From Latin 'influere' (to flow in) — a large-scale inflow of people, capital, or ideas, preserving the image of a stream.
An arrival or entry of large numbers of people or things; an inflow of water into a river, lake, or the sea.
From Late Latin influxus (a flowing in, an inflow), from Latin influere (to flow in, to stream into), composed of in- (into) and fluere (to flow, to stream), from PIE *bhleu- (to swell, to overflow, to well up). The same Latin fluere underlies one of the most productive fluid metaphor clusters in English: fluid (from Latin fluidus), fluent (speaking as if water flows), influence (originally the flowing of astral power down to earth — medieval astrologers believed the stars influenced humanity through invisible streams), affluent (flowing toward wealth), effluent (flowing out as waste), confluence (flowing together), reflux (flowing back), and flux itself. PIE *bhleu- also produced Latin flōs/flōris (flower — a swelling-up of plant growth),
English uses 'influx' almost exclusively for large-scale arrivals — an influx of tourists, an influx of capital, an influx of new ideas. The word carries an implicit sense of volume and force: you would not normally say 'an influx of three people.' The Latin root's connection to flooding and swelling (PIE *bhleu-) may explain