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Preventive Veterinary Medicine 80 (2007) 9–23
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The potential role of wild and feral animals
as reservoirs of foot-and-mouth disease
Michael P. Ward a,*, Shawn W. Laffan b, Linda D. Highfield a
a
Department of Veterinary Integrative Biosciences, Texas A&M University College of Veterinary
Medicine & Biomedical Sciences, College Station, TX 77845-4458, USA
b
School of Biological, Earth and Environmental Sciences, University of New South Wales,
Sydney, NSW 2052, Australia
Received 16 May 2006; received in revised form 16 January 2007; accepted 22 January 2007
Abstract
We investigated the potential role of feral pigs and wild deer as FMD reservoirs with a
susceptible–latent–infected–recovered geographic-automata model, using spatially referenced data
from southern Texas, USA. An uncontrolled FMD outbreak initiated in feral pigs and in wild deer
might infect up to 698 (90% prediction interval 181, 1387) and 1557 (823, 2118) cattle and affect an
area of 166 km2 (53, 306) and 455 km2 (301, 588), respectively. The predicted spread of FMD virus
infection was influenced by assumptions we made regarding the number of incursion sites and the
number of neighborhood interactions between herds. Our approach explicitly incorporates the spatial
relationships between domesticated and non-domesticated animal populations, providing a new
framework to explore the impacts, costs, and strategies for the control of foreign animal diseases with
a potential wildlife reservoir.
# 2007 Elsevier B.V. All rights reserved.
Keywords: Foot-and-mouth disease; Simulation model; Spatial model; Geographic-automata; Wildlife; Cattle;
Deer; Feral pig; Texas; USA
* Corresponding author. Tel.: +1 979 862 4819; fax: +1 979 847 8982.
E-mail address: [email protected] (M.P. Ward).
0167-5877/$ – see front matter # 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.prevetmed.2007.01.009
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M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
1. Introduction
Foot-and-mouth disease (FMD) is a highly contagious disease of cloven-hoof animals.
Outbreaks can be economically devastating in countries free of infection (Ferguson et al.,
2001). Estimates of the cost of disease outbreaks (approximated in US$) include $1.6
billion in Taiwan in 1997 (Yang et al., 1997), >$15 billion in the United Kingdom in 2001
(Kao, 2003), $1.5–10 billion in Australia (Gee, 2003), and $14 billion in the United States
(Paarlberg et al., 2002). In recent large outbreaks in Taiwan, the United Kingdom and
Argentina, non-domesticated animal species did not form reservoirs of FMD. If reservoirs
had existed, these countries would not have been able to control FMD in the absence of
surveillance and response programs focused on potential reservoir species, because nondomesticated animal reservoirs potentially reduce the effectiveness of control strategies
(Pinto, 2004; Sutmoller et al., 2000). Lack of effective control might increase the
likelihood of having to use vaccination as a control method in livestock populations,
prolonging the time required to regain FMD-free status and increasing costs to the national
economy. Even in the absence of foreign animal diseases, the control of feral species in
many parts of the world has been a major challenge.
The United States has been free of FMD since the 1920s, when several outbreaks
occurred in California. A 1924 Californian outbreak began in pigs, and infection spread to
cattle and deer across the central portion of the state. It took 2 years to eradicate FMD from
the local deer population in one national park, and 22,000 deer were slaughtered (McVicar
et al., 1974). In areas of the United States where livestock are extensively grazed, potential
interaction with susceptible species such as wild white-tailed deer and feral pigs exists. For
example, wild deer densities in parts of Texas, USA are high, most deer exist on private
land, and deer have formed metapopulations because of extensive land-use changes. Pigs
are highly susceptible to infection by FMD virus and can act as amplifiers in disease
outbreaks, excreting large amounts of the virus (Durand and Mahul, 2000; Pech and
Mcllroy, 1990). The high density of feral pigs in southern Texas (>50 km 2 in areas), for
example, would provide an ideal mechanism for spreading the infection. The potential for
transmission of FMD virus from wildlife to domesticated livestock is heightened in areas
such as Texas where wildlife receive supplemental feed and are hunted for sport.
Although spatial models have been developed to describe the farm-to-farm spread of
FMD virus (Gerbier et al., 2002; Keeling et al., 2001; Morris et al., 2001; Bates et al.,
2003), these models have generally ignored the involvement of feral and wild animal
species. Published models of FMD virus spread that do involve these potential host species
(Dexter, 2003; Pech and Hone, 1988) have generally not included the spatial component of
spread. Artificial life models such as geographic-automata – that explicitly incorporate
spatial relationships – are an alternative modeling approach (Doran and Laffan, 2005).
