India in fact is part of that steep decline, as you can see in the per-country breakdown. On average the "Middle East & North Africa" has also seen a moderate reduction over the last 50 years, from 2.7 to 1.8, while the "Arab World" has gone from 2.7 to 2.0. The only region with a generally upward trend over that time is "Sub-Saharan Africa", and even that has started to level off.
The reasons for this are fairly well understood, and are covered in this Kurzgesagt video on Overpopulation.
TLDW: disease, war, and famine are not a result of population growth so much as they are a cause. The more people fear their children won't reach adulthood the more children they have. The more developed the country, the more likely children are to reach adulthood, the less children they have. Every country that has undergone significant economic development experiences a (relatively) brief "bubble" in which the older birth rate exceeds the newer death rate before everyone realizes so many children aren't necessary.
Overall Africa is one of the last areas in the world to undergo this normal economic/technological transformation of population growth so they're at the tail end of this cycle. However current data seems to indicate that they're finally moving into Stage 3. So unless something (more) happens to wreck their economy they should start progressing into Stage 4 within a few decades and pretty much all areas of the world will have declining population growth.