Some people are too busy to go to the hospital, so they just have to rely on getting their prescriptions refilled.
この場合、次のような言い方ができます。
ーSome people are too busy to go to the hospital, so they just have to rely on getting their prescriptions refilled.
「ある人は忙しすぎて病院に行けないので処方薬を再補充してもらうことに頼らなければいけない」
too busy to go to the hospital で「忙しすぎて病院に行けない」
to rely on で「頼る」
to get one's prescriptions refilled で「処方薬を再補充してもらう」
ご参考まで！
カナダ 
