Alex has been staying in the hospital for two days now.------这一句强调他住院已经两天了,并且还可能继续住下去.（现在完成进行时）
Alex has stayed in the hospital for two days.--------这一句只强调到今天为止他住院两天了（现在他仍然住院）,对以后是否继续住院不感兴趣.（现在完成时）
Alex stayed in the hospital for two days.-------这一句告诉我们,他已经离开医院了.