Geometrization of Disease Spread using Dynamic Voronoi Diagram

Abstract

Disease spread has been critical in human history. Abundant approaches exist for spread modeling such as the ordinary differential equation (ODE), stochastic, agent-based models. Agent-based models have attracted attention because they can be better-suited for modeling systems of higher complexity, e.g, the truly global COVID-19 requires a mechanism to accommodate extreme complexity. However, agent-based models have not been sufficiently used because their computational, statistical properties have not been rigorously addressed and often require many parameters to tune and advanced computer programming skills. Here we introduce a novel agent-based model for predicting disease spread using geometrization with dynamic Voronoi diagrams of moving disks. With the dynamic Voronoi diagrams, contacts between agents are correctly and efficiently found and various disease transmission strategies can be modeled. We found the proposed Voronoi-based agent (VoA) method showed experimental properties that were consistent with those of prior works: A simple ODE-model and the COVID-19 spread processes in ten large U.S. metropolitan area. For the COVID-19 spread processes, the population size is upto about 20 million people, which is difficult to model in agent-based models using a geometry approach because of large computational resources. As like recent researches using human mobility data from cell phones, VoA-method used the human mobility represented by origin-to-destination data between census tracts in metropolitan area. Given a preprocessing data, called metacontact data, researchers can efficiently perform diverse experiments with different conditions. We anticipate the VoA-method together with its application program interfaces can be used for easy development of computer program to model any disease spread systems.