Population density probably has more to do with how common rats are. They seem to be plentiful enough in most big cities.

Pretty sure first world cat catching initiatives increase the rat populations.

Not sure if being in a poor country would make them bigger.

Seem to get big enough in well off Sweden

https://www.bbc.com/news/world-europe-26764929

https://www.dailymail.co.uk/news/article-5869015/Swedish-town-told-doors-windows-closed-plague-GIANT-RATS-size-cats.html