As COVID-19 transmissions spread worldwide, governments have announced and enforced travel restrictions to prevent further infections. Such restrictions have a direct effect on the volume of international flights among these countries, resulting in extensive social and economic costs. To better understand the situation in a quantitative manner, we used the Opensky network data to clarify flight patterns and flight densities around the world and observe relationships between flight numbers with new infections, and with the economy (unemployment rate) in Barcelona. We found that the number of daily flights gradually decreased and suddenly dropped 64% during the second half of March in 2020 after the US and Europe enacted travel restrictions. We also observed a 51% decrease in the global flight network density decreased during this period. Regarding new COVID-19 cases, the world had an unexpected surge regardless of travel restrictions. Finally, the layoffs for temporary workers in the tourism and airplane business increased by 4.3 fold in the weeks following Spain's decision to close its borders.