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extent on spatially derived information. David et al. (1982) proposed a simple model
of vulpine rabies that included much of the same biological components we utilize
in our model: reproduction, dispersal, and spatial distribution. The spatial compo-
nent of the David model is not linked to habitat resources however, and the display
mechanisms of the SME offer a much more explicit depiction of possible scenarios.
Vulpine rabies poses a serious problem in Europe due to increasingly large fox
populations and its zoonotic potential, increasing the probability of human contact
in heavily populated areas
7
. Fox densities in Bristol, England for example, range
from 1.82 to 3.64 foxes per square kilometer over a home range size of 0.45 square
kilometers
8
. In comparison, densities in the United States are lower: 0.15 foxes per
square kilometer over a larger home range size of 9.6 square kilometers
9
.Inthe
United States, rabies in the red fox,
Vulpes vulpes
, has reached epidemic levels in
western Alaska and northern New York.
Previous linear models using data collected from European fox populations show
a dramatic decrease in the number of foxes when rabies is introduced into a healthy
population. These decreases reduce the population below an apparent disease thresh-
old, and the disease is shown to die out
10
. These models typically demonstrate an
inversely proportional relationship between infected and healthy foxes when rabies
is first introduced into the population. As the disease becomes established, the num-
ber of infectious foxes increases and the susceptible fox population decreases
11
.
Murray (1987) describes these density decreases as “breaks,” where the population
becomes too low for the disease to persist in the environment. Gardner et al. (1990)
concluded that the disease could be eradicated from a fox population when fox num-
bers are reduced to a critical level below the carrying capacity. Most rabid epizootics
do not drive fox populations to extinction however.
Several models demonstrated that both healthy and infected fox populations sta-
bilized over a period of 20 to 30 years
12
. At this time, healthy populations reached
levels that were half of the total carrying capacity and infected foxes were reduced
below 10 percent of the total population
13
. Other models have concluded that rabies,
a cyclical virus, can reemerge between 3.9 to 5 years after a period of quiescence
14
.
We concluded that vulpine rabies could be viewed as a cyclical, nonlinear dis-
ease. When a susceptible population becomes infected, it decreases the healthy pop-
ulation but does not eliminate it. When the population rebuilds to a critical mass the
disease is then able to reestablish, and the cycle begins again. In this way, vulpine
7
Steck, F. and A. Wandeler. 1980. Epidemiologic Reviews 2 71-96.
8
Trewhella, W.J., S. Harris, and F.E. McAllister. 1988. Journal of Applied Ecology 25 423-434.
9
Storm, G.L., R.D. Andrews, R.L. Phillips, R.A. Bishop, D.B. Siniff, and J.R. Tester. 1976.
Wildlife Monograph 49 1-81.
10
White, et al. 1995; Murray, et al. 1986; Gardner, et al. 1990; Bacon and MacDonald. 1980; and:
Murray, J.D. 1987. American Scientist 75 280-284.
11
Murray, et al. 1986; Murray 1987; Gardner, et al. 1990.
12
Gardner, et al. 1990; R.M. Anderson, H.C. Jackson, R.M. May, and A.M. Smith. 1981. Nature
289 765-771.
13
Murray 1987; Anderson, et al. 1981.
14
Murray et al. 1986; Gardner et al. 1990.
