plus the Limitanei in Scythia Minor. Granted, this is on paper, but unit strengths in the East were fairly high, and we know the Notitia Dignitatum is extremely accurate for the East (despite the missing sections) due to studies of extensive documentary evidence from late antique Egypt.
The eastern administration was very much prepared for Attila the Hun. And he wiped the floor with them.
Attila had a big advantage over Rome's opponents before him: he had brought an organized state with him into Europe. Unlike the Sarmatians and Alans, the Huns had a real organized government, taken from their Xiongnu predecessors (whether or not they were directly related doesn't matter, but there current scholarship tends to agree there was some sort of relationship). They weren't just a loose confederation, but a tightly organized one with excellent political and diplomatic strategy utilizing intermarriage and taking advantage of the natural size limitations of a clan-based society to create a regimented, decimally organized army. They also had a vassal-lord relationship probably similar to the Wei Chinese and the Persian models of feudalism and may have even introduced it to Europe, leading to the development of medieval feudalism.
After renegotiating the Treaty of Margus in 439, Attila ended up attacking the East over what was in all probability a border dispute from the acquisition of Pannonia mentioned above. We know Aetius in about 440 negotiated with him and recognized his authority over "the lands along the River Sava", this being part of modern day Serbia the Romans called Pannonia Secunda, and included the former capital and military stronghold of Sirmium (Sremska Mitrovica). The problem was in 438, Valentinian III had probably gifted these lands to Theodosius II, as authority over Illyricum had always been contested, although we know from Priscus in 448 that Pannonia Prima, Pannonia Sava, and both of the provinces of Noricum were under Roman control, so the lines drawn seem to have been along Pannonia Valeria, Pannonia Secunda, and Dalmatia. All provinces exposed to the Huns and their Germanic vassals and difficult to defend for the West. Naturally this would have caused a dispute over who controlled these regions, in this case Pannonia Secunda in particular, and Sirmium was a rather juicy political target to sack for Attila. So despite the story of the Bishop of Margus allowing the looting Hunnic tombs for treasure (which was, in fact, a rampant issue that Theodosius II passed a law against and probably on Attila's list of grievances), this seems to have been a cover for Attila's real aim, which was to force the empire vacate the middle Danubian limes. This also shows just how politically and diplomatically adept Attila really was; he wasn't some lumbering barbarian warlord, but as Priscus points out he really was a rather shrewd and intelligent man.
In 441 Attila crossed at Constantia near Viminacium (Kastolacz), and then followed the Roman road through Margus, Singidunum, Bassianae, and Sirmium. At this time, the Roman armies were away in Sicily, preparing for a massive expedition against the Vandals in Africa, so the Balkans was completely exposed. He razed Viminacium to the ground, a tactic famously employed by the Mongols (and the Romans) as well to keep their large army moving with rapidity. By razing one fortress, it persuaded others to surrender quickly and be spared, which made it a highly effective form of psychological warfare and compensated for a technologically and administratively limited logistical supply chain. Margus surrendered without a fight and its Bishop was spared. Singidunum and Sirmium, however, were fortified military centers and did not surrender, so Attila razed them too.
In 442 the Roman army returned to the Balkans after negotiating a treaty with Gaiseric in response to Attila's invasion, leaving Aetius and the west on their own with the situation in North Africa (while the west had a field army, it was tied up in Gaul and they didn't have the extra resources to spare mounting a campaign to Africa barring what they could scrape out of the reassigned Italian forces). Attila suspended campaigning for the year, and sent diplomats to negotiate a truce demanding the exchange of fugitives and the payment of back-owed tribute. However, it seems to have failed, and in 443 he responded by attacking and destroying the arms manufacturing center at Ratiaria (Archar) and then razing Naissus (Nis), both apparently before the Roman army could respond. In 443, Theodosius II capitulated and negotiated a a new treaty, vacating Pannonia and probably conceding to a doubling of the tribute to 1400 pounds of gold annually, as well as the rest of the terms of the Treaty of Margus.
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