These models of physical systems treat space and time as discrete units and interactions
occur between local neighbors (Torrens and Benenson, 2005). Geographic-automata are
generalizations of cellular-automata: they are not restricted to a regular lattice of cells
(geographic locations). Each population interacts with neighboring populations based on a
set of rules and states at earlier time steps. The repetitive application of transmission rules
within this local neighborhood allows the replication of complex spatial behavior such as
occurs in disease outbreaks. Geographic-automata models can deal with complex initial
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
11
conditions and geographical boundaries, are conceptually simple, can model complex
spatial interactions, are more general than differential equations and do not depend on
generalized probability distributions derived from observations or hypothetical data.
Following detection of an incursion of FMD virus in a country previously free of
infection, the application of appropriate control measures is a decision that needs to be
made rapidly yet with little current or empirical data. Models can serve not only as
response and decision-making tools but also as avenues to increase awareness and
collaboration with stakeholders (Taylor, 2003).
Southern Texas, bordering Mexico, is a region of concern for the introduction of foreign
animal diseases, particularly through the uncontrolled movement of wild and feral animal
species. It is also generally representative of the many similar eco-climatic regions
throughout the world, and is an ideal model landscape to simulate FMD incursions. In this
research, we developed a susceptible–latent–infected–recovered model of the spread of
FMD virus within and between populations of feral pigs and wild deer, and herds of
domesticated cattle, using a geographic-automata framework and estimated animal
densities. We focused on determining the potential spread of FMD virus prior to detection
in cattle herds in the absence of control measures.
2. Materials and methods
Several factors – including population density and distribution, habitat requirements,
social organization, age structure, home range, and barriers to dispersal – determine
whether an infection will be maintained within feral or wild animal populations, and
therefore whether these populations might act as reservoirs of infection for domesticated
species. These factors must be incorporated into models, either implicitly or explicitly. We
generally assume that all animals within a herd or social organization would rapidly
become infected if FMD virus were to be introduced (Alexandersen et al., 2001; Sørensen
et al., 2000). However, the speed at which FMD virus spreads within herds of livestock
raised in extensive grazing systems – and feral and wild animals within social groups in
these same environments – is poorly understood. The most important factors determining
the propagation and maintenance of FMD virus between susceptible populations (so-called
‘‘inter-herd’’ spread) are their geographical density, connectivity and size (Durand and
Mahul, 2000).
Automata models have been used to investigate the theoretical basis of disease-spread
phenomena, often incorporating the conceptual susceptible–latent–infected–recovered
model framework (Ahmed and Agiza, 1998; Duryea et al., 1999; Filipe and Gibson, 1998;
Johansen, 1996). Application of this class of models to specific disease situations is much
less common (Doran and Laffan, 2005; Benyoussef et al., 1999). Apparently this
geographic-automata approach has not been used previously to model infectious diseases
in non-domesticated animal populations and the spread of infections from these to
livestock.
The study site selected to simulate incursions of FMD virus is an area of southern Texas,
USA, bordering Mexico, consisting of nine counties (Fig. 1A). The annual rainfall ranges
between 750 and 1200 mm and the land area is approximately 24,000 km2. Approximately
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M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
Fig. 1. Spatial distribution of feral pig (B), wild deer (C) and farmed cattle (D), per km2, in southern Texas, USA
(A) derived using land-use data and ecological site carrying capacity from expert opinion.
85,000 domestic cattle (3.5 km 2), 134,000 feral pigs (5.6 km 2) and 395,000 deer
(16.4 km 2) are estimated to be present is this region. The study region is predominantly
rangeland characterized by plains of thorny shrubs and trees, and scattered patches of
palms and subtropical woodlands. The primary vegetation includes species such as
mesquite, acacia, and prickly pear mixed with areas of grasses. Seasonal variation is
characterized by hot, dry summers and mild, moist winters. Livestock production is
predominantly extensive grazing with beef cattle and goats. However, there are pockets of
intensive operations such as feedlots, dairies and small-scale confined swine operations.
