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. 2021 Mar 23;11:6626. doi: 10.1038/s41598-021-85555-1

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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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Anti-vaccine views are shared on a network of $N = 5000$ individuals, where some randomly-selected nodes initially share the views. The top panel shows the evolution of those who are exposed for the first time to anti-vaccine views (dark purple) and are convinced by them (dark blue), those who are exposed for the first time (yellow) but do not adopt them (green) and individuals who never have contact with them (light blue). The odds of a person sharing anti-vaccine views, comparing the top 10% most central nodes against the bottom 10% (central left panel) shows that for extreme values of $θ$ , centrality does not have an impact (since all individuals share similar views), but for values in between, the most central nodes are two or more times more likely to share anti-vaccination views since they are more likely to be exposed. Since individuals are equally likely to adopt the views after their first exposure, more central individuals are more likely to adopt them. The impact is more pronounced on a proximity network (yellow) even when the network does not have nodes with a high degree, and a scale-free network (blue) than on a small-world network (green). By the end of the diffusion process of the anti-vaccination views (bottom left panel), even with a small persuasiveness $θ$ , most individuals will have contact with those views. On a scale-free network, with persuasiveness of $θ = 0.3$ , around 70% of the population has contact with the views (even if most of them reject them and do not pass them onwards). The impact of the size of the anti-vaccine community (AV) is relevant in terms of the years of life lost $D_{S} (ν)$ (central right) and has some impact in terms of the time to finish $T_{S} (ν)$ , considering a vaccination rate of 30%. Assuming a Degree vaccination strategy, we see that if 20% of the people support anti-vaccination views, nearly two years of life are lost (so that $D_{S} (0.3) \approx 2$ years). However, with a vaccination rate of 0.3 and the Degree vaccination strategy, only 0.3 years of life are lost.