@tintin,
"distribute themselves" is kind of an awkward way to make the point that the rural doctors cant "be at all places at the same time" (thats another English expression also but less awkward than the one you were given in that sentence) The people are moving out to the country and have settled on plots of land that may be separated from each other by tens of miles, thus making travel inconvenient to the doctors.
Countryside is an ENglish expression for the entire area that is outside the city and suburbs. It is the rural area that , in US can have populations of just a few people per square mile.
Fleeing the urban lifestyle is almost a cliche for moving from the city to the countryside (use the word "countryside" as a collective noun like "city"). We dont really "flee" we choose to leave the city life for the country as a conscious lifestyle decision, not a response to some calamity.
ENglish has a lot of these little phrases, most of us think nothing of the phraqse "fleeing the city", but I suspect that it may imply some kind of panic response when its not. We often over emphasize phrases for dramatic impact . After a while, these kinds of phrases lose favor and then they officially become cliches , and cliches are to be avoided like the plague.