Panic won't be a viable option in an influenza outbreak. It won't improve your situation, unlike other emergencies where "fight or flee" response can maybe get a singularly selfish individual an improved position, even if it is at the expense of "women and children first".
In fact, one of the dynamics in play will be the truly affected (Dead, dead loved ones etc) will cut across all socio economic strata- Just as likely Bill Gates as Joe Sixpack will be impacted. Look at the plagues where the grim reaper took its toll across the board- kings and paupers alike.
Even the goblins and preditors in society will be nervous about "jacking me" for fear I may sneeze in their general direction.
This is not to say there won't be panic, it just won't obviously get one ahead as it might in other emergencies.
As far as comparing it to Y2K, well, influenza preparedness doen't have the same momentum behind it precisely because many of the "worst case scenario" doomsayers in the run up to Y2K were enterprise software providers who knew that preparing was synonimus with creating a big budget pie to split up, IMHO.