The seventh century in Byzantine sources is not a well documented period as I'm sure you've gathered. For the reign of Heraclius/Herakleios who was on the throne from 610-641 this is even more true. Our sources for his reign are by Theophanes Confessor, a monk world chronicle written in the ninth century and George of Pisidia, a court poet of Herakleios who at the least is contemporary.

The real source for the Christian side of things comes from pseudo-Sebeos, an Armenian priest who wrote the Chronichon Paschale, or 'Easter Chronicle' which covers the Byzantine-Sassanian war (which brought both empires to ruin). Pseudo-Sebeos does at least talk about the rise of Islam but Armenia is a long way from Arabia.

The bloody early years of Islam as it rampaged through the Eastern Empires draw concern but only really from the Battle of Yarmouk onwards. Sebeos believes this is the end of the world as the Roman state that has stood for over 700 years is overturned and he makes many calls to prophecy that ultimately begin the eschatological movement of many other eighth century sources.