先進国では虫歯が激減し、自分の歯で一生食べられる人が増えています。

、。

In developed countries, cavities have plummeted, and more and more people can eat with their own teeth their whole lives.

Literal

Developed-countries [at-では] cavities [subject-が] drastically-decrease-[ren'yōkei-stem-し], self [attributive-の] teeth [with/by-で] whole-life can-eat [attributive] people [subject-が] are-increasing-[polite-ています].

Public-health reportage register. 激減 ('drastic decrease') is a compact kango compound; 激減し uses the 連用中止法 (ren'yōkei stem-linking) to connect clauses in a written/formal register. で marks instrument/means on 自分の歯 ('with one's own teeth'). 食べられる is the potential form of 食べる ('can eat'), and the whole relative clause 自分の歯で一生食べられる modifies 人 from the left — a typical case where Japanese packs a long pre-nominal modifier where English would need a relative clause.