In an alternate timeline, Ceasar lives, forges an alliance by marriage with Egypt and dominates the entire Mediterranean. He then performs a raft of economic and political reforms that basically skip the dark ages and land the Universal Republic in, socio-politically and even technologically, the early modern period. After 16 years he hands power to a newly elected leader from the plebeian classes whose name is lost to history in our timeline, setting of a chain of peaceful transitions that continue for centuries and even millenia with only minor interruptions.
Back in Caesar's time, the ambitious young Octavian becomes a naval captain and discovers the new world. This is both a product of and a reason for the rise of the the Universal Republic.
Point of my question - to what extent would Roman contact with the new world have the same effect that european contact did after colombus in terms of disease spread?
Would the population still have been decimated (in which case I imagine there would still have been a large settler population from the old world arrive)? Or would they have had a higher survival rate (leading to a situation where it was the exercise of military force and "soft power" that brought them under Roman control).