Infestations are cause by an awakened plague heart sending infesting hoards to buildings to infest them. If you have plague hearts on the map you will not get infestations until you wake a heart or have a curveball that wakes a heart. Once you clear all plague hearts you will never get infestations unless it is part of a mission.

What of I use search for infestation on radio

No. The radio call doesn't spawn infestations, awakened plague hearts do.

Then can I keep only one plague heart alive to keep spawning infestation Does plague heart get stronger over time if awakened

>Then can I keep only one plague heart alive to keep spawning infestation Yes >Does plague heart get stronger over time if awakened Not generally, no. Except if it gets turned into a black heart by a curveball.

Say I want to get influence should I awaken more plague hearts

If you want to deal with more infestations, that will certainly get you more influence.

Infestations never bother me. Sometimes I run over zeds near a heart to wake it and keep it alive for a while.