Plagues used to spread to adjacent areas. Occasionally ships would carry it some distance and it would just pop up.
Now with air travel if disease reaches a “civilized” area it spreads by air transport all around the world.
Ebola pops up in African towns with no transport system. So it spreads in the town and then to nearby areas. The airlines canceled flights to the country to prevent it from spreading.
As a biogeographer (who specializes in the distribution of forests not bacteria) my thought is *both*.
That is, a large-scale pattern of expanding territory of most species would be characterized by a gradual wave-like migration with sporadic long-range jumps that inspire waves from those points of colonization.
With plants and animals and such their populations are limited by the environment, their available habitat. With bacteria transmitted by humans the best habitat would be people, so the flu would find good habitat in larger interconnected populations (eg cities).
When you say cold (flu), do you mean rhinovirus and influenza respectively? Rhinovirus mutates at such a quick rate, it’s not something worth tracking unless something wiping people out emerges. As for the flu, they use trending outbreaks in other countries, gather tons of data, and that’s how/why our flu shot is different every year. To protect against what’s been most prevalent. Consider the flu and how it’s spread. It has the capability of inoculating a person from an infected persons droplets, making it easier to spread. So the map of widespread infection will be a mixed bag of adjacent and sporadic areas. Mode of transmission is everything when it comes to tracking outbreaks. When it comes to fecal-oral route, you tend to see outbreaks spread faster in areas where hygiene isn’t the greatest.
[As it happens, the CDC has a map of that!](https://www.cdc.gov/flu/weekly/usmap.htm) You can watch it both rise and fall in swaths across the country.
*Edit:* [Here’s a similar map for Europe.](http://flunewseurope.org/)
*Edit:* Thanks to /u/d_lowl for [this worldwide map](https://nextstrain.org/flu/seasonal) (scroll down).
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