South Korean graduate student Kim Hyun-jin sits with her thumbs flailing away at the screen of her phone, hoping to land a click on an online map that will get her the leftover coronavirus vaccine that someone in her Seoul neighbourhood missed.

But after 10 days of "mad clicking," Kim, 32, has come away with nothing as vaccines are scarce amid a surge of new Covid-19 cases that started last week and is setting daily records.

"It's like war," Kim said, showing a map on her phone that shows...