Smallpox Model

In this model, two towns can be seen, Circletown and Squaretown, inhabited respectively by circle individuals and square individuals. (Circles and squares are used simply to make commuting individuals discernible and to depict the hospital workers’ hometowns.) As runs progress, individuals return home at night and go to work and school during the day, a process that iterates indefinitely. That summarizes the social contact process. Meanwhile, the epidemic is running its course.

Smallpox Assumptions

Before we release our index case—the first infective individual—into the population, we assume all individuals to be susceptible; that is, we assume no background of immunity (for example, from previous vaccinations). Susceptible individuals are colored blue. Referring to the timeline, let us assume an individual contracts the infection at day 0. At that point, she/he is colored green. Although the person is infected with smallpox, she/he is asymptomatic and noncontagious for twelve days. However, unless the infected individual is vaccinated within four days of exposure, the vaccine is ineffective.

At the end of day 15, Smallpox rash is finally evident. After twelve hours in this state, individuals are assumed to be hospitalized. After eight more days (day 23 of illness), during which they have a cumulative 30 percent probability of mortality, surviving individuals recover and return to circulation permanently immune to further infection. Dead individuals are colored black and placed in the morgue. Immune individuals are colored white. Contagiousness varies in the course of the infection. Individuals are assumed to be 2 times as infectious during days 16 through 19 as during days 12 through 15. In the final phases of the rash, infectivity returns to the day 12 value, as indicated in figure 2. In the simulated epidemics above, individuals will be colored by their state: healthy (blue), infected (green), contagious early rash (yellow), rash (red), dead (black), or immune (white). At any time, the population will be heterogeneous by health status.

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