We ran a series of models to gain an understanding of FMD virus spread through space
and time. We used a purpose-built geographic-automata model implemented using the Perl
programming language, and a set of baseline model parameters (Table 1). Animal
distributions were represented as number of animals per unit area (km2), displayed as raster
surfaces developed within a geographic information system (Fig. 1). Animals (feral pigs,
wild deer or cattle) within each unit area represented a herd or social group.
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
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Table 1
Baseline parameter values used to simulate an outbreak of foot-and-mouth disease in cattle in southern Texas,
following introduction of infection via feral pig or wild deer populations, using a two-species susceptible–latent–
infected–recovered geographic-automata model
Parameter
Value
Latency, min–max (days)
Cattle
Feral pigs
Deer
4–7
7–13
3–5
Duration of infectiousness, min–max (days)
Cattle
Feral pigs
Deer
2–7
14–17
3–14
Duration of resistance to re-infection, min–max (days)
Minimum daily infection-induced mortality rate (%)
Maximum daily infection-induced mortality rate (%)
Timing of maximum infection-induced mortality during period of infectiousness
Maximum number of neighboring herds with which each infected herd can interact
Maximum distance of neighboring herds within which each infected herd can interact (m)
90–180
0
1.5
0.50
8
2000
Density scaling parameters, min–max
Cattle
Feral pigs
Deer
0–5
0–40
0–30
In the model, herds can pass, sequentially, through four model states: from susceptible
to latent, to infectious, to immune and then to susceptible (recovered) again. These
transitions partly determine the dissemination rate between herds (Garner and Lack, 1995).
As in previous models (Doran and Laffan, 2005; Garner, 1992), the first transition depends
on contact rates between susceptible and infected herds in the previous time step. One of
the main assumptions of this approach is that mixing of animals within herds – but not
between herds – is homogeneous. The probability of transmission from one herd to another
is the product of the relative animal densities of the two herds, modified by the distance
(km) by which they are separated. Transmission probabilities are reduced as neighboring
herds are located further away from each other. The relative densities are calculated by
scaling herd animal densities into the interval [0, 1]: herd animal densities are divided by an
a priori maximum threshold value representing a density above which a herd’s maximum
transmission capacity has been reached. Herds with a density greater than this threshold are
assigned a value of 1. The threshold value used is equivalent to >80% of the cumulative
density of species-specific distributions: 40, 30 and 5 km 2 for feral pig, deer and cattle
distributions, respectively. Relative densities could be calculated using non-linear and
discontinuous functional forms where these are supported by known responses. For each
animal species, we evaluated – within an a priori specified maximum neighborhood
distance and up to a maximum number of neighbors – interactions between each infectious
herd and its neighbors. Interactions between animal species occurred with the herd nearest
to each species-specific infectious herd, within the maximum neighborhood of this
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infectious herd. For baseline simulations, no interactions took place beyond a distance of
2 km from each infected herd, with interactions limited to these nearest eight herds
surrounding each herd-of-interest.
Once a herd is infectious the second, third, and fourth transitions in the model depend on
the specified length of the latent, infectious and immune periods, with values for each herd
for each transition drawn from a uniform random distribution. Sensitivity analysis of the
model results to assumptions regarding duration of the latent and infectious periods, and
the minimum and maximum probability threshold values used, has previously been
undertaken (Doran and Laffan, 2005). Based on study findings, and information from
laboratory and field studies of FMD virus infection in cattle, we used a baseline model in
which latency and infectious periods in cattle were assumed to be uniformly distributed
from 6 to 8 days and from 10 to 18 days, respectively (Garner, 1992; Garner and Lack,
1995). Estimates for these values are unknown in feral pigs. In the baseline model of FMD
virus transmission in feral pigs, latency and infectious periods were assumed to be
uniformly distributed from 4 to 14 days and from 7 to 14 days, respectively (Pech and
Hone, 1988; Pech and Mcllroy, 1990; Garner, 1992; Garner and Lack, 1995). For deer,
corresponding values of 3–5 days and 3–14 days were used (Forman and Gibbs, 1974;
McVicar et al., 1974; Gibbs et al., 1975). For all species, we assumed that infected herds
could become susceptible to infection again after 90–180 days.
To incorporate chance into the model, interactions between an infectious herd and a
susceptible neighbor occurred when a random value from a pseudo-random number
generator (PRNG) was below their joint probability threshold. We used the Mersenne
Twister PRNG (Matsumoto and Nishimura, 1998) to generate all random values in this
research, as recommended by Van Neil and Laffan (2003). This algorithm has a large
period length before the sequence of random values repeats (219,937 1) and good spectral
properties where correlation structures within the random number sequence are very small.
