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. 2019 Dec 16;9:19172. doi: 10.1038/s41598-019-55574-0

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© The Author(s) 2019

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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Illustration of how individual reproductive numbers were calculated (panel A) and the difference between the spatially adjusted and non-adjusted methods (panel B). The transmission probability from individual j to all potential infectees $(p^{i_{1} j}, p^{i_{2} j}, p^{i_{3} j})$ is estimated first. The sum of these probabilities is, by definition, the expected number of infectees caused by individual j, i.e., the individual reproductive number. The transmission probability itself is estimated based on solely temporal relationships (non-adjusted) or in combination with spatial relationships (spatially adjusted). In the non-adjusted method, p^·j is proportional to the temporal weight g(a) determined by the generation interval between infector j and its infectees. Cases in the same temporal cohort (i.e., with the same onset day, a₁ = a₂ = a₃) share the same transmission probability from previous infectors. They also share the same individual reproductive number since their relationship to subsequent cases is again identical. For the spatially adjusted method, p^·j is proportional to the spatial weights f(d), modulated by the distance between the infector and the infectees in space. Therefore, individual reproductive numbers of cases in the same cohort can be distinguished.