These are the official population projections. My understanding of Africa is not great, but I don't think they're going to get away with this without running into fundamental Malthusian limits at some point.
If they are going to rely on a well-run agricultural economy in Africa to feed all these folks, that relies on political stability, which is historically in short supply in the post-colonial era. With the shifting geopolitical situation, that many desperate young African men, and continuing the historical trends of stability in Africa, agricultural production may be unreliable. A fluctuating malthusian limit produces really ugly scenarios.
With a declining and aging population in the West, increasing transportation and communication ubiquity, a decreasing willingness on the part of civilized people to callously stand by and watch billions of people starve or kill each other, and growing open-borders movements, this phenomenon is unlikely to stay contained in Africa, especially if it gets ugly.
Further, White Westerners are likely to be less and less willing to force their new neighbours to assimilate. Political divides over racism and multiculturalism and such are sure to complicate any effort to cope with the influx. Also relevant is the historical failure of all efforts to fully assimilate Africans in bulk into Western behavioural, cultural, and economic norms, presumably due to certain hard-to-change genetic and cultural factors.
So we might be looking at a billion unassimilated African migrants entering Western societies over the next century, which have a population of approximately a billion. They would become the majority in most cities, especially among the youth.
The influx of Africans into Western societies will likely lead to declining social trust as per Putnam, ethnic conflict, and Whites abandoning the commons as happened in Detroit and South Africa. The rich will retain the ability to live in pleasant gated and rural communities, and otherwise make sure the system stays functional as far as they are concerned.
Beyond that, it is hard to predict how things will go. There are a lot of things that can happen over the next century. Business as usual is the one outcome we can probably disregard.
If this projection is accurate, it is likely to be one of the most significant issues of the next century, and something we will want to know how to navigate for our families and communities. There are a couple general things that are likely to be good preparation:
Wealthier and better-connected people will handle the transition better. It's hard to choose to be wealthier, but we might want to look into that.
Tighter-knit high-trust communities that can retain their form in a low-trust demographic substrate will survive and flourish better than naively trusting boundaryless communities. We should build or join some of these for ourselves.
This is all highly speculative, of course, and maybe I'm being overly pessimistic in this analysis, but stuff like this is in the historical distribution, and thus wise to consider. Our ancestors sacked Rome. And 50000 years before that, as the ice age thawed, our more distant ancestors were unleashed from Africa to overrun the entire world and wipe out and assimilate all previous hominid inhabitants.