The densities of feral pigs were derived using land-use data and estimated ecological
site carrying capacity (Fig. 1B). We used a similar method to estimate deer density
(Fig. 1C). Cattle densities (Fig. 1D) were based on county estimates of cattle numbers
derived from the United States Department of Agricultural National Agricultural Statistics
Service (2004). These were disaggregated at 1 km resolution, based on land-use
information from the National Land Cover Dataset and stocking rates derived from the
United States Department of Agricultural Natural Resources Conservation Service
Ecological Site (Range) Descriptions (2004). The likely stocking rates of different land-use
classes (open grassland, pastureland, shrubland and forestland) derived from expert
opinion were used to allocate county estimates of cattle numbers to individual
30 m 30 m cells. The fractional density counts were then aggregated to 1 km resolution
and merged. The resulting density surface was expressed as the number of cattle per km2 in
the form of a digital raster surface.
The population data sets were used to simulate the spread of FMD virus within feral pig,
deer and cattle, including the transmission from feral pigs to cattle and from deer to cattle.
By using estimated-population data sets, population density, distribution, and habitat
requirements within the study area were explicitly incorporated in the model. We ran
simulations with only two animal species at a time. In each coupled set (pig–cow, deer–
cow) of scenarios, 1–10 randomly selected feral pig or deer herds were designated the
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
15
primary source of infection to initiate each scenario. We simulated the model to represent a
time period of 100 days. The outcomes of interest were the number of cattle infected and
land area affected, and the time to FMD detection in cattle.
We varied interaction between feral pig herds and between wild deer herds, based on
number of nearest neighboring herds (4, 12 or 28), modifying the maximum distance
parameter as required. We modeled FMD-induced mortality for herds in the infectious
state using piecewise linear functions to specify the minimum and maximum fraction
dead at each simulated time step (day). Values were drawn from a random distribution: in
this study a constant value of zero was used for the minimum, and the maximum rate was
drawn from a triangular (two-piece linear) distribution with zero at the first and last time
steps and a peak at a specified time step. We varied the peak maximum FMD-induced
mortality from 0 to 1.5%, and we set maximum mortality to occur at 25, 50 or 75% of the
infection period. When evaluated over a range of eight time steps (days), for example, a
maximum peak of 1.5% in the middle time step will result in approximately 5% total
mortality. In the absence of empirical data, we assumed the home ranges of feral pigs and
of deer in the study area were within 3.6 km. For each scenario, we simulated 100 model
runs. Each set was characterized using medians and 90% (5 and 95%) prediction
intervals.
3. Results
Cumulative epidemic curves of the predicted number of infected cattle (sum of cattle in
infectious herds), during the period of 100 days after introduction of FMD virus in feral
pigs and wild deer, are shown in Fig. 2. The number of cattle infected following FMD virus
introduction via deer was consistently greater than if introduction was via feral pigs. At
day 100, 2.2 times as many cattle were predicted to be infected from introduction via deer
(1557 cattle; 90% prediction interval 823, 2118) versus via feral pigs (698 cattle; 90%
prediction interval 181, 1387). The corresponding areas predicted to be affected were
455 km2 (90% prediction interval 301, 588) and 166 km2 (90% prediction interval 53,
306), respectively. These areas represented 562 and 205 cattle ranches, respectively. An
example of the spatial distribution of predicted FMD virus infection in cattle, following
infection at either five wild deer or five feral pig herd locations and baseline parameter
values, is shown (Fig. 3).
The effect of systematically increasing the number of herd locations initially infected is
shown in Table 2. In wild deer and feral pig-initiated outbreaks, the predicted number of
infected cattle generally increased as the number of initially infected locations increased.
The greatest increases in outbreak size occurred within the range of one to five FMD virus
incursions. When the introduction of FMD virus was simulated to occur via infected feral
pigs at four or fewer locations, no outbreak occurred in at least 5% of model simulations. In
contrast, infection of deer always resulted in an FMD outbreak, except when only one
location was infected; in this case, an outbreak failed to occur in only 5% of model runs.
