productive cough

Reader's Digest 10月号に掲載の広告の一部を引用します。
Treating your COPD and still struggling?
Chronic productive cough?
Repeated antibiotic use for chest infections?
"productive cough" とはどんな咳でしょうか？　"productive" からは生産性を直ぐに連想するのですが。 辞書を見ます。
・Oxford English Dictionary: (medicine)(of a cough) that raises mucus from the respiratory tract.: He had a sick contact with an upper respiratory infection and productive cough for the past two weeks.

・Wiktionary: (medicine) Of a cough, producing mucus or sputum from the respiratory tract.

・online medical dictionary: Producing or forming, said especially of an inflammation that produces new tissue or of a cough that brings forth sputum or mucus.
なるほど、医学用語で痰を伴う咳ですね。