Fig 1.
Datasets used in the study are listed on top, and the four main modules of our framework are highlighted in the system diagram. The Travel Module uses long distance airline travel data and short-range commuter flow data to construct the county to county temporal travel matrix. This is used by the Disease Dynamics Module for simulating national scale epidemic spread via the metapopulation model. Additional inputs to this module include the seeding and vaccination schedule, disease model parameters, and vaccine efficacy. While some of these are fixed based on the study design, the Calibration Module uses historical incidence data to estimate the remaining disease model parameters. The calibrated disease model is then used as an oracle to compute the optimized vaccine allocation in the Optimization Module.
Fig 2.
Datasets used to capture short-range and long-range mobilities in the United States are depicted as networks on top (commuter data on the left, airline data on the right). Commuter data is shown between counties, whereas airline network is shown for key domestic airports in the United States for a chosen month (January). The distribution of flow volume with respect to pairwise county distances in shown as heatmaps for both the commuter and airline data. Airline flows are fractional because they are mapped to the counties that are served by them.
Fig 3.
Spatio-temporal spread of influenza, for a sample scenario, seeded in Louisiana. Counties where the epidemic emerges by Day 7, 30, 90 or 180 are respectively shaded in red, orange, brown and yellow. We observe that the evolution of influenza spread exhibits both spatially local spread (aided by the commuter flow), and long range transmission events (aided by the domestic airline flow). This is especially evident in the transition between Day 7 to Day 30, where the epidemic originally seeded in southern counties of Louisiana spreads to other neighboring counties, as well as far away counties which have major airport cities (such as Seattle, Chicago, DC).
Fig 4.
(a) Normalized cumulative weighted ILI% (normh) for each HHS region, across past influenza seasons. (b) Results of multi-stage calibration. Target attack sizes for each HHS region and peak time are shown relative to the results of the calibration. For each HHS region, green circle represents the ground truth attack size, and the associated green dashed line represents the peak timing. In blue (purple) we show the targets achieved by best model chosen after first (second) stage of calibration. All combinations of attack sizes, peak timing achieved by the particles in the design space are shown in grey.
Fig 5.
Episizes achieved by optimized allocation for different baseline episizes and vaccine efficacies.
Fig 6.
Weekly allocation of vaccines across states for the optimized allocation with 10 week lookahed, vaccine efficacy of 0.5 and baseline episize of 40M.
Fig 7.
Population normalized total allocation of vaccines per state under the optimized schedule.
A value of 1.0 indicates that the state received exactly the same amount of vaccines it would have received under the pro-rata schedule. Values greater (less) than 1.0 correspond to more (fewer) vaccines allocated under the optimized schedule than the pro-rata schedule.
Fig 8.
Effect of hyperparameters (lookahead duration and allocation stepsize) on algorithm performance.