Alien Infiltration (Apocalypse)
Alien Infiltration occurs when the aliens directly deploy alien life forms into buildings. Aliens will then spread through the organization that owns the building and other buildings next to the original one (thus infiltrating other organizations). If left unchecked it will progress as time goes by. When infiltration crosses a threshold (above 50%) the organization may revert to alien control and will turn hostile to X-COM.
It is possible to see the UFO deploying the aliens on Cityscape Screen when using the Isometric Map View) (it hovers above a building and uses a grey tube, as shown in the image).
This alien tactic can be stopped by shooting down the UFOs or by conducting an early search on the building without waiting for the alien alert. It is better to kill the infiltration right at its source before it can spread to nearby buildings, which will be the case if X-COM chooses to wait until alerts are generated.
Alien Subversion
Subversion can turn immediately the organization to the alien's side, depending on luck. It will done by UFOs hovering above a building and dropping a blue 'rain' over its target (again visible with Isometric Map View.
The only way for X-COM to stop this method is to shoot down any UFOs before they are able to finish their actions over the buildings, which implies a quick response time to any UFO incursions. However, since these incursions are made with fast UFOs and the location of the Dimension Gates is changed without notice this can lead to gaps on X-COM's aerial coverage of the city that will limit response times to this attack and allow the UFOs to perform their missions.
Thus, the only permanent solution to these subversion missions is to completely destroy the alien fleet of UFOs at the Alien Dimension.