During the Great Plague of London of 1665, for example, Defoe wrote “Nothing was to be seen but wagons and carts, with goods, women, servants, children, coaches filled with people of the better sort, and horsemen attending them, and all hurrying away”.
Once the better off city people reach the countryside there will be instant resistance from the host population, not least because they will not want potentially infected people entering their communities.
Meanwhile, the poor people who are left in the cities will run out of food in short order as suppliers refuse to enter the city.
Those who fled London in 1665 had somewhere to go: they were returning to the fields that fed them.
Today, the fields which feed us are largely in other countries, and the ones which are in our own are mainly owned by large corporations.