I know that there's no immune response/adaptation of some (relatively) new viruses like HIV for which it's estimated that it would take at least 32,000 years for humans to develop a non-pathogenic response similar to that that some monkeys have to SIV.
But for more "run of the mill" viruses like new strains of influenza etc., do doses below the minimum infective dose (MID) sometimes act like a vaccine, i.e triggering immune system adaptation that later helps preventing a pathogenic response to a higher dose (above MID)?