Answer :

The swift population rise in the last 2,000 years was caused by an increase in disease immunity. With the increase of vaccinations that prevent disease, the death rate has gone down with the average age of death going up.

I believe the answer is: increase in food supply and disease immunity.

Prior to 2000 years ago, society experience massive shortage in food supply which cause a lot of people died due to hunger which always keep the population low.

The fact that there is no vaccine also contribute to the low population because it cause a lot of death for infants and children before they grow up.