Fewer people these days believe in the efficacy of vaccinations against infectious diseases.
More people have started to doubt the immunity of vaccinations against infectious diseases.
この場合、次のような言い方ができますよ。
ーFewer people these days believe in the efficacy of vaccinations against infectious diseases.
「最近感染症に対するワクチンの効き目を信じる人が少なくなってきている」
efficacy of vaccinations で「ワクチンの効き目」
ーMore people have started to doubt the immunity of vaccinations against infectious diseases.
「感染症に対するワクチンの免疫性を疑い始めた人が増えてきている」
immunity of vaccinations で「ワクチンの免疫性」
ご参考まで!