Mass panic in the face of a crisis like a flu pandemic is something of a myth. People do not normally 'contaminate' each other with fear. On very rare occasions, a display of panic can spark a similar reaction in those who witness it - but only when there are extenuating circumstances and, even then, the effect is short-lived.
On the contrary, most people in most disasters think and act with a great deal more wisdom and courage than they, and those around them, might have expected. They rise to the occasion.