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. 2021 Apr 12;6:51. doi: 10.1038/s41541-021-00316-5

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — Best fit trendline analysis of observed vaccine efficacy (VE_observed) as a function of observed force of infection (FoI_observed) is shown as a logarithmic relationship (blue dotted line) with a R² of 0.807. A regression analysis of VE_observed as a function of ln FoI_observed shown in the embedded table has a Significance F of 0.006. Using the VE_{natural log} equation (see Box 2, Vaccine efficacy as a function of force of infection), the observed VE_max, VE_min, FoI_max, FoI_min, and FoI_observed were used to calculate the VE_{natural log} in the embedded table and the calculated VE_{natural log} shown graphically (orange dotted line).