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unknown parameter, the “Bite Coefficient”—the parameter that multiplies the prod-
uct of the sick and healthy population,—was adjusted to give this rate of spread.
Moving from left to right, the initial map depicts the state of the system at
present—that is, the initial number of healthy foxes across the state of Illinois—
black areas are indicative of cells with low fox populations. The initial map also
gives the reader an indication of the scale of the typical fox home range (each pixel
in the picture represents the 6-square-mile cell size in the model) and the complexity
of the computational problems involved.
The second map shows the incipient waves of disease that are created by the
introduction of just three rabid foxes in the first month of the model run (these three
rabid foxes are introduced into the model only once). Easily visible at the eastern
border of the state, the dark areas in this map are areas of minimal fox survival. The
map displays the dramatic impact that rabies can have on a healthy population.
After 2.6 years, the advance of the first wave of disease is clearly recognized. In
the third map, the disease has spread halfway across the state, and is calculated to
be advancing at about 24 miles per year. Also visible at this point is the reintroduc-
tion of the disease at its origin. This wave phenomena has also been noted in the
construction of other dynamic epidemic disease models
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.
The fourth panel (7 years) describes a mature disease, and the wave of disease is
in its epizootic stage. The traveling wave is continuously repeated, with each suc-
cessive wave peak of the disease more spatially diffused in the east-west direction
of the advance. This traveling epizootic wave can be seen as the slow cycle on the
annual cycle in Figure 15.9. The successive waves develop because the disease does
not eradicate the entire population and some of the disease remains viable in the sur-
viving foxes. The disease is unable to move at this point, however, because the pop-
ulation of available foxes is not large enough to encourage much migration. Once
the population builds to critical mass however, migratory behavior resumes and the
disease begins to spread again. Perhaps augmented by the occasional healthy im-
migrant from Indiana, they re-grow to a substantial healthy population but again
are infected by the strays heading east from the disease front. The epidemic builds
more slowly in each ensuing repetition, since it begins with a smaller healthy popu-
lation each time. Finally, although difficult to display in a static format, the disease
becomes endemic—without epidemic pulse. In this stage, the number of diseased
foxes in the state is nearly constant (5,586).
Mapped images are extremely powerful for displaying the spatial interactions
and dynamic movement of the rabies disease. Although difficult to represent in sta-
tic format, the animations of these images provide a strong case for the use of spa-
tial simulation modeling for numerous applications. The mapped images will also
become important in future work regarding the most efficient disease control strate-
gies. A more quantified approach for displaying the results of our calibrated model
runs follows.
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Hannon and Ruth 1997.
