Modern Earth; a series of connected events (natural disasters, mass migration, drug-resistant pandemic, collapse in biodiversity, armed conflict) have led to a significant reduction in human population over a single generation.
Does "civilisation" continue? Societies could certainly adapt to short-term disruptions—but if the complex, global, inter-connected supply chains upon which they currently depend do not recover sufficiently quickly, would they not collapse entirely?
For example, a number of contemporary industries (unfortunately) depend upon oil: not only is most transportation fuelled by petroleum; but most fertilisers, pesticides, pharmaceuticals and plastics are also derived from it. If oil extraction, refinery and distribution were to suddenly cease for a sustained period (before such dependent industries have identified and adapted to alternatives), oil reserves would deplete and those industries themselves could collapse. That in turn could lead to a collapse of further dependent industries, including the manufacture of machines used in virtually any given supply chain.
Do we have any idea how many people are required to keep "it" (the modern industrial world) functioning?
Please give due consideration to the fact that disaster-struck areas may be uninhabitable, with their populations migrating en-masse and seeking refuge in other areas—thereby placing further strains on the system.
There have been some very probing and helpful comments, which have prompted me to spend some considerable time reflecting on exactly what my question is and this edit is an attempt to elaborate. My thanks to all those commenters who contributed to this discussion.
By "significant reduction in human population over a single generation", let's assume the reduction is unforeseen, uniform across all demographics and complete within 10 years. To be clear, it is an "unmitigated apocalypse".
By "maintain the modern industrial world", I meant maintain our current technological capabilities. It strikes me that a good measure of this is the smartphone—it requires mining and refining many minerals, including some that are so rare that viable ore has only been found in a few locations on the planet; even once refined, maufacture of some parts (e.g. 7nm-process semiconductor fabrication) is so specialist that the number of capable facilities can be counted on one hand; even once assembled and distributed, their function depends on an infrastructure of components (antennæ, switches, routers, servers, etc) that themselves require such parts and maintenance thereof. Other yardsticks of technological capability might include space exploration, subatomic research (particle accelerators, quantum computing, etc), artificial intelligence, nanotechnology, ...