Use of the scan statistic on disaggregated province-based data: foot-and-mouth disease in Iran

The spatial scan statistic was applied to density-smoothed data that approximated the spatial distribution within the area and reduced the potential bias produced when location data have been aggregated for large areas. The method is illustrated, using data on the location of foot-and-mouth disease (FMD) outbreaks in Iran. Data examined were 4477 FMD outbreaks reported on a per province basis between June 1996 and September 2003. A kernel density of the outbreak locations was estimated, using a fixed radius and the centroid of each province as the designated location of all cases reported for the province. The radius that produced a density map with the highest correlation with expert opinion was 4° (latitude/longitude). Livestock density was used as a proxy for the underlying population at risk of acquiring FMD. Livestock and outbreak density maps were overlain to obtain the number of outbreaks and livestock in each of 15,599 cells covering the mapped surface of the country. A spatial scan statistic was applied to the density-smoothed data assuming that the outbreaks had a Poisson distribution. Results were compared with those obtained using a spatial scan statistic on provincially aggregated data. Application of the spatial scan statistic on the density-smoothed data allowed identification of clusters (P < 0.01) related more to the actual geographic distribution of cases (expert opinion) and of animals at risk, than to the distribution of the provinces. Significant clusters of FMD were identified that coincided with roads, neighboring countries, and high-density population areas, suggesting that the region may represent a route for cross-continent transmission of FMD.     

Representation of animal distributions in space: how geostatistical estimates impact simulation modeling of foot-and-mouth disease spread

Modeling potential disease spread in wildlife populations is important for predicting, responding to and recovering from a foreign animal disease incursion. To make spatial epidemic predictions, the target animal species of interest must first be represented in space. We conducted a series of simulation experiments to determine how estimates of the spatial distribution of white-tailed deer impact the predicted magnitude and distribution of foot-and-mouth disease (FMD) outbreaks. Outbreaks were simulated using a susceptible-infected-recovered geographic automata model. The study region was a 9-county area (24 000 km(2)) of southern Texas. Methods used for creating deer distributions included dasymetric mapping, kriging and remotely sensed image analysis. The magnitudes and distributions of the predicted outbreaks were evaluated by comparing the median number of deer infected and median area affected (km(2)), respectively. The methods were further evaluated for similar predictive power by comparing the model predicted outputs with unweighted pair group method with arithmetic mean (UPGMA) clustering. There were significant differences in the estimated number of deer in the study region, based on the geostatistical estimation procedure used (range: 385 939-768 493). There were also substantial differences in the predicted magnitude of the FMD outbreaks (range: 1 563-8 896) and land area affected (range: 56-447 km(2)) for the different estimated animal distributions. UPGMA clustering indicated there were two main groups of distributions, and one outlier. We recommend that one distribution from each of these two groups be used to model the range of possible outbreaks. Methods included in cluster 1 (such as county-level disaggregation) could be used in conjunction with any of the methods in cluster 2, which included kriging, NDVI split by ecoregion, or disaggregation at the regional level, to represent the variability in the model predicted outbreak distributions. How animal populations are represented needs to be considered in all spatial disease spread models.     

A decision-tree to optimise control measures during the early stage of a foot-and-mouth disease epidemic

A decision-tree was developed to support decision making on control measures during the first days after the declaration of an outbreak of foot-and-mouth disease (FMD). The objective of the tree was to minimise direct costs and export losses of FMD epidemics under several scenarios based on livestock and herd density in the outbreak region, the possibility of airborne spread, and the time between first infection and first detection. The starting point of the tree was an epidemiological model based on a deterministic susceptible–infectious–recovered approach. The effect of four control strategies on FMD dynamics was modelled. In addition to the standard control strategy of stamping out and culling of high-risk contact herds, strategies involving ring culling within 1 km of an infected herd, ring-vaccination within 1 km of an infected herd, and ring-vaccination within 3 km of an infected herd were assessed. An economic model converted outbreak and control effects of farming and processing operations into estimates of direct costs and export losses. Ring-vaccination is the economically optimal control strategy for densely populated livestock areas whereas ring culling is the economically optimal control strategy for sparsely populated livestock areas.     

