My family

[theol]

My family has just tested positive for Covid-19.

I wonder if family can mean just a member of my family.

For example, there are five people in my family, but only one tested positive, and the rest are negative.

 

[JillN]

My family has just tested positive for Covid-19.

I wonder if family can mean just a member of my family.

For example, there are five people in my family, but only one tested positive, and the rest are negative.

No. Then you would say "A member of my family/Someone in my family has tested positive."

"My family member has tested positive" is also possible but it doesn't sound as good to me.