Increasing healthcare index will cause your population to age. People are living longer on average. New births will remain low if you have a high country population. Trying to combat population loss by building more hospitals will only increase the ratio of retirees to working population thus increasing social security payments and having a lower working population to contribute to the economy. The only way to balance the ratio of workers/retirees/children would be to allow population numbers to fall. Keeping all indexes high for the overall welfare index, which keeps birth rates higher. While lowering healthcare to lower the number of retirees.
To answer your question more directly. There is a soft gradual cap to natural population growth. Starting around 200m+ population age group 0-4 will slowly begin to decrease which will eventually cause 4-8 8-12 and 12-15 to also begin to decline. I've yet to figure out how to reverse the trend of declining 0-4 population beyond 200m.