continue with / keep with the medicine

continue with / keep with the medicine
阅读里面的一篇文章,大意是医生看过病人的病之后让他继续吃原来的药
Everything is going as it should do.
Just ____ with the medicine I gave you last time.
有两个选项：A.continue B.keep
为什么是continue
有什么用法吗,谢谢