A contagious disease can be caught by touching someone who has the disease or by touching an infected object, or by an infected person coughing, sneezing, etc. near you:
The infection is highly contagious, so don't let anyone else use your towel.
There were fears the contagious disease could wipe out livestock over a wide area.
A contagious person has a disease that they can pass to other people:
Keep him out of school until he's not contagious anymore.
The patient is most contagious for the first 3 weeks from their earliest symptom.
A contagious feeling spreads quickly among people:
Fear is contagious.
His presence was warm and his wit was contagious.