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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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The states, transition parameters and dynamics. (a) States are shown in circles and transition parameters in squares. The transition parameter, μ, is the rate at which individuals lose natural immunity and p, is the probability that an individual infected with the wildtype strain transmits a resistant strain, so it is not a deterministic parameter. Example dynamics of the number of individuals infected with the wildtype (blue) and resistant strains (red) for p = 10^–6, θ₀ = 1/365 and F_h = 15,000. The period of vaccination is highlighted (green). Under the same parameters the resistant strain may emerge and go extinct, (b), or become established, (c).