Lively American relative's dangerous illness (9)

I believe the answer is:

pertussis

I'm a little stuck... Click here to teach me more about this clue!

'dangerous illness' is the definition.
'pertussis' can be an answer for 'illness' (pertussis is a kind of illness). I'm not certain of the 'dangerous' bit.

'lively american relative's' is the wordplay.
'lively' becomes 'pert' (I've seen this in another clue).
'american' becomes 'US' (abbreviation for United States).
'relative' becomes 'sis' (short for sister).
'pert'+'us'+'sis'='PERTUSSIS'

Can you help me to learn more?

(Another definition for pertussis that I've seen is " Whooping cough".)

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