I have never heard that the population growth rate for Iran is falling. CIA has it growing at 1.1% per year which is faster than the US.
Because the birth rate was once so high, statistically Iran may continue to grow for quite some time. But I remember reading somewhere (maybe Spengler) that the current birthrate is about 1.8 children per woman, compared with America's 2.1.
But as I said in an earlier post, I am not sure that a collapsing birthrate necessarily equals reckless national behavior.
They might well have a crisis, but the part where the population is falling like a rock in that 2050 chart is pure speculation.