Infect: the action of giving some thing a disease or illness
Contract: is the action of receiving or getting a disease or illness.
Ex)
After work, the doctor washed his hands so he did not infect anyone else.
The girl had contracted an illness from her sick friend.
就是说Infect是具有主动性，翻译成传染(给别人)比较容易理解。
传染，使感染（疾病，计算机病毒，某种情感）
而Contract具有被动性，就是说（被）感染，传染了（疾病），其实它的名词意思“合同，契约”更常见一些。