Unlike previous papers on international logistics and cross-border e-commerce trade, this paper sets Organization for Economic Co-operation and Development (OECD) countries as an example to explore the dynamic interaction between international logistics and cross-border e-commerce trade. The panel data for the period 2000–2018 will be employed to perform an empirical analysis via a host of econometric techniques, such as panel unit root tests, panel cointegration tests, panel causality tests and the panel vector error correction model. Incorporating with other control variables, we find that there is a long-term relationship between international logistics and cross-border e-commerce trade. Specifically speaking, in the long-run, international logistics has a positive and significant effect on cross-border e-commerce trade. However, in the short-run, international logistics has a negative and significant effect on cross-border e-commerce trade. Furthermore, the results suggest that deviation from a cointegration system of cross-border e-commerce trade and international logistics will lead to the cross-border e-commerce trade and international logistics changing within the range of approximately 2.2% to 47.2% in the next period. Therefore, referring to these findings, each OECD country’s government should take up corresponding policies to ensure the sustainable development of both international logistics and cross-border e-commerce trade.

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This paper proposes a compartment model (SVEIHRM model) based on a system of ordinary differential equations to simulate the pandemic of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).Emergence of mutant viruses gave rise to multiple peaks in the number of confirmed cases. Vaccine developers and WHO suggest individuals to receive multiple vaccinations (the primary and the secondary vaccinations and booster shots) to mitigate transmission of COVID-19. Taking this into account, we include compartments for multiple vaccinations and mutant viruses of COVID-19 in the model. In particular, our model considers breakthrough infection according to the antibody formation rate following multiple vaccinations. We obtain the effective reproduction numbers of the original virus, the Delta, and the Omicron variants by fitting this model to data in Korea. Additionally, we provide various simulations adjusting the daily vaccination rate and the timing of vaccination to investigate the effects of these two vaccine-related measures on the number of infected individuals. We also show that starting vaccinations early is the key to reduce the number of infected individuals. Delaying the start date requires increasing substantially the rate of vaccination to achieve similar target results. In the sensitivity analysis on the vaccination rate of Korean data, it is shown that a 10% increase (decrease) in vaccination rates can reduce (increase) the number of confirmed cases by 35.22% (82.82%), respectively.