Potential impact of an introduction of foot-and-mouth disease into the California State Fair

OBJECTIVE: To estimate the potential spread of foot-and-mouth disease (FMD) if infected livestock had been exhibited at the 2005 California State Fair. DESIGN: Epidemic model. ANIMALS: Dairy cattle, dairy goats, and pygmy goats exhibited between August 24 and August 28 by 195 exhibitors. PROCEDURES: 2 stochastic models were used to simulate epidemics of FMD that might originate from 1, 3, 5, 7, or 10 index cases at the state fair. Data obtained from state fair exhibitors were used to determine the spatial distribution and types of herds to which livestock visiting the state fair returned. RESULTS: Mean estimated numbers of latently infected animals on day 5 were 12.3 and 75.9, respectively, when it was assumed that there were 1 and 10 index cases. Regardless of the number of index cases, mean estimated numbers of subclinically infected and clinically infected animals were low throughout the 5-day study period. Mean estimated duration of the resulting epidemic ranged from 111 to 155 days, mean number of infected premises ranged from 33 to 244, and mean probability that at least 1 animal that became infected with FMD would subsequently leave the state ranged from 28% to 96% as the number of index cases increased from 1 to 10, respectively. CONCLUSIONS AND CLINICAL RELEVANCE: Results suggested that following introduction of FMD at the California State Fair, infection would likely go undetected until after animals left the fair and that the subsequent outbreak would spread rapidly.     

Characterisation of a SAT-1 outbreak of foot-and-mouth disease in captive African buffalo (Syncerus caffer): clinical symptoms, genetic characterisation and phylogenetic comparison of outbreak isolates

African buffalo (Syncerus caffer) play an important role in the maintenance of the SAT types of foot-and-mouth disease (FMD) in southern Africa. These long-term carriers mostly become sub-clinically infected, maintaining the disease and posing a threat to other susceptible wildlife and domestic species. During an unrelated bovine tuberculosis experiment using captive buffalo in the Kruger National Park (KNP), an outbreak of SAT-1 occurred and was further investigated. The clinical signs were recorded and all animals demonstrated significant weight loss and lymphopenia that lasted 100 days. In addition, the mean cell volume and mean cell haemoglobin values were significantly higher than before the outbreak started. Virus was isolated from several buffalo over a period of 167 days post infection and the molecular clock estimated to be 3 × 10⁻⁵ nucleotide substitutions per site per day. Seven amino acid changes occurred of which four occurred in hypervariable regions previously described for SAT-1. The genetic relationship of the outbreak virus was compared to buffalo viruses previously obtained from the KNP but the phylogeny was largely unresolved, therefore the relationship of this outbreak strain to others isolated from the KNP remains unclear.     

Potential revenue impact of an outbreak of foot-and-mouth disease in the United States

OBJECTIVE: To estimate potential revenue impacts of an outbreak of foot-and-mouth disease (FMD) in the United States similar to the outbreak in the United Kingdom during 2001. DESIGN: Economic analysis successively incorporating quarantine and slaughter of animals, an export ban, and consumer fears about the disease were used to determine the combined impact. SAMPLE POPULATION: Secondary data for cattle, swine, lambs, poultry, and products of these animals. PROCEDURE: Data for 1999 were used to calibrate a model for the US agricultural sector. Removal of animals, similar to that observed in the United Kingdom, was introduced, along with a ban on exportation of livestock, red meat, and dairy products and a reduction and shift in consumption of red meat in the United States. RESULTS: The largest impacts on farm income of an FMD outbreak were from the loss of export markets and reductions in domestic demand arising from consumer fears, not from removal of infected animals. These elements could cause an estimated decrease of $14 billion (9.5%) in US farm income. Losses in gross revenue for each sector were estimated to be the following: live swine, -34%; pork, -24%; live cattle -17%; beef, -20%; milk, -16%; live lambs and sheep, -14%; lamb and sheep meat, -10%; forage, -15%; and soybean meal, -7%. CONCLUSIONS AND CLINICAL RELEVANCE: Procedures to contain an outbreak of FMD to specific regions and allow maintenance of FMD-free exports and efforts to educate consumers about health risks are critical to mitigating adverse economic impacts of an FMD outbreak.     

Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model

We describe an approach to modelling the spatio-temporal spread of foot and mouth disease through feral animal and unfenced livestock populations. We used a susceptible-infected-recovered model, implemented in a cellular automata framework, to assess the spread of FMD across two regions of Queensland, Australia. Following a sensitivity analysis on the infectious states, scenario analyses were conducted using feral pigs only as the susceptible population, and then with the addition of livestock, and initiated in the wet season and in the dry season. The results indicate that, depending on the season the outbreak is initiated, and without the implementation of control measures, an outbreak of Foot and Mouth Disease around Winton could continue unchecked, while an outbreak around Cape York may die out naturally. The approach explicitly incorporates the spatial relationships between the populations through which the disease spreads and provides a framework by which the spread of disease outbreaks can be explored through varying the model parameters. It highlights the emergence and importance of spatio-temporal patterns, something that previous modelling of FMD in feral animal and unfenced livestock populations has lacked.     

A comparison of predictions made by three simulation models of foot-and-mouth disease

AIMS: To describe results of a relative validation exercise using the three simulation models of foot-and-mouth disease (FMD) in use by the quadrilateral countries (QUADS; Australia, Canada, New Zealand, and United States of America; USA). METHODS: A hypothetical population of farms was constructed and, following the introduction of an FMD-like disease into a single farm, spread of disease was simulated using each of the three FMD simulation models used by the QUADS countries. A series of 11 scenarios was developed to systematically evaluate the key processes of disease transmission and control used by each of the three models. The predicted number of infected units and the size of predicted outbreak areas for each scenario and each model were compared using the Kruskal-Wallis test. Agreement among the three models in terms of geographical areas predicted to become infected were quantified using Fleiss' Kappa statistic. RESULTS: Although there were statistically significant differences in model outputs in terms of the numbers of units predicted to become infected, the temporal onset of infection throughout the simulation period, and the spatial distribution of infected units, these differences were generally small and would have resulted in the same (or similar) management decisions being adopted in each case. CONCLUSIONS: Agreement among the three models in terms of the numbers of premises predicted to become infected, the temporal onset of infection throughout the simulation period, and the spatial distribution of infected premises provides evidence that each of the model developers are consistent in their approach to simulating the spread of disease throughout a population of susceptible individuals. This consistency implies that the assumptions taken by each development team are appropriate, which in turn serves to increase end-user confidence in model predictions. CLINICAL RELEVANCE: Relative validation is one of a number of steps that can be undertaken to increase end-user confidence in predictions made by infectious disease models.     

A comparison of predictions made by three simulation models of foot-and-mouth disease

AIMS: To describe results of a relative validation exercise using the three simulation models of foot-and-mouth disease (FMD) in use by the quadrilateral countries (QUADS; Australia, Canada, New Zealand, and United States of America; USA).

METHODS: A hypothetical population of farms was constructed and, following the introduction of an FMD-like disease into a single farm, spread of disease was simulated using each of the three FMD simulation models used by the QUADS countries. A series of 11 scenarios was developed to systematically evaluate the key processes of disease transmission and control used by each of the three models. The predicted number of infected units and the size of predicted outbreak areas for each scenario and each model were compared using the Kruskal-Wallis test. Agreement among the three models in terms of geographical areas predicted to become infected were quantified using Fleiss' Kappa statistic.

RESULTS: Although there were statistically significant differences in model outputs in terms of the numbers of units predicted to become infected, the temporal onset of infection throughout the simulation period, and the spatial distribution of infected units, these differences were generally small and would have resulted in the same (or similar) management decisions being adopted in each case.

