In this paper, a mathematical model of regionalization based on graph theory to investigate the patterns induced by movements of livestock vehicles in cities under outbreaks of highly pathogenic avian influenza (HPAI) is proposed. We then compare the results of simulation from the regionalization model to actual HPAI outbreaks in 2016/2017 to evaluate the validity of the model. Specifically, we (1) configured a complex network structure with analytic tools and properties in graph theory to abstract the paths among farms and livestock facilities; (2) employed statistical methods to estimate the possibility of propagation between two clusters; (3) applied the developed method to an actual HPAI outbreak in Korea in 2016 and conducted a simulation to determine if the proposed modeling for regionalization is an effective prediction measure. The clustered regions proposed by the simulation correctly reflected the regional clustering of actual cases, while simultaneously contain the cities exposed to potential damage when separated. Based on these findings, we conclude that our proposed regionalization model is suitable for making policy judgments to establish a preemptive biosecurity system.

New empirical relations between stellar CaII emission and rotation or age are derived by analyzing Wilson's CaII flux measurements (1968, 1978) of lower main sequence stars, and then we correlate them with their age and rotation rate. It is found that stellar chromospheric emission decays smoothly with age as a star slows down rotationally, establishing that both the emission level and rotation rate decrease with the square root of age.