Containing a large bioterrorist smallpox attack: a computer simulation approach

The natural history of ordinary smallpox in terms of time lines. Parameter values were determined through group consensus from the Smallpox Modeling Working Group and Chapter 4 of Fenner et al.¹⁴ The length of the incubation period follows the probability distribution shown in the top line. At the end of the incubation period, cases develop a fever, and then pass though a series of disease states. Before smallpox is recognized in the hospital (i.e., the first period), an ordinary case of smallpox would be recognized on the fourth day of rash. After this (i.e., the second period), smallpox is known to be present and all ordinary smallpox would be recognized in the hospital on the third day of rash. For infectiousness, the per contact transmission probability x (Table 1), is set to 1x for the first day of fever, increased to 2x for the second day of fever, 4x at the onset of rash, etc., with an upper limit of 1.0. Thirty percent of ordinary smallpox cases would die between days 7 and 14, according to a uniform distribution. In the behavior time line, cases withdraw to the home or go to the hospital according to the pattern indicated. In surveillance and containment, close contacts of identified cases are vaccinated.

The natural history of modified smallpox in terms of time lines. Modified smallpox is assumed to have the same incubation period as ordinary smallpox, but to have a milder course of disease. The infectiousness of people with modified smallpox would be 33% of that for people with ordinary smallpox, with a case fatality rate of 10%. However, it would be harder to recognize modified smallpox and cases would be slower to withdraw to the home or go to the hospital than for ordinary smallpox. Before smallpox is recognized in the hospital (i.e., the first period), 75% of cases would be recognized on the fourth day of rash and the remaining 25% on the seventh day of rash. After this, the smallpox is known to be present (i.e., the second period), and all ordinary smallpox would be recognized in the hospital on the third day of rash.

The natural history of hemorrhagic smallpox in terms of time lines. Hemorrhagic smallpox is assumed to have a shorter natural history and more severe disease progression than ordinary smallpox. Infected people would begin internal bleeding four days after the onset of fever, and 100% would die on the seventh day after the onset of bleeding. Before smallpox is recognized, we assumed that 50% of hemorrhagic smallpox cases would not be recognized and 50% would be recognized on the fifth day of fever. After smallpox is recognized, all hemorrhagic cases would be recognized on the fourth day of fever.

Structure of the populations. (A) The 2000 person subpopulations consist of households and household social clusters depicted by the connecting lines in neighborhood 2. Each subpopulation is partitioned into four neighborhoods. Small children mix in playgroups and daycare centers within their neighborhoods. The school mixing groups link neighborhoods as shown. (B) Clusters of the subpopulations are created by allowing ten percent of high school students in each of the clusters of subpopulations to mix with high schools in other subpopulations in the same cluster. All adults who work are randomly assigned to work in mixing groups of size 25 throughout the whole population. In addition, all people can attend a single hospital.

A plot showing the relationship between the transmission probability x during the second day of fever from an unvaccinated case of smallpox to an exposed unvaccinated person in a mixing group and the maximum household secondary attack (SAR) rate if he circulated in the mixing group for his entire infectious period. This relationship is based on the smallpox natural histories given in Figures 1–3.

The first 60 days of one stochastically simulated smallpox epidemic with 500 randomly selected initially infected people from all age groups. (A) Epidemic surveillance and containment (scenario 3). This epidemic had a duration of 196 days, while the average duration of the epidemics under scenario 3 was 194 days. (B) Epidemic with surveillance and containment, 50% preemptive hospital vaccination and 80% reactive mass vaccination with reactive school closure for ten days (scenario 9). This epidemic had a duration of 91 days, while the average duration of epidemics under scenario 9 was 87 days.