The verb 持续 emphasizes that an action continues uninterrupted and without pauses.
A word that refers to this action or indicates the time of its completion is placed after 持续.
Examples
这场大雨持续下了五天
The rain lasted for five days
zhè cháng dàyǔ chíxù xià le wǔ tiān
死亡人数持续增加
The death toll continues to rise
sǐwáng rénshù chíxù zēngjiā
会谈预料将持续到明天
Negotiations are expected to last until tomorrow
huìtán yùliào jiāng chíxù dào míngtiān
These are collocations often used with 持续:
持续下降 持续发展 持续作用 持续改变
The verb 延续
The verb 延续 also emphasizes that an action continues uninterrupted.
But we often use it with words denoting an abstract concept. For example: dreams, life, traditions.
Examples
中国的历史延续了五千年
The history of China goes back five thousand years
zhōngguó de lìshǐ yánxù le wǔqiān nián
地球上的生命将无法延续,除非人口增长得到控制
Life on Earth will not continue unless population growth is brought under control