Sensitivity analyses. (A) The variation in values of R₀* (average number of secondary cases) versus n_PG (average size of a peer group). High values of R₀* were only consistent with high average peer-group sizes. (B) The variation between R₀*, μ_ER (average duration of early rash), and a (household attack rate) for fixed n_PG = 12. Parameter combinations with the proportion of transmission which was presymptomatic θ > 20% were excluded from this chart. High μ_ER and high a are required for high R₀*. (C) The relationship between the average cumulative number of infections in the first four generations and p_WP (proportion of peer-group members who are contacts). Average was taken over 100 model realizations with constant parameter values. Higher numbers of cumulative infections are associated with lower connectivity in peer groups. (D) The relationship between spatial extent after four generations and cumulative infections. Spatial extent is defined to be the average (over model realizations) of the maximum distance of cases from the center of seeding.

Model assumptions and inputs. (A) The natural history of smallpox with k states (see Methods) given explicitly. The six disease states were as follows: k_i = 0, susceptible; k_i = 1, latent (infected but not yet infectious or symptomatic); k_i = 2, fever (infected and infectious but not yet overtly symptomatic); k_i = 3, early rash (infected, infectious and with visible skin lesions but assumed to still be spending time outside the home); k_i = 4, late rash (infected, infectious, with visible skin lesions and confined to either the home or hospital); and k_i = 5, recovered (assumed to be immune from further infection for life). Individuals could enter the final disease state of recovered, k_i = 5, after either natural infection or successful vaccination. (B) The waiting time distributions for the three disease stages. These distributions were obtained by fitting γ distributions with integer-valued shape parameters (see Supporting Text) to historical data (1), incubation period (green; average 11.6 days, variance 3.36 days²), fever period (orange; 2.49 days, 0.89 days²), and rash period (red; 16.0 days, 18.3 days²). (C) The distribution of population densities (per km²) of GB with 5-km resolution based on 1991 GB census data. (D) The observed and fitted journey-to-work distributions. To infer the pair-wise choice kernel (see Methods) from the distribution of journeys to work, we divided the number of actual journeys of length d by the number of possible journeys of length d for all possible intervals (d − Δd, d + Δd). Fig. 5 shows the agreement between the inferred pair-wise choice kernel of the model and the functional form fitted to census data (see Supporting Text).

Spatiotemporal dynamics. Low transmission (A), medium transmission (B), and high transmission (C) scenarios (see also text and Table 2). The density maps show expected cumulative infections for the first 75 days of the outbreak averaged over 100 model realizations. Each “pixel” is a 5-by-5 km tile and the scale is in infections per km². The color legend is on a log scale and is defined so that a single infection in a 5-by-5 km tile in any of the 100 realizations will register at the lower end of the scale, i.e., the average number of infections was equal to 0.0004 per km². Middle and Bottom for A–C are averages (solid line) of 1,000 realizations with 95% prediction intervals (dashed lines). Spatial extent is the maximum distance of the household of an infected individual from the center of the seeding radius (central London). Apparent oscillations in infection incidence are caused by nonoverlapping early generations of infection.