Run down and Sick as a dog

Run down verb - To come upon after searching, study, or effort.

Sick as a dog and run down are semantically related In some cases you can use "Sick as a dog" instead an adjective "Run down".

Run down and sick as a dog are semantically related in sick topic. Sometimes you can use "Run down" instead an adjective phrase "Sick as a dog", if it concerns topics such as not feeling well, not healthy.