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. 2021 Aug 11;11:16312. doi: 10.1038/s41598-021-95494-6

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© The Author(s) 2021

Open AccessThis 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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Compartment diagram of the alternative SEIRD(s) model, modified in order to accommodate protected individuals, P, to discriminate between detected, I $_{d}$ , and non-detected, I, infectious cases, and to include the process of vaccination. The flows between compartments are normalized and mathematically related to the model parameters, which are listed and briefly described in the box on the right hand side.