these leaders are living proof that prevention works and

that we can manage the health problems that come naturally with age.

骨干：these

leaders are living proof that…and that

同位语从句：that prevention works and that we can manage the health problems。and并排的两个同位语从句。

定语从句：that come naturally with age. 润饰health problems。

翻译：这些领导人就是活生生的根据，证明对疾病的防治是有意义的，证明咱们可以抵挡年纪带来的安康疑问。