Antonym of "exodus"

Consider "influx":

World English Dictionary — n 1. the arrival or entry of many people or things

Though I have not been able to find this anywhere quoted as an antonym, I feel fairly sure the modern word, in current use would be influx.

Oxford Dictionaries provides its literal meaning to do with an inflow of water into a lake, secondary significance. Its first meaning, according to OD is: an arrival or entry of large numbers of people or things. e.g 'a massive influx of tourists'

Its etymology is late 16th century (denoting an inflow of liquid, gas, or light) from Latin influxus, from influere flow in (see INFLUENCE).

Here's a more literal antonym: Exodus, or Exodos, is Greek for exit. So an antonym could be entrance: είσοδος or eisodos.

I've looked up larithmics terms and they refer to it as surges in population

Inrush as in "The inrush of Settlers"

The winning of the West / by Theodore Roosevelt. ... v.4. Roosevelt, Theodore, 1858-1919.