An outbreak is the sudden occurrence of a disease in a community

Epedemic: is an occurrence of a group of illnesses of similar nature and derived from a common source

These definitions indicate the both the phases of an epedemic disease which begins with and outbreak (a sudden one) and ends in the form of a disease.

According to this I simply suggest this translation:

تفشى فيروس إنفلونزا الطيور في الصين
انتشر فيروس إنفلونزا الطيور في الصين

تفشى.... إلى أن أصبح وباءً