Variation in human mobility and its impact on the risk of future COVID-19 outbreaks in Taiwan

Abstract Background As COVID-19 continues to spread around the world, understanding how patterns of human mobility and connectivity affect outbreak dynamics, especially before outbreaks establish locally, is critical for informing response efforts. In Taiwan, most cases to date were imported or linked to imported cases. Methods In collaboration with Facebook Data for Good, we characterized changes in movement patterns in Taiwan since February 2020, and built metapopulation models that incorporate human movement data to identify the high risk areas of disease spread and assess the potential effects of local travel restrictions in Taiwan. Results We found that mobility changed with the number of local cases in Taiwan in the past few months. For each city, we identified the most highly connected areas that may serve as sources of importation during an outbreak. We showed that the risk of an outbreak in Taiwan is enhanced if initial infections occur around holidays. Intracity travel reductions have a higher impact on the risk of an outbreak than intercity travel reductions, while intercity travel reductions can narrow the scope of the outbreak and help target resources. The timing, duration, and level of travel reduction together determine the impact of travel reductions on the number of infections, and multiple combinations of these can result in similar impact. Conclusions To prepare for the potential spread within Taiwan, we utilized Facebook’s aggregated and anonymized movement and colocation data to identify cities with higher risk of infection and regional importation. We developed an interactive application that allows users to vary inputs and assumptions and shows the spatial spread of the disease and the impact of intercity and intracity travel reduction under different initial conditions. Our results can be used readily if local transmission occurs in Taiwan after relaxation of border control, providing important insights into future disease surveillance and policies for travel restrictions. Supplementary Information The online version contains supplementary material available at 10.1186/s12889-021-10260-7.

For simplicity, we assumed that the majority of travel is work-related travel and on average travelers spend eight hours in the travel destination ( # =1 given the unit of time is 8 hours) and that Tij is proportional to Mij, leaving Fi the only parameters to be fitted. We used a gradient descent algorithm to find the local optimum solution for Fi, where the cost function is defined by the sum of the squared difference between normalized mij and the normalized value of Mij from the model. We calculated !" " under fitted parameters to obtain estimates of Pij.

Residence model
The model shown in Methods considered both that (1) non-travelers get infected by infectious visitors to their home location (the first part in the following equation) and that (2) susceptible travelers get infected when they travel (the second part in the following equation).
Because it is possible that visitors from different cities interact inside another third city, to address how this influences the model outcome, we constructed another model where infected individuals in the city susceptible travelers travel to include infected visitors from other cities.
Because the difference between models with and without considering the interaction occurring between visitors from different cities inside another third one were minimal ( Figure S11), we reported results from the simpler model in this study. The impact of Ching Ming Festival (4-day) and Dragon Boat Festival (4-day) is less apparent. Colors represent the different timing of when initial infections occurred (blue: at the beginning of holidays; red and green: 7 days and 14-days before holidays, respectively). After holidays, mobility changed back to that during normal days and stayed the same until the end of each simulation. R0=2.4. Figure S7. The impact of travel reduction on time to reach 1000 accumulated infections. If initial infections were in a big city, it took less time to reach 1000 infections in the contact model. The difference between big and small cities was not significant in the residence model. Intracity and overall travel reduction delayed the time to reach 1000 infections in both models, while intercity reduction did not. For some conditions, P1000,3 was 0 and no bar was shown. Here travel reduction was applied during the whole time and R0=2.4.

Figure S8. The impact of travel reduction on the geographic distribution of infections.
Standard deviation of infection numbers across different cities when there are 1000 infections (V1000,3) was shown. Intercity travel reduction increased the variation in infection numbers across cities in both models. Here travel reduction was applied during the whole time and R0=2.4. Figure S9. T1000,3 and V1000,3 under different lengths of intercity travel reduction. T1000,3 (upper panel) and V1000,3 (lower panel). Here initial infections were in Taipei city and R0=2.4. Figure S10. P1000,3 when travel reduction started at different conditions. P1000,3 when travel reduction started from the beginning of the simulations (denoted by 0), or when there were 10, 20, 30, 50, and 100 infections in both contact (left) and residence (right) models. Two different lengths of travel reduction duration were shown: (A) 10 days (B) 1 month. Only intracity travel reduction was shown here because intercity travel reduction only had minimal impact on P1000,3 and the results from overall reduction and intracity reduction were qualitatively similar. It was best to reduce travel at the beginning if the duration was for 10 days or 1 month. Here initial infections were in Taipei city and R0=2.4.
(A) (B) Figure S11. The comparison in P1000,3 under two types of residence model. The results from residence models with and without considering the interaction occurring between visitors from different cities inside another third one were similar. Table S1. Intracity R0, intercity R0, risk of infection, and risk of importation.