Optimizing quarantine regions through ellipsoidal geographic networks

• The introduction of ellipsoidal geographical networks along with a mathematical definition of a quarantine.
• An totally unimodular integer programming formulation of an optimal quarantine region.
• Theoretical results classifying feasible and optimal quarantine regions.
• A computational study that shows the negative impact of implementing a heuristic instead of the IP.

Epidemics have killed millions of people throughout history. One of the most common techniques to attempt to contain an epidemic is to quarantine towns or cities. This paper develops a new network class called ellipsoidal geographic networks to properly define a feasible quarantine region. Some properties of optimal quarantines are provided. An integer program, which is totally unimodular, is presented that optimizes the quarantine region. This integer program is shown to outperform heuristical solutions and officials should implement the integer program to identify optimal quarantine regions.