Fig 1.
Flow diagram of the mathematical model of the smallpox epidemic.
Fig 2.
Contact matrices used for the model simulation: Close contact (A) and social contact (B).
Table 1.
Model parameters.
Fig 3.
Age-group population distribution used in the model.
The horizontal bar graph represents the population size for each age group. The numbers above the bars indicate the population size in millions (e.g., 3.5 represents 3.5 million people).
Fig 4.
Baseline scenario simulation results.
The curves represent the mean values of the model simulations, and shaded areas indicate the 95% prediction interval. The red graph shows the daily confirmed cases, whereas the blue curves represent isolated patients. Among the blue curves, the solid and dashed lines indicate patients with non-severe and severe patients.
Fig 5.
Outbreak outcomes from the baseline scenario simulations.
Panels (A) and (B) show the distribution of confirmed cases by age group and in total, respectively. Panels (C) and (D) present the corresponding distributions of deaths. Results are displayed as violin plots, which illustrate both the variability and the probability density of outcomes across stochastic simulation runs.
Table 2.
Mean and 95% prediction interval of outbreak outcomes with a 50% reduction in contacts due to social distancing.
Table 3.
Mean and 95% prediction interval of outbreak outcomes with a 60% reduction in contacts due to social distancing.
Table 4.
Mean and 95% prediction interval of outbreak outcomes with a 70% reduction in contacts due to social distancing.
Fig 6.
Outbreak outcomes under different assumptions for vaccination growth rate and contact reduction, given a baseline initial vaccination number of 1,000.
Results are shown on a log scale for confirmed cases (A), deaths (B), and peak severe patients (C). Each color denotes a different vaccination growth rate, while the horizontal axis indicates the level of contact reduction.
Fig 7.
Distribution of the number of hosts who had hazardous contact until the outbreak recognition in different stages.
Fig 8.
Vaccination numbers in the baseline scenario simulations.
Panel (A) shows the mean daily number of vaccinations for ring vaccination (magenta) and mass vaccination (black), with the inset highlighting the early outbreak period. Panels (B) and (C) present the probability distributions for the total number of doses administered and the duration of the ring vaccination campaign, respectively, across stochastic simulation runs.
Table 5.
Odds ratios and confidence intervals for scenarios considering vaccine prioritization compared to the baseline scenario.
Fig 9.
Simulation results under different vaccine prioritization strategies.
Panel (A) shows daily confirmed cases, and Panel (B) shows the number of severe patients over time. The scenarios compared are: baseline (uniform vaccination, dotted blue), ascending order of age (solid orange), descending order of age (solid yellow), transmissibility-based prioritization (dashed purple), and fatality-based prioritization (dashed green).
Table 6.
The final value and range of PRCC of model inputs considering different model outputs. There is no range if the target model output is the peak number of severe patients as there is a one-time point of it.
Fig 10.
Absolute partial rank correlation coefficients (PRCC) over time for key model parameters.
Panel (A) shows PRCC values with respect to cumulative confirmed cases, and Panel (B) shows PRCC values with respect to cumulative deaths. Each color denotes a different input parameter: outbreak recognition timing (yellow), impact of social distancing (green), isolation rate for traced cases (blue), isolation rate for non-traced cases (purple), contact-identification ratio (orange), and growth rate of the daily vaccination (red). For the sensitivity analysis, parameter ranges were generated based on ±25% variability around baseline values.