The real fact is that regardless of disease, natural disasters, wars and famine, human population has never stopped growing.
And your demonstration of this "real fact" is?
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Humans, like other animals, cannot outgrow their food supply. For the population to expand, we had to develop methods to increase our supply of food --- either colonization of new lands such as Australia, or better methods of hunting and fishing, or agriculture, or pest control, or ... etc.
Long periods of cultural stasis would have corresponded to long periods of stasis in population.