The effect of changing assumed home ranges of deer and feral pigs within the study area is
shown in Table 3. Increasing the potential number of neighboring herds increased the size
of the outbreak. The increase was greatest between four and eight interactions, and was
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M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
Fig. 2. Epidemic curves of predicted median number of cattle in southern Texas, USA, infected 100 days
following foot-and-mouth disease virus introduction in feral pig (lower curve) or wild deer (upper curve)
populations, using a two-species susceptible–latent–infected–recovered geographic-automata model. Ninety
percent prediction intervals are indicated.
Fig. 3. Spatial distribution of infected cattle populations in southern Texas, USA following simulated incursions
of foot-and-mouth disease virus in feral pigs (A) or wild deer (B) at five sites, using a two-species susceptible–
latent–infected–recovered geographic-automata model.
more pronounced for deer-initiated outbreaks than for feral pig-initiated outbreaks. The
effect of changing assumed potential FMD-induced mortality within wild deer and feral
pigs is shown in Table 4. Increasing mortality and extending the period of infection during
which the maximum mortality rate occurs had only a minor effect – compared to the effect
of changes in the number of locations infected or the neighborhood interaction assumed –
on decreasing the size of the predicted outbreaks (Table 5).
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
17
Table 2
Predicted size of an outbreak of foot-and-mouth disease in cattle in southern Texas, following introduction of
infection via 1–10 randomly assigned feral pig or wild deer populations, using a two-species susceptible–latent–
infected–recovered geographic-automata model
Incursions
Feral pig-initiated outbreak
Area (km )
Number of cattle
5
1
2
3
4
5
6
7
8
9
10
a
0
0
0
0
181
104
82
163
316
422
Wild deer-initiated outbreak
2
Area (km2)
Number of cattle
50
95
5
50
95
5
50
95
5
50
95
0
221
384
523
698
741
758
1013
923
1173
501
613
727
1129
1387
1294
1485
1607
1666
1819
0
0
0
0
53
45
35
63
85
96
0
61
95
123
166
173
186
231
230
275
109
142
176
255
306
300
348
376
395
416
135
582
586
760
823
1000
1104
1138
1256
1394
668
1061
1180
1317
1557
1666
1761
1800
1904
2030
1005
1517
1783
2031
2118
2311
2378
2329
2465
2712
32
241
240
274
301
319
336
348
371
376
173
350
375
417
455
480
504
508
522
556
280
455
526
560
588
623
640
653
683
712
Each scenario was simulated 100 times, and results represent land area grazed by cattle (km2) and total number of
cattle infected at day 100 post-introduction. The baseline scenario is given in bold.
a
5th, 50th, 95th percentiles.
4. Discussion
In a substantial number of model runs, an outbreak of FMD failed to develop in either wild
deer or feral pigs, and therefore a cattle outbreak did not occur. This was particularly
noticeable when the incursion occurred at four or fewer feral pig herd locations. Our finding
supports the conclusions of Durand and Mahul (2000): if susceptible animal population
densities are low, then FMD virus might become extinct within specific localities before it is
able to infect a critical number of animals. Thus, if FMD virus were introduced at only one or
a few feral pig locations in southern Texas, an outbreak in cattle might not occur. Further
Table 3
Predicted size of an outbreak of foot-and-mouth disease in cattle in southern Texas, following introduction of
infection via five feral pig or five wild deer populations, using a two-species susceptible–latent–infected–
recovered geographic-automata model
Neighbors
4
8
12
28
Feral pig-initiated outbreak
Wild deer-initiated outbreak
Number of cattle
Area (km2)
Area (km2)
5a
50
95
5
50
95
5
50
95
5
50
95
0
181
116
943
270
698
1020
2310
663
1387
1864
3347
0
53
50
201
58
166
255
612
146
306
446
839
435
823
1088
1339
809
1557
1855
2158
1169
2118
2574
3460
171
301
335
326
259
455
523
521
345
588
737
804
Number of cattle
The maximum possible interaction between FMD virus infected populations and neighboring populations was
varied from 4 (1000 m radius; first-order) to 28 (3000 m radius; third-order), to simulate potential feral pig and
wild deer home ranges. Each scenario was simulated 100 times, and results represent land area grazed by cattle
(km2) and total number of cattle infected at day 100 post-introduction. The baseline scenario is given in bold.
a
5th, 50th, 95th percentiles.
