Fig 1.
Graphical overview of a simulation run.
(A) Generation of a physical interaction network, (B) Assignment of d correlated binary attribute values to each node. If d = 2, the attributes represent e.g. attitude towards vaccines (color) and social distancing (shape), (C) Computation of the relative clustering level (a measure of homophily) of each attribute, (D) Overview of the clustering algorithm used to assign attributes so that the network exhibits a desired level of homophily for each attribute. Values to the right of each node indicate its dissimilarity index: the proportion of neighbors with a different attribute value. (E) Vaccination of all nodes with a positive (blue) attitude towards vaccines and removal of those successfully vaccinated (green) from the pool of susceptible individuals; the probability that an all-or-nothing vaccine awards protection equals its effectiveness, (F) Infection of a randomly selected susceptible node (red), (G) Simulation of the spread of the infection and recording of outcomes. The likelihood of interaction (edge weight) depends on whether nodes practice social distancing (circles) or not (triangles).
Fig 2.
Comparison of outbreak frequency in networks with and without homophily.
Contour plots were generated from 10,000,000 independent simulation runs with four vaccine and social distancing parameters chosen uniformly at random (axes show parameter ranges). The difference in outbreak frequency (where an outbreak was defined as >1% of the population eventually becoming infected) from a reference scenario of no vaccine and no social distancing was calculated for two scenarios: social interaction networks with 50% homophily of those who vaccinate and of those who practice distancing and networks without homophily (see S1 Fig). Data was binned and smoothed using a two-dimensional Savitzky-Golay filter [18] (details in Methods). Each subplot shows the effect of variation of two parameters on the difference in outbreak frequency between the two different homphilly scenarios (see S1 Fig). (A) vaccine coverage (x-axis) and vaccine effectiveness (y-axis), (B) vaccine coverage (x-axis) and proportion of those who distance, (C) contact reduction (in %) by those who practice social distancing (x-axis) and proportion of those who distance (y-axis). An equivalent analysis for the basic reproductive number is shown in S2 Fig.
Fig 3.
Effect of homophily and correlation of opinions on outbreak frequency.
(A) The relative outbreak frequency is compared for different scenarios with respect to homophily and correlation of those who vaccinate and those who distance, and for different levels of vaccine effectiveness. Reference level for comparisons is a vaccine with 0% effectiveness and no homophily nor correlation of vaccinated and distancers. This reference level is set to 100%. (B) For each level of vaccine effectiveness, the change in relative outbreak frequency is compared to the homogeneous case of no homophily and no correlation, which is set to 100%, respectively. (C-D) Absolute difference in relative outbreak frequency (from A) when comparing physical interaction networks where (C) vaccinated, (D) distancers cluster (homophily = 50%) versus networks without homophily.
Fig 4.
Effect of increased activity levels by individuals who have received a vaccine.
The outbreak frequency (relative to the reference case of no vaccine, which is set to 100%) is shown for different levels of vaccine effectiveness (x-axis) and increased average activity levels by those who received a vaccine (y-axis). A black line depicts the x,y-coordinates at which the presence of the vaccine does not change the outbreak frequency. To the left (right) of this line, the presence of the vaccine is detrimental (beneficial). Two different scenarios regarding homophily and correlation of those who vaccinate and those who distance are considered: (A) 0% homophily and no correlation, (B) 50% homophily of those who vaccinate and those who distance and 0.45 correlation. In both plots, a fixed proportion of 65% of all individuals receive a vaccine and 65% of all individuals practice social distancing, i.e., reduce their social contacts by 50%. Data was binned and smoothed using a two-dimensional Savitzky-Golay filter [18] (details in Methods). See S1 Table for a sensitivity analysis where these proportions are varied.
Fig 5.
Relative mortality in the COVID-19 model compared to the homogeneous case of no homophily and no correlation.
(A) For each line, the vaccine effectiveness and one homophily or correlation variable is fixed at a negative (−0.15 correlation; yellow diamond), positive (0.15 correlation or 50% homophily; green cross) or zero value (black circle), and average mortality is calculated across all other values and compared to the homogeneous case of no homophily and no correlation (dotted line; relative mortality = 100%). (B-C) Relative mortality is shown when three variables and the vaccine effectiveness are fixed. Red (blue) indicates higher (lower) mortality than in the homogeneous case of no homophily and no correlation. In (B) the three most influential variables from (A) are fixed, while in (C) the three correlations are fixed.
Fig 6.
Level of contact reduction by high-risk individuals influences vaccination priorities.
(A) The average mortality at a given additional contact reduction by high-risk individuals is shown for three different scenarios: negative (−0.45; yellow), zero (black) and positive (0.45; green) correlation between vaccinated and high-risk individuals. (B) Relative mortality compared to the case of no correlation (black line in A), at 50% homophily of both high-risk individuals and individuals who vaccinate. Black dashed lines and a gray triangle highlight the three intersection points of the three curves. (A-B) homophily of those who vaccinate and of high-risk individuals: 50%, vaccine effectiveness: 80%. Background colors indicate the prioritization (high-risk or low-risk individuals) that leads to lower overall mortality. (C) The location of the intersection points from (B) is shown for all combinations of homophily of those who vaccinate (0% vs 50%) and of high-risk individuals (0% and 50%), as well as two levels of vaccine effectiveness: 50% (gray) and 80% (blue). S4 Fig contains the full curves for all eight considered combinations.