Police patrols should be entirely proactive otherwise they are responses instead of patrols. The only point of police patrols is to have a moving and visible presence in the community.
I assure you mathematicians aren't optimizing the "visbile presence in the community". That's not something you need a mathematician for. Mathematicians are optimizing the ability of police to maximize the number of arrests by deciding which areas they should patrol in order to maximize crime.
How, is this your line of work?