18
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
Table 4
Predicted size of an outbreak of foot-and-mouth disease in cattle in southern Texas, following introduction of
infection via five feral pig or wild deer populations, using a two-species susceptible–latent–infected–recovered
geographic-automata model
Mortality
Feral pig-initiated outbreak
Area (km )
Number of cattle
5
0
0.005
0.010
0.015
a
142
197
62
181
Wild deer-initiated outbreak
2
Area (km2)
Number of cattle
50
95
5
50
95
5
50
95
5
50
95
708
691
549
698
1315
1480
1231
1387
47
53
21
53
169
160
130
166
316
313
280
306
799
934
939
823
1533
1505
1460
1557
2059
1952
2175
2118
171
326
335
301
259
521
523
455
345
804
737
588
The minimum FMD-induced mortality rate in feral pig and wild deer populations was varied from nil to 1.5% per
day during the period of infection; maximum FMD-induced mortality, occurring at the mid-point of the period of
infection, was assumed to be 1.5% per day in all simulations. Each scenario was simulated 100 times, and results
represent land area grazed by cattle (km2) and total number of cattle infected at day 100 post-introduction. The
baseline scenario is given in bold.
a
5th, 50th, 95th percentiles.
Table 5
Predicted size of an outbreak of foot-and-mouth disease in cattle in southern Texas, following introduction of
infection via either five feral pig or five wild deer populations, using a two-species susceptible–latent–infected–
recovered geographic-automata model
Period (%)
Feral pig-initiated outbreak
Number of cattle
5
75
50
25
a
0
181
1
Wild deer-initiated outbreak
2
Area (km )
Area (km2)
Number of cattle
50
95
5
50
95
5
50
95
5
50
95
603
698
704
1088
1387
1342
0
53
1
140
166
161
254
306
306
1006
823
884
1567
1557
1449
2106
2118
2081
288
301
261
414
455
408
558
588
566
The time during the period of infection when the maximum mortality rate of 1.5% per day is reached was varied.
Each scenario was simulated 100 times, and results represent land area grazed by cattle (km2) and total number of
cattle infected at day 100 post-introduction. The baseline scenario is given in bold.
a
5th, 50th, 95th percentiles.
investigations are needed to define what conditions (including population density, seasonal
and landscape) might lead to an FMD outbreak in domesticated cattle, when the incursion of
FMD virus occurs via wild or feral animal populations.
The current model is particularly suited to simulating foreign animal diseases in feral
and wild animal populations. Geographic variations are explicitly included within this
modeling framework in a simple manner, rather than needing exhaustive animal-census
data (which is often unavailable or unreliable for wild or feral species) or complex
mathematical structures (Kao, 2002). This model structure also means that landscape
factors – such as soil, water availability, vegetation, and topography – can be easily
included. In addition, modes of disease-spread other than direct contact between
neighboring herds can be incorporated. For example, longer-distance contact between
cattle herds can be included by incorporating distance matrices (Ferguson et al., 2001;
Bates et al., 2001; Perez et al., 2004) and a distance-weighted random function. Empirical
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
19
data describing the probability distribution of such direct contacts, for example herd-toherd and herd-to-auction contacts, can be included as they become available. Windborne
spread of FMD virus could easily be included where relevant (Alexandersen et al., 2001;
Sørensen et al., 2000; Cannon and Garner, 1999; Mikkelsen et al., 2003). Finally, given
various assumptions, it is possible to simulate the model in reverse to identify potential foci
of FMD virus introduction. This ‘‘forensic epidemiology’’ capability would assist efforts to
define pathways and vulnerabilities. Such refinements of this model system depend on the
aims of analysis and the level of prediction desired. For broad insights into the possible
origins, potential magnitude and effects of proposed mitigation strategies, we believe the
current model formulation is likely to be adequate.
The model used to simulate FMD virus incursions focused on local spread of infection.
This is a reasonable assumption for wildlife populations: in the absence of human
interventions, feral pigs and deer are very unlikely to move outside their local home range.
However, we made the same assumption in this model regarding spread of infection within
cattle populations. Compared to some other epidemiologic models of FMD virus spread
among the wild-animal component – which do not consider spatial relationships explicitly
– this represents herd-to-herd spread (for example, across ‘‘fencelines’’, windborne,
environmental and herd-to-herd direct contact). Longer-distance contact – for example,
direct contact via transportation of cattle and indirect contact, such as veterinary personnel
visiting multiple farms – were not modeled in this case because we were focusing on the
wild- and unfenced-animal component. Although local disease-spread was apparently
responsible for about 80–90% of infected herds in the 1967 and 2001 outbreaks of FMD in
the United Kingdom (Gibbens et al., 2001; Sanson et al., 2006), it would be useful to focus
future development of the automata-model system on incorporating longer-distance spread
mechanisms, because these are important in the geographical (rather than quantitative)
spread of the infection in countries free of infection (Ferguson et al., 2001). Such spread
could be modeled using kernel distributions based on known trends in direct and indirect
contact patterns within the study region.
