Will it ever end? In November, we were celebrating the announcement that the BioNTech/Pfizer vaccine seemed to be highly effective against Covid-19, followed with bewildering speed by similar claims for the Sputnik V, Moderna and Oxford/AstraZeneca vaccines. Nearly three months later, hospitals are overwhelmed and the global death toll is climbing twice as fast as in the worst days of the first wave.

At a time like this, I reach for my calculator. Without minimising the suffering so many people are enduring, I think there is potential for rapid progress very soon. There are two reasons why these vaccines, some highly effective, have not yet done anything obvious to save lives or protect hospitals.

The first is evident: not enough people have been vaccinated so far. Israel and the United Arab Emirates are well into a remarkable mass vaccination campaign, but most major economies have given a first dose to 2 or 3 percent of their population.

The second reason is that the vaccine takes time to work. In the UK, Margaret Keenan received the first dose of vaccine bright and early on December 8, but it needs a couple of weeks to provide much protection. She and her fellow first-day vaccines were much safer by Christmas.

Infection takes on average five days to develop into symptoms, so there would have been little sign of any benefit before New Year’s Eve. It usually takes another 10 days before there is much risk of admission to an intensive care unit, and still, more before there is a risk of death. Only now are those first few vaccines, weeks ago, beginning to reduce the death toll. It is like turning around the proverbial oil tanker.