The adjective pervasive means the wide spread of an unwelcome influence to all parts of something.

Synonyms are prevalent, omnipresent, epidemic or universal.

The word origins from Middle French (1580s) persuasif, Medieval Latin persuasivus, Latin persuas-, past participle stem of persuadere meaning “persuade, convince”.

A pervasive bacteria that invades the whole body.

She has a problem pervasive in her mind.

Cigarette smoking is still a pervasive hobby among high school students.