Holy shit, that's some bad statistics. I mean you do know that well into the 20th century there were all sorts of nasty illnesses going around that dropped children and the elderly like flies and left survivors with shit like reduced lung capacity, permanent brain damage, sterility, etc? 1-2% a year is after the worst shit like smallpox had regularly used vaccines against it, doctors started doing shit like washing their hands and tools before operating on patients, and cities realized they might need to do something about all that stagnant water and human waste.
Yet somehow we still hit 2 billion people by 1927, and that's with almost 15 years of massive fucking wars, famine, and yes, plagues including Spanish flu and all sorts of other nasty shit all over Europe, Asia, Africa (10% of Africans died in World War I because colonial nations systemically looted food to feed themselves), and parts of Latin America. We hit 1 billion people around 1800 right in the middle of yep, another global war where we had barely any idea what vaccines were and how they worked and common medical knowledge in many parts of the world was hacking people open with dirty tools and letting them bleed.
You seriously overestimate how dangerous this is.