Fig 1.
Distribution of tweet sentiment and profile stance.
Tweets expressing anti-vaccine sentiment constitute an estimated 17% of vaccination-related tweets, where only about 3% of profiles stance are classified as antivaxx. Error bars are too small to depict visually, see S1 Appendix for uncertainty analyses.
Fig 2.
The top 10 most linked to domains by strongly antivaxx and provaxx profiles.
Bar length shows percentage of the total number of links shared by profiles in the given category and hence do not sum to 100. For each domain, the red bars going right represent antivaxxers and blue bars going left provaxxers. Antivaxxers rely heavily on links to YouTube, and the page ‘natural news’, which promulgates pseudoscience and sells products related to health and nutrition. Provaxxers link to a wide array of news and science sites, which is why a lower overall percentage of their links are contained in the top 10. Error bars are too small to depict visually, see S1 Appendix for uncertainty analyses.
Fig 3.
Frequency of various categories of links for profiles grouped by vaccination stance (provaxx, antivaxx, or neutral).
Antivaxx profiles often post links to Youtube videos, and to sites that sell health related products and thus have a vested financial interest in the vaccine discourse. Error bars are too small to depict visually, see S1 Appendix for uncertainty analyses.
Fig 4.
Representation of the repeated mutual interaction graph from 2013–2016.
Profiles frequently interact with others who share their own stance, and antivaxx profiles are localized in relatively few, tightly nit clusters. Profiles with and anti- and provaccine stances are illustrated in red and blue, respectively. Only the giant conected component of the interaction graph is depicted.
Fig 5.
Interplay between average vaccination sentiment and user interactions.
a: Users tend to disproportionally interact with users of similar stance, both in cases where users only interact during a single, and multiple, three-month time windows. Specifically, we compute for all users the average probabilities of that user’s tweets expressing pro/anti-vaccine sentiment. Comparing these averages for all nodes and their neighbors, we find a positive correlation between the average pro- and antivaccine sentiments. Similarly, the average pro-vaccine sentiment of nodes exhibits a negative correlation with the anti-vaccine sentiments of their neighbors. The number of nodes in the interaction network decreases exponentially as the minimum number of time windows is increased. The negative correlation between pro- and antivaxx probabilities of neighbors tends slightly toward zero as the threshold for repeated interaction grows. b: As increasingly repeated interactions are considered, users in the interactions graph are increasingly well connected. However, the number of vaccination-related tweets posted by users decreases for interactions occurring very frequently, indicating that at this point, the graph likely includes users who are highly active on Twitter, yet do not discuss vaccination-related topics very often. Error bars on Pearson correlations represent one standard deviation of the Fisher-transformed variables z, i.e. the bounds on the error bar on a correlation r of n data points, is given by tanh(z±σz), where z = arctanh(r) and
Fig 6.
Profiles that express fringe vaccine sentiments are also exposed via their interaction networks to sources of information that are highly dissimilar to link frequencies in the overall discussion.
Here we consider users who posted a minimum of 5 tweets containing vaccine-related keywords, and partition them into deciles based on their tweets’ mean probability of expressing anti- and pro-vaccine sentiment. For each such decile and vaccine stance, the plot shows the Jensen-Shannon distance between the frequencies at which links from the domains shown in Fig 2 are shared in the vicinity of users in that decile, and in the interaction network overall. The error bars are computed using a bootstrap technique in which users in the target stance-decile combination where randomly sampled with replacement and the JS-distance to the overall distribution calculated. The error bars depict the standard deviations of each 1000 such samples.
Fig 7.
a: The degree distribution of the MMR graph, truncated at degree 500 to exclude automated profiles. The dashed line indicates the best fit for a stretched exponential (Weibull) function. b: The Jaccard similarity index of the sets of edges in the MMR graph for different 3-month periods. Each row and column correspond to a three-month time windows in the period from 2013–2016. The diagonal is therefor left out, as it represents the self-similarity of the interaction network in each time window, and so the Jaccard similarity is 1 by construction.
Fig 8.
Representation of the final classifier.
An initial input layer, in which strings are represented by a sequence of one-hot encoded words, is passed to a) a deep neural network similar to the DeepMoji classifier [70], and b) a fasttext classifier [71]. After being pre-trained to predict hashtags from the surrounding text (source dataset), the model is fine-tuned to instead predict vaccine sentiment from tweet text (target dataset).
Table 1.
Qualitative summary of classifier performance.
The classifier correctly assigns a large probability of antivaxxness to text snippets the express conspiracist notions about vaccines being part of a global scam. Similarly, texts highlighting the positive qualities of vaccinations are assigned a high probability of being provaxx. In addition, text snippets concerning the band named The Vaccines are recognized as irrelevant. A text snippet expressing how much more expensive it is to kill, rather than vaccinate, badgers is also categorized as irrelevant with a high certainty, despite containing negative words like ‘kill’.