CONCLUSIONS: Agreement among the three models in terms of the numbers of premises predicted to become infected, the temporal onset of infection throughout the simulation period, and the spatial distribution of infected premises provides evidence that each of the model developers are consistent in their approach to simulating the spread of disease throughout a population of susceptible individuals. This consistency implies that the assumptions taken by each development team are appropriate, which in turn serves to increase end-user confidence in model predictions.

CLINICAL RELEVANCE: Relative validation is one of a number of steps that can be undertaken to increase end-user confidence in predictions made by infectious disease models.     

Factors associated with spatial clustering of foot-and-mouth disease in Nepal

The purpose of this study was to quantify associations between hypothesized epidemiological factors and the spatial distribution of foot-and-mouth disease (FMD) in Nepal. Spatial clustering of reports of at least one FMD case by Village Development Committee (VDC) in 2004 was examined by use of the spatial scan statistic. A Bayesian Poisson multivariate regression model was used to quantify the association between the number of reports and 25 factors hypothesized to be associated with FMD risk. The spatial scan statistic identified (P < 0.01) two clusters of FMD reports. Large numbers of people, buffalo, and animal technicians in a district were associated with an elevated risk of a VDC reporting ≥1 FMD case. The knowledge of high-risk areas and factors associated with the risk of FMD in Nepal could be applied in future disease control programs.     

The impact of seasonal variability in wildlife populations on the predicted spread of foot and mouth disease

Modeling potential disease spread in wildlife populations is important for predicting, responding to and recovering from a foreign animal disease incursion such as foot and mouth disease (FMD). We conducted a series of simulation experiments to determine how seasonal estimates of the spatial distribution of white-tailed deer impact the predicted magnitude and distribution of potential FMD outbreaks. Outbreaks were simulated in a study area comprising two distinct ecoregions in South Texas, USA, using a susceptible-latent-infectious-resistant geographic automata model (Sirca). Seasonal deer distributions were estimated by spatial autoregressive lag models and the normalized difference vegetation index. Significant (P < 0.0001) differences in both the median predicted number of deer infected and number of herds infected were found both between seasons and between ecoregions. Larger outbreaks occurred in winter within the higher deer-density ecoregion, whereas larger outbreaks occurred in summer and fall within the lower deer-density ecoregion. Results of this simulation study suggest that the outcome of an FMD incursion in a population of wildlife would depend on the density of the population infected and when during the year the incursion occurs. It is likely that such effects would be seen for FMD incursions in other regions and countries, and for other diseases, in cases in which a potential wildlife reservoir exists. Study findings indicate that the design of a mitigation strategy needs to take into account population and seasonal characteristics.     

Risk factors for foot-and-mouth disease in Zambia, 1981–2012

The aim of this study was to describe the spatial distribution of foot-and-mouth disease (FMD) outbreaks in Zambia for the period January 1981–December 2012 and to quantify the association between geographical features (proximity to roads, national parks, wetland areas) and the spatial distribution of FMD using a Poisson point process model.     

Effectiveness of vaccines and vaccination programs for the control of foot-and-mouth disease in Uganda, 2001–2010

Foot-and-mouth disease (FMD) is a highly contagious disease of cloven-hoofed animals. In Uganda, FMD outbreaks are mainly controlled by ring vaccination and restriction of animal movements. Vaccination stimulates immunity and prevents animals from developing clinical signs which include lameness, inappetence, and decreased production. Ring vaccination and restriction of animal movements have, however, not successfully controlled FMD in Uganda and outbreaks reoccur annually. The objective of this study was to review the use of FMD virus (FMDV) vaccines and assess the effectiveness of vaccination programs for controlling FMD in Uganda (2001–2010), using retrospective data. FMD vaccine distribution patterns in Uganda (2001–2010) matched occurrence of outbreaks with districts reporting the highest number of outbreaks also receiving the largest quantity of vaccines. This was possibly due to “fire brigade” response of vaccinating animals after outbreaks have been reported. On average, only 10.3 % of cattle within districts that reported outbreaks during the study period were vaccinated. The average minimum time between onset of outbreaks and vaccination was 7.5 weeks, while the annual cost of FMDV vaccines used ranged from US $58,000 to 1,088,820. Between 2001 and 2010, serotyping of FMD virus was done in only 9/121 FMD outbreaks, and there is no evidence that vaccine matching or vaccine potency tests have been done in Uganda. The probability of FMDV vaccine and outbreak mismatch, the delayed response to outbreaks through vaccination, and the high costs associated with importation of FMDV vaccines could be reduced if virus serotyping and subtyping as well as vaccine matching were regularly done, and the results were considered for vaccine manufacture.     

