in such 3world country, misuse/overuse of antibiotic are make for development of resistant. then poor sanatation are make for it easy for to spread to other persons. https://wwwnc.cdc.gov/eid/article/5/1/99-0103_article
"Developing Nations" or "Developing World" is better.
"Third world" contributes to exactly the kinds of stereotypes that this comment reinforces — the backwardness of poor countries, where doctors don't know better, science is ignored, etc. It's just not accurate; medical knowledge and competence is on the rise all over the world, among both professionals and volunteers.
i have not in previous heard it "offensive" and am not changing because some person sayes it. i have been to many nation, those i call "third world" are backward. improvement you describe make them moving away from third world, not make term wrong, this is move to second then to first. i will not call different word because somebody say so.