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How Large Fraction of a Population must be Vaccinated before a Disease is Controlled?

Robin Halamicek, Dirk W Schubert, Fritjof Nilsson

The ongoing COVID-19 pandemic has already caused more than 5 million casualties despite hard restrictions and relatively high vaccine coverage in many countries. The crucial question is therefore, how large vaccination rate and how severe restrictions are required to terminate the spread of the decease, assuming that the vaccine efficiency and the basic reproduction ratio (R₀) are known? To answer this question, a mathematical equation was applied to visualize the required vaccination level as function of vaccine efficiency, restriction efficiency and basic reproduction ratio (R₀). In addition to the modeling study, COVID-19 data from Europe was collected during 19/11-26/11 (2021) to assess the relation between vaccination rate and incidence. The analysis indicates that a vaccination rate of ~ 92% (2 doses) is required to stop Delta (B.1.617.2) without severe restrictions, under conditions like those in Europe late November 2021. A third vaccine dose, improved vaccines, higher vaccination rates and/or stronger restrictions will be required to force Omicron (B.1.1.529) to expire without infecting a large fraction of the population.