Prevention is much more effective than treating something after it's already happened.
Literal
Prevention-[one-のほう] [topic-が] matter [subject-が] happen-[after-て] cure-than much effect be.
A longer rewording of the same idea, using ~のほうが ('the side of X is more...') for explicit comparison. 事が起こっての治療 is a nominal phrase: 起こる becomes 起こって with a subordinating て, then の links it to 治療 — 'treatment after something has happened.' ずっと ('by far, much') is a casual-to-neutral intensifier for comparisons.