Both "alertness to" and "alertness of" are correct, but they are used in different contexts.
"Alertness to" is used to indicate being aware or vigilant about something. For example, "alertness to potential dangers" means being mindful and attentive to possible risks or threats.
"Alertness of" is used to indicate a state or quality of being alert or awake. For example, "She showed great alertness of mind" means she demonstrated sharp mental awareness or attentiveness.