Estimation of the first arrival time on the epidemic disease transmission network

Abstract

In this study, we propose a method to estimate the first infection arrival time of each node in an infectious disease network, which is a crucial indicator for disease control in the context of inter-regional transmission of infectious diseases. Unlike previous research, our approach accounts for variations in the basic reproduction number($R_0$) across different regions within the infectious disease network. We develop a recursive algorithm that utilizes a probabilistic aggregation of numerous infection pathways, significantly reducing the computational complexity. By applying our methodology, we estimate the time of first infection arrival for the network of 17 cities in South Korea and the network of 25 major Asian countries. We define the average first arrival time as an epidemic distance, which serves as a metric for representing the spatial relationships and their implications for disease control between cities or countries. Furthermore, we demonstrate the potential applications of our methodology, including the epidemic maps and epidemic control districts. We anticipate that our research will contribute to more efficient decision-making in implementing disease control policies in future infectious disease outbreaks.