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. 2018 Aug 20;8:12476. doi: 10.1038/s41598-018-30945-1

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© The Author(s) 2018

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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Evolutionary trajectories as a function of the initial infection period. Parameters of the simulations are D = 0.35, β₀ = 0.8 and L = 150, with τ_I0 as shown in the legend. The dashed black line shows the expected mean-field behaviour τ_I = β+ constant. The system either displays a behaviour indistinguishable from the D = 0 case or follows a curve of steady increase in R₀, as predicted in the mean-field theory. The region where stochastic fluctuations can lead the system to any of the two states stretches to a point in the limit L → ∞.