How fast must vaccination campaigns proceed in order to beat rising Covid-19 infection numbers?

We derive an analytic expression describing how health costs and death counts of the Covid-19 pandemic change over time as vaccination proceeds. Meanwhile, the disease may continue to spread exponentially unless checked by Non Pharmacological Interventions (NPI). The key factors are that the mortality risk from a Covid-19 infection increases exponentially with age and that the sizes of age cohorts decrease linearly at the top of the population pyramid. Taking these factors into account, we derive an expression for a critical threshold, which determines the minimal speed a vaccination campaign needs to have in order to be able to keep fatalities from rising. Younger countries with fast vaccination campaigns find it substantially easier to reach this threshold than countries with aged population and slower vaccination. We find that for EU countries it will take some time to reach this threshold, given that the new, now dominant, mutations, have a significantly higher infection rate. The urgency of accelerating vaccination is increased by early evidence that the new strains also have a higher mortality risk [1]. We also find that protecting the over 60 years old, which constitute one quarter of the EU population, would reduce the loss of live by 95 percent.