For each individual and each day, we calculated the cumulative outdoor travel distance recorded using the ArcGIS Tracker app from their registered household address. This was calculated by summing up the distance (d) computed by the Euclidean distance method (equation 1) between the 2 sequential outdoor GPS records. Considering the accuracy of the GPS records, we set up a 25 m radius buffer zone (the average horizontal accuracy is 25 m) around a participant’s home location. Points that fall within the buffer are considered as at-home travel activities and therefore considered as zero distance in analyses.
The equation to calculate the distance travelled by each participant is as follows:
where d(pi, pj) is the Euclidean distance between 2 sequential GPS points (ie, pi and pj); the Cartesian coordinates are (pix, piy) for pi and (pjx, pjy) for pj. We used the British National Grid as the reference system.
Our statistical analysis was conducted using an interrupted time series, where we used segmented linear regression to estimate the trends in travel patterns, with the first segment estimating the median travel distance for the cohort before vaccination and the second segment estimating the median travel distance for the cohort after vaccination. Therefore, we defined the interruption time point in our analysis as the date of the first vaccination for each individual, with negative days denoting days prior to vaccination and positive days denoting days after vaccination; for each day, we then calculated the median travel distance.
To calculate the travel trajectory before vaccination, we conducted linear regression analysis using data before vaccination to estimate the sample’s median daily travel distance from their home with time (days before vaccination) as the explanatory variable. To calculate the travel trajectory after vaccination, we conducted linear regression analysis using data after vaccination to estimate the sample’s median daily travel distance from their home with time (days after vaccination) as the explanatory variable. For both models, each day represented 1 data point, with the points for each day being the median travel distance of those who submitted readings on that day. The segmented regression equations can be found in equation 2; linear regression was chosen a priori as we expected the limitations on movement to create a stable pattern in movement. Our alternative hypothesis was that after vaccination, we would see an increase in movement that would be expressed if a2 > a1 (a slope change) or b2 > b1 when a2 ≥ a1 (a level change) [27 (link)] in equation 2.
Equation 2 uses segmented linear regression models with model (and subscript) 1 representing the trends before vaccination and model (and subscript) 2 representing the trends after vaccination; yn represents the estimated median daily travel distance with coefficient an, x represents the days since vaccination (negative for model 1 and positive for model 2), and bn is a constant:
y1 = a1x + b1 for x < 0(2) y2 = a2x + b2 for x > 0
The UK vaccination program prioritized people by (older) age and clinical risk groups, which, in addition to differences in the socioeconomic backgrounds between those invited and accepting a vaccination, meant that selecting an appropriate control group for this analysis was not feasible.
The equation to calculate the distance travelled by each participant is as follows:
where d(pi, pj) is the Euclidean distance between 2 sequential GPS points (ie, pi and pj); the Cartesian coordinates are (pix, piy) for pi and (pjx, pjy) for pj. We used the British National Grid as the reference system.
Our statistical analysis was conducted using an interrupted time series, where we used segmented linear regression to estimate the trends in travel patterns, with the first segment estimating the median travel distance for the cohort before vaccination and the second segment estimating the median travel distance for the cohort after vaccination. Therefore, we defined the interruption time point in our analysis as the date of the first vaccination for each individual, with negative days denoting days prior to vaccination and positive days denoting days after vaccination; for each day, we then calculated the median travel distance.
To calculate the travel trajectory before vaccination, we conducted linear regression analysis using data before vaccination to estimate the sample’s median daily travel distance from their home with time (days before vaccination) as the explanatory variable. To calculate the travel trajectory after vaccination, we conducted linear regression analysis using data after vaccination to estimate the sample’s median daily travel distance from their home with time (days after vaccination) as the explanatory variable. For both models, each day represented 1 data point, with the points for each day being the median travel distance of those who submitted readings on that day. The segmented regression equations can be found in equation 2; linear regression was chosen a priori as we expected the limitations on movement to create a stable pattern in movement. Our alternative hypothesis was that after vaccination, we would see an increase in movement that would be expressed if a2 > a1 (a slope change) or b2 > b1 when a2 ≥ a1 (a level change) [27 (link)] in equation 2.
Equation 2 uses segmented linear regression models with model (and subscript) 1 representing the trends before vaccination and model (and subscript) 2 representing the trends after vaccination; yn represents the estimated median daily travel distance with coefficient an, x represents the days since vaccination (negative for model 1 and positive for model 2), and bn is a constant:
y1 = a1x + b1 for x < 0
The UK vaccination program prioritized people by (older) age and clinical risk groups, which, in addition to differences in the socioeconomic backgrounds between those invited and accepting a vaccination, meant that selecting an appropriate control group for this analysis was not feasible.
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