adj

• (immunology) Involving the contraction of a disease by a person with a decreased susceptibility, such as a person who has been vaccinated to help prevent that disease.
  "Breakthrough infections (urine infections that develop in children on antibiotics) can occasionally occur, and if they do, different preventative antibiotics can be given or sometimes surgery to fix the leaky valve can be undertaken."

noun

• (military) An advance through and past enemy lines.
• (sports) The penetration of the opposition's defence.
  "But with the lively Dos Santos pulling the strings behind strikers Pavlyuchenko and Defoe, Spurs controlled the first half without finding the breakthrough their dominance deserved."
• (construction) The penetration of a separating wall or the remaining distance to an adjacent hollow (a crosscut in mining) or between two parts of a tunnel build from both ends; knockthrough.
• (medicine, sometimes attributive) The emergence or one or more symptoms of a condition despite medication or other medical treatment.
  "She was on two antiepileptics for five years but then had a breakthrough seizure."