I think you can say isolate in this context and it would be well understood. But I think that the most specific word you could go for is "quarantine." "I quarantined my brother because we didn't want to be infected."

You can say isolate and it is correct. You would be understood. However, when we isolate someone specifically to prevent them from giving someone else a disease, we often use the word quarantin. For example, “my brother has to be quarantined until he recovers from measles.” When we want to prevent someone from a disease, we usually say isolate. For example, “my sister has to remain isolated until she finishes chemotherapy, because she gets sick easily.”