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. 2021 Jul 30;11:15729. doi: 10.1038/s41598-021-95025-3

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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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Time of initial emergence of a resistant strain that has become established. Probability density that the resistant strain emerges as a function of time since the start of the simulation, t, rescaled by the time at which 60% of the individuals are vaccinated, t_V60, averaged across simulations with θ (0.001 through 0.015), F_h (2000 through 20,000) and p = 10^–6. Without any extraordinary periods of low transmission (blue line) the peak of the likelihood of emergence of a new strain is at t/t_V60 = 1. The likelihood of emergence of a resistant strain can be reduced by an extraordinary period of low transmission centered at t/t_V60 = 1 with a stronger reduction when such period is longer, T (colour-coded), or when the rate of transmission is more strongly reduced (a) β_l = 0.055, (b) β_l = 0.03, (c) β_l = 0.01.