The Byzantine pagan historian Zosimus lived in the second half of the fifth century AD. He wrote the 'New History' in Greek, covering the period 295-410 AD.
[AD 409] Meanwhile in Italy, when Alaric neither gained peace on the terms he proposed nor received any hostages, he again attacked Rome and threatened to storm the city if the citizens would not join him against the emperor Honorius. And when they hesitated over his demand, he besieged the city and, going down to the harbour, persisted in the siege for a few days until he finally captured it. Finding all the city's provisions stored there, he threatened to distribute them among his own army unless the Romans promptly did as he ordered. An assembly of the whole senate acceded to all Alaric's demands; for death was inevitable when no provisions could be brought to the city from the port.
Translation: Ridley 1982.