The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (Appl. Math. Comput. 236:184–194, 2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.

Mesoscale Spatial Variability of Linear Trend of Precipitation Statistics in Korean Peninsula

This study analyzed the spatial variability of the linear trend of the precipitation mean, variance, lag-1 autocorrelation coefficient, and probability of dryness (PD) based on the precipitation data between 1981 and 2015 observed at 65 rain gages located across Korean Peninsula. While the result of the Mann-Kendall test based on the yearly statistics showed no temporal trend at most of the gage locations, the same test based on the 20-yearly statistics showed that statistically significant temporal trend exists at 54% (mean), 60% (variance), 61% (autocorrelation), and 61% (PD) among the total 65 rain gages. In addition, this study produced the map of the linear trend of the precipitation statistics. The map showed a clear regional and seasonal tendency implying that the impact of the climate change varies significantly within Korea. The variogram analysis revealed that the approximate characteristic scale of linear trend of hourly and daily precipitation statistics ranges between 50 km and 200 km and between 100 km and 250 km, respectively. This characteristic scale is significantly smaller than the spatial scale of atmospheric circulation, which suggests that future water resources management plans of Korea should consider this mesoscale variability that otherwise can be missed if it is based only on the GCM simulation results.