Summary paragraph
The epidemiological transition from young to old deaths in high-income countries reduced mortality at all ages, but a major role was played by a decline of infant and child mortality from infectious diseases1,2 that greatly increased life expectancy at birth2,3. Over time, declines in infectious disease continue but chronic and degenerative causes persist4,5, so we might expect under-5 deaths to be concentrated in the first month of life. However, little is known about the age-pattern of this transition in early mortality or its potential limits. Here we first describe the limit using detailed data on Denmark, Japan, France, and the USA— developed countries with low under-5 mortality. The limiting pattern of under-5 deaths concentrates in the first month, but is surprisingly dispersed over later ages: we call this the early rectangularization of mortality. Then we examine the progress towards this limit of 31 developing countries from sub-Saharan Africa (SSA)—the region with the highest under-5 mortality6. In these countries, we find that early deaths have large age-heterogeneities; and that the age patterns of death is an important marker of progress in the mortality transition at early ages. But a negative association between national income and under-5 mortality levels, confirmed here, does not help explain reductions in child mortality during the transition.