Optimizing quarantine regions through graph theory and simulation

Abstract

Epidemics have been modeled mathematically as a way to safely understand them. For many of these mathematical models, the underlying assumptions they make provide excellent mathematical results, but are unrealistic for practical use. This research branches out from previous work by providing a model of the spread of infectious diseases and a model of quarantining this disease without the limiting assumptions of previous research. One of the main results of this thesis was the development of a core simulation that rapidly simulates the spread of an epidemic on a contact network. This simulation can be easily adapted to any disease through the adjustment of many parameters. This research provides the first definition for a quarantine cut and an ellipsoidal geographic network. This thesis uses the ellipsoidal geographic network to determine what is, and what is not, a feasible quarantine region. The quarantine cut is a new approach to partitioning quarantined and saved individuals in an optimized way. To achieve an optimal quarantine cut, an integer program was developed. Although this integer program runs in polynomial time, the preparation required to execute this algorithm is unrealistic in a disease outbreak scenario. To provide implementable results, a heuristic and some general theory are provided. In a study, the heuristic performed within 10% of the optimal quarantine cut, which shows that the theory developed in this thesis can be successfully used in a disease outbreak scenario.