Fig 1.
An illustration of our hybrid gravity-metapopulation model for four regions. Interactions and movements between the regions (left) and stratification of the population of each region based on disease stages (right). Model compartments are defined as follows: Susceptible (Sj); exposed (Ej); pre-symptomatic infectious (Pj); symptomatic infectious (I1j and I2j); and recovered (Rj) for region j. Our model assumes that there are no re-infections. The black arrows show the movement of individuals from one region to another (left) and the transition of individuals through the different stages of COVID-19 at the rates indicated beside the arrows (right). The red dashed arrows indicate disease transmission (see (1) for more details).
Table 1.
Model parameters, their descriptions, and values.
The estimated parameters are presented in the Results section. The population sizes for the regions are presented in Table C in S1 Text.
Fig 2.
Map of the local health areas in Fraser Health, British Columbia (BC), Canada.
The population size of each region is given in Table C in S1 Text. The base layer of the map can be found in https://catalogue.data.gov.bc.ca/dataset/health-authority-boundaries for the regions and https://www.naturalearthdata.com/downloads/110m-cultural-vectors/ for the country. Their respective licenses are avaliable at https://www2.gov.bc.ca/gov/content/data/open-data/open-government-licence-bc and https://www.naturalearthdata.com/about/terms-of-use/.
Fig 3.
Physical distances (in km) between the local health areas (LHAs) based on population-weighted centroid (left) [59] and the probability matrix (π) computed using (5) (right). πji is the probability that an individual who came from one of the 13 regions to region j, originated from region i.
Fig 4.
Probability matrix (π) computed from the Telus mobility data for week 1 (left) and week 30 (right), corresponding to July 1–7, 2020 and January 21–27, 2021, respectively. πji is the probability that an individual who came from one of the 13 LHAs to region j, originated from region i. Mobility matrices for the remaining weeks are presented in Figs (B—F) in S1 Text.
Fig 5.
Weekly time-series mobility rates for each region from July 2020—January 2021, computed from the Telus mobility data.
Fig 6.
Observed and estimated COVID-19 cases.
Weekly reported cases of COVID-19 and model prediction (columns 1 and 3). Disease transmission rate, βj(t) and the contribution of mobility to disease transmission, (green curves in columns 2 and 4). Model types: fixed distance matrix (blue) and weekly mobility matrices (gold). Black dots are the weekly reported cases of COVID-19, the solid lines are the mean estimates of cases/parameters, the darker bands are the 50% CrI, while the lighter bands are the 90% CrI. Similar results for the remaining regions are presented in Figs G and H in S1 Text.
Fig 7.
Baseline disease transmission rate.
The distributions for the baseline disease transmission rate, , for each region computed using the estimated parameters c0j for j = 1, …, 13 (see Tables A and B in S1 Text for the estimates of c0j). Scenarios: fixed distance matrix (blue) and weekly mobility matrices (gold).
Fig 8.
Contribution of other factors to disease transmission.
The distributions for the contribution of other factors that affect disease transmission (eg(t)) to the transmission rate (β(t)), computed every four weeks and for the last two weeks: g1 = 0 (weeks 1–4), g2 (weeks 5–8), g3 (weeks 9–12), g4 (weeks 13–16), g5 (weeks 17–20), g6 (weeks 21–24), g7 (weeks 25–28), g8 (weeks 29 & 30). Scenarios: fixed distance matrix (blue) and weekly mobility matrices (gold). The estimated means with 90% credible interval are presented in Tables A and B in S1 Text.
Table 2.
Model comparison using leave-one-out cross-validation (LOO) and the widely applicable or Watanabe-Akaike information criterion (WAIC).
Model ranking (in descending order) is shown in the first column. The difference between the expected log pointwise predictive density (ELPD) for each scenario and that of the best scenario with standard errors are shown in the second column. In the third column, we have the Bayesian LOO estimate of the expected log pointwise predictive density (ELPD LOO) and its standard error. The LOO information criteria (LOOIC) and its standard error are given in the fourth column. Lastly, the computed Watanabe-Akaike information criterion (WAIC) for each model is shown in the fourth column.