yes, europeans have a very low childhood death rate. But they also have a very long effective childhood. In the middle east it takes less than 20 years for a female to begin producing babies. In europe, more than 30 years.
That’s why demographers use children born per woman, rather than children born per fertile woman; it makes the data trail for decades, but reduces the effect on overall population growth of the age of the mother at childbirth: This way, it doesn’t matter if the woman giving birth is 15 or 40, a woman will still give birth to x number of children in her life. But birth rates in Europe are still statistically depressed by 60-year-old women who never had kids. It also makes it very impressive that fertility rates have plunged so far in North Africa and the Middle East, since such a high proportion of the women in those regions are still fertile.
Yet in much of the middle east there are also horribly debilitating genetic diseases due to inbreeding. This is more among the worse inbreeders like the Saudis and Gulf Arabs but less among north Africans or Iranis or Turks. In the case of Saudis I think something like 10% or more have genetic diseases (no comments on the large numbers with mental problems!! ;0)