Welcome, and thanks for posting a picture with your question! In my opinion, mold is a primary problem if it is affecting the health of the homes occupants. If occupants are getting crazy allergies and constant colds it may be caused by mold.
However, mold is indicitave of moisture and that can cause serious damage to the house itself. Make sure your attic space has plenty of ventilation at the bottom and top of the attic space. Also, provide adequate thermal insulation in the attic. The ceiling joists are not showing in your picture so you're off to a good start. The insulation should probably be around 12" minimum thickness for most geographical locations. Then, all bath fans and/or kitchen fans must be vented to the outside and not into the attic space.
If you want to combat the mold, spray it lightly with a bleach solution then provide plenty of additional attic ventilation while everything dries. Around here, you can also rent "foggers" that mechanically fog chemicals that kill the mold.
Good luck and hope this advice helps.... Doug