how can we model the distribution of the population from a facility to other near facilities (for example a school or a hospital) when it is decided to be destroyed
Once you have the addresses of the members of the original facility (which is to be closed) use geocoding in ARCGIS or other mapping software to obtain the locations of people's residences. Then you can do Thiessen polygon or some other such allocation method to see how the people will be apportioned to other open facilities.