The word 密切 (mìqiè) means "close" or "closely" and describes a tight, attentive relationship or level of involvement. It is frequently used in formal or written Chinese, such as 密切关注 (closely monitor) or 密切合作 (closely cooperate). It conveys a stronger sense of attention than simply using 近.
我们两个部门一直密切合作。
Wǒmen liǎng gè bùmén yìzhí mìqiè hézuò.
Our two departments have always worked closely together.
医生让家属密切观察病人的情况。
Yīshēng ràng jiāshǔ mìqiè guānchá bìngrén de qíngkuàng.
The doctor asked the family to closely monitor the patient's condition.
这件事跟我们的利益密切相关。
Zhè jiàn shì gēn wǒmen de lìyì mìqiè xiāngguān.
This matter is closely related to our interests.