随时着人们交往的范围日益扩大，各种传染性疾病有愈演愈烈之势。 英语表达

随时着人们交往的范围日益扩大，各种传染性疾病有愈演愈烈之势 =
Following more frequent (wider) human contacts (interactions), various communicable (infectious) diseases would become more widely spread (serious).

With the expand of interaction between peole, various kinds of diseases are gaining momentumn