The potential role of wild and feral animals as reservoirs of foot-and-mouth disease

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1 Preventive Veterinary Medicine 80 (2007) 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 , 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 km 2 (53, 306) and 455 km 2 (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.: ; fax: address: mward@cvm.tamu.edu (M.P. Ward) /$ see front matter # 2007 Elsevier B.V. All rights reserved. doi: /j.prevetmed

2 10 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 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), $ 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

3 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 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 km 2. Approximately

4 12 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 km 2, 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 (km 2 ), 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.

5 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 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 4 7 Feral pigs 7 13 Deer 3 5 Duration of infectiousness, min max (days) Cattle 2 7 Feral pigs Deer 3 14 Duration of resistance to re-infection, min max (days) Minimum daily infection-induced mortality rate (%) 0 Maximum daily infection-induced mortality rate (%) 1.5 Timing of maximum infection-induced mortality during period of infectiousness 0.50 Maximum number of neighboring herds with which each infected herd can interact 8 Maximum distance of neighboring herds within which each infected herd can interact (m) 2000 Density scaling parameters, min max Cattle 0 5 Feral pigs 0 40 Deer 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

6 14 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 9 23 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 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 (2 19,937 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 km 2 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

7 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 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 pigsandwilddeer,areshowninfig. 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 km 2 (90% prediction interval 301, 588) and 166 km 2 (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

8 16 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).

9 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 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 Wild deer-initiated outbreak Number of cattle Area (km 2 ) Number of cattle Area (km 2 ) 5 a Each scenario was simulated 100 times, and results represent land area grazed by cattle (km 2 ) 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 Feral pig-initiated outbreak Wild deer-initiated outbreak Number of cattle Area (km 2 ) Number of cattle Area (km 2 ) 5 a 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 (km 2 ) and total number of cattle infected at day 100 post-introduction. The baseline scenario is given in bold. a 5th, 50th, 95th percentiles.

10 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 Wild deer-initiated outbreak Number of cattle Area (km 2 ) Number of cattle Area (km 2 ) 5 a 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 (km 2 ) 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 Wild deer-initiated outbreak Number of cattle Area (km 2 ) Number of cattle Area (km 2 ) 5 a 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 (km 2 ) 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

11 M.P. Ward et al. / Preventive Veterinary Medicine 80 (2007) 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.

12 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,

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