A.T. Robertson Commentary Mark 1:36

"And Simon and they that were with him followed after him;" — Mark 1:36 (ASV)

Followed after him (κατεδιωξεν αυτον). Hunted him out (Moffatt). Perfective use of the preposition κατα (down to the finish). The verb διωκω is used for the hunt or chase, pursuit. Vulgate has persecutus est. The personal story of Peter comes in here. "Simon's intention at least was good; the Master seemed to be losing precious opportunities and must be brought back" (Swete). Peter and those with him kept up the search till they found him. The message that they brought would surely bring Jesus back to Peter's house.