Contemporary Mathematics
Volume 410, 2006
The Impact of Environmental Variation on Hantavirus
Infection in Rodents
Linda J. S. Allen, Edward J. Allen, and Colleen B. Jonsson
ABSTRACT. Hantaviruses are rodent-borne zoonotic agents that cause han-
tavirus pulmonary syndrome and hemorrhagic fever with renal syndrome in
humans. Severe changes in environmental conditions have been linked to out-
breaks of hantavirus in rodent and human populations. We formulate han-
tavirus models for rodents based on a male/female SEIR epidemic model. In
the models, the environmental carrying capacity has two sources of variation,
seasonal and random. Deterministic and stochastic SEIR epidemic models are
formulated and numerically simulated. The computational simulations using
the models produce realistic dynamics of hantavirus outbreaks.
1. Introduction
Hantaviruses are rodent-borne zoonotic agents that result in two different dis-
eases when transmitted to humans: hantavirus pulmonary syndrome-HPS in the
Americas and hemorrhagic fever with renal syndrome-HFRS in Europe and Asia
[23].
Both illnesses are acute and proceed with either cardiopulmonary complica-
tions (HPS) or renal complications (HFRS). Human infection occurs through the
inhalation of infectious, aerosolized excreta and it has also been reported, albeit
rarely, that the virus can be transmitted from the bite of an infectious rodent
[7, 12].
Close to thirty different hantaviruses are recognized throughout the world
but not all them are pathogenic to humans
[20, 23].
Each hantavirus is gener-
ally maintained in a single rodent reservoir species
[23].
Four hantaviruses in the
United States are known to be pathogenic to humans: Sin Nombre virus carried
by the deer mouse (Peromyscus maniculatus)
[20],
New York virus carried by the
white-footed mouse (Peromyscus leucopus)
[24],
Black Creek Canal virus carried
by the cotton rat (Sigmodon hispidus)
[14],
and Bayou virus carried by the rice rat
( Oryzomys palustris) [18, 19].
Outbreaks of hantavirus in rodent and human populations have been associ-
ated with increased rodent densities. HPS was first identified in 1993 after it was
confirmed that the deaths of several people in New Mexico were attributed to a
newly named virus, Sin Nombre virus
[23].
Additional studies found that rodent
densities increased from less than one deer mouse per hectare prior to 1991 to 20
1991
Mathematics Subject Classification.
Primary 92D30; Secondary 60H10.
Key words and phrases.
epidemic, hantavirus, stochastic differential equation.
LJSA and CBJ were supported in part by a grant from the Fogarty International Center
#
ROl TW006986-02 under the NIH NSF Ecology of Infectious Diseases initiative.
@2006 American Mathematical Society
http://dx.doi.org/10.1090/conm/410/07717
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