The fall of the Roman empire is a pretty big topic, both in itself and in the sheer volume of writing that has been dedicated to it for the past... oh, 250 years.

My own take on the subject can be found here in some posts I wrote last year that I still mostly agree with.

I should note though that although everything under the sun has been forwarded as a possible explanation for the fall of Rome at some point or other, neither "internal corruption" or "declining birth rates" is considered to be much of an explanation by any of the historians I've read. (Any recent and credible ones at least.)

Whether the population in the Roman world declined at all is surprisingly difficult to tell due to the limited surviving evidence, and the figures vary heavily from place to place. (What's true for Roman Britain might not be true for Roman North Africa or Roman Syria, and vice versa.) But if the population did decline, the causes were things like plagues, climate change, and the upheaval caused by war. There's no evidence that any birth rates declined.

As for internal corruption: the Romans had plenty of it. But they had plenty of it during the Republic, during the early empire, during the late empire, and whilst the west was falling apart it didn't seem to have had any more corruption than in earlier periods. That makes it of limited value as an explanatory factor.

As for drawing parallels to the modern day western world: Well, that is forbidden according to the rules of this sub. (No discussions about stuff less than 20 years old, no speculation.)

But even if it were not, it is not a very good idea. The Roman world was very different from our own. Sure, Americans in particular like to draw parallels between themselves and the Romans, and if we read authors like Cicero or Lucianus of Samosata we might discover some thoughts and phrases that seem startlingly familiar and applicable to our current lives. But then we flip the page and encounter attitudes we can scarcely credit. To name an example: Slaves were only allowed to testify in court if they had been tortured first, since it was believed they would always lie if you didn't. The Romans were not like us.

Their political situation was also very different. They had a vast empire where it took weeks to send messages from one end to another and they had no technology more advanced than a watermill. They lived in a world where the Roman empire was the only form of government anyone could conceive of, including the "barbarians" who ended up taking over, but where armed coups and civil wars happened several times in each generation, where sources of legitimacy for emperors were hazily defined, and where the throne could end up being occupied by children for decades on end whilst generals fought amongst themselves over who could control them. These are not the kinds of problems our modern world is likely to face.