The need to use spatially explicit models to simulate the spread of FMD virus has been
recognized (Ferguson et al., 2001; Kao, 2003). Capturing spatial heterogeneity is probably
the major challenge in realistically representing FMD virus spread through a landscape
(Ferguson et al., 2001). The most common method of estimating the density of animal
species across the landscape is generally based on land-use characteristics and estimated
carrying capacity. For domestic livestock the usual starting point is census data produced at
a local-government area level. Estimating distributions of feral and wild animal
populations is more problematic, because census data is generally unavailable and spatial
processing are often based on limited expert opinion, surveys and other indirect
observations. To enable more accurate modeling of the impact of the introduction of
foreign animal disease infections into feral and wild animal populations, better estimates of
the distributions of these species are required. In addition, such distributions need to be
seasonally dynamic, because these species are particularly subject to variations in climate
and resources. Such temporal dependency can have a profound impact on the spread of
infections within feral and wild animal populations, and hence, into domesticated animal
populations of interest (Doran and Laffan, 2005). Another area of data uncertainty is the
assumed home range of feral and wild animal species.
20
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
It is important in disease modeling to estimate the threshold density of susceptible
animal species below which the infection would die out and above which it would become
well established and persist indefinitely (Pech and Mcllroy, 1990; Caley, 1997). The
interaction of feral- and wildlife-densities and seasonal variation in the spread of FMD
virus is a phenomenon with both theoretical (Doran and Laffan, 2005) and observed
(Sutmoller et al., 2000) relevance. However, the actual interactions between feral and wild
animal species and domesticated livestock – and therefore the potential for the infection to
spread between these populations – are likely to vary substantially between regions,
species and seasons. Spatial fragmentation – in which herds of livestock under the same
ownership are managed on separate, disjoint land parcels – is important in the spread of
FMD virus within cattle populations (Kao, 2001). Spatial fragmentation of wild and feral
animal populations (for example the presence of barriers such as urban areas and unsuitable
habitat) is probably at least as important in disease-spread. Our assumption that wild deer
or feral pigs were as likely to interact with domesticated cattle as with each other, and
thereby spread FMD virus into the domesticated cattle population, was fundamental to the
functioning of the model. This assumption is reasonable when susceptible species share the
same habitat (Pech and Mcllroy, 1990; Bastos et al., 2000). Feral pigs will come into
contact with livestock at water sources. Contact between wild deer and domesticated cattle
in Texas is less certain. Transmission of Mycobacterium bovis between deer and cattle in
Michigan demonstrates that such a spread pathway might exist (Palmer et al., 2002). An
issue that needs to be considered in future model development is potential FMD virus
transmission between feral pigs and wild deer. Although these species likely occupy
different ecological niches within the study area, FMD virus transmission might occur via
contaminated environmental sites such as water sources or pastures. The effect of
infection-induced mortality in feral pigs and deer simulated in the current study was
negligible. With water points serving as critical contact points within an environment such
as southern Texas, it is unlikely that morbidity or mortality in feral or wild populations will
slow the progression of an FMD outbreak.
5. Conclusions
The geographic-automata model of FMD virus spread provides a framework for
exploring the potential impact of FMD virus incursions via wild deer and feral pigs. Our
geographic-automata model predicted that an FMD outbreak in domestic cattle in southern
Texas is likely to occur if there are multiple FMD virus incursions via wild deer and feral
pigs. Such an outbreak could continue for several weeks before being detected, at which
time a large land area could be affected. Wild deer and feral pigs might both amplify
disease-spread and form a potential reservoir of FMD virus infection in this region.
Acknowledgements
We gratefully acknowledge the assistance of R. Srinivasan and J. Jacobs (Spatial
Sciences Laboratory, Texas A&M University) in preparing spatial distributions of cattle,
M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9–23
21
feral pigs and wild deer used in this study; and partial funding support for this study from
the United States Department of Homeland Security via the National Center of Excellence
for Foreign and Zoonotic Disease Defense, Texas A&M University.
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