Description of an epidemic simulation model for use in evaluating strategies to control an outbreak of foot-and-mouth disease

OBJECTIVE: To develop a spatial epidemic model to simulate intraherd and interherd transmission of foot-and-mouth disease (FMD) virus. SAMPLE POPULATION: 2,238 herds, representing beef, dairy, swine, goats, and sheep, and 5 sale yards located in Fresno, Kings, and Tulare counties of California. PROCEDURE: Using Monte-Carlo simulations, a spatial stochastic epidemic simulation model was developed to identify new herds that would acquire FMD following random selection of an index herd and to assess progression of an epidemic after implementation of mandatory control strategies. RESULTS: The model included species-specific transition periods for FMD infection, locations of herds, rates of direct and indirect contacts among herds, and probability distributions derived from expert opinions on probabilities of transmission by direct and indirect contact, as well as reduction in contact following implementation of restrictions on movements in designated infected areas and surveillance zones. Models of supplemental control programs included slaughter of all animals within a specified distance of infected herds, slaughter of only high-risk animals identified by use of a model simulation, and vaccination of all animals within a 5- to 50-km radius of infected herds. CONCLUSIONS AND CLINICAL RELEVANCE: The FMD model represents a tool for use in planning biosecurity and emergency-response programs and in comparing potential benefits of various strategies for control and eradication of FMD appropriate for specific populations.     

A stochastic-modeling evaluation of the foot-and-mouth-disease survey conducted after the outbreak in Miyazaki, Japan in 2000

When foot-and-mouth-disease (FMD) was identified in Miyazaki prefecture in March 2000, Japan conducted an intensive serological and clinical survey in the areas surrounding the index herd. As a result of the survey during the 21 days of the movement-restriction period, two infected herds were detected and destroyed; there were no other cases in the months that followed. To evaluate the survey used for screening the disease-control area and surveillance area, we estimated the herd-level sensitivity of the survey (HSe) through a spreadsheet model using Monte-Carlo methods. The Reed-Frost model was incorporated to simulate the spread of FMD within an infected herd. In the simulations, 4, 8 and 12 effective-contact scenarios during the 5-day period were examined. The estimated HSes of serological tests (HSeE) were 71.0, 75.3 and 76.3% under the 4, 8 and 12 contact scenarios, respectively. The sensitivity analysis showed that increasing the number of contacts beyond 12 did not improve HSeE, but increasing the number of sampled animals and delaying the dates of sampling did raise HSeEs. Small herd size in the outbreak area (>80% of herds have <20 animals) seems to have helped in maintaining HSeE relatively high, although the serological inspection was carried out before sero-positive animals had a chance to increase in infected herds. The estimated herd-level specificity of serological tests (HSpE) was 98.6%. This HSpE predicted 224 false-positive herds (5th percentile estimate was 200 and 95th percentile was 249), which proved close to the 232 false-positive herds actually observed. The combined-test herd-level sensitivity (serological and clinical inspections combined; CTHSe), averaged 85.5, 87.6 and 88.1% for the 4, 8 and 12 contact scenarios, respectively. Using these CTHSes, the calculated probability that no infected herd was overlooked by the survey was > or =62.5% under the most-conservative, four-contact scenario. The probability that no more than one infected herd was overlooked was > or =89.7%.     

Temporal-spatial epidemiology of foot-and-mouth disease outbreaks in Mongolia, 2000 – 2002

Prior to 2000, foot-and-mouth disease (FMD) had not been observed in Mongolia since 1973; however, between April 2000 and July 2002, Mongolia reported 44 FMD outbreaks that affected cattