come down with vs shake off

come down with

verb
  • To contract or get (an illness); to show symptoms of. 

  • To lay down (money) in payment; to pay. 

shake off

verb
  • To rid oneself of a malady or its symptoms 

  • Some rumors that the governor had smoked pot as a teenager were flying around, but he has finally managed to shake them off. 

  • To remove (something attached to, on or clinging to an object) by shaking. 

  • To lose someone who is tracking you 

  • To dissociate oneself from (an allegation or rumour). 

How often have the words come down with and shake off occurred in a corpus of books? (source: Google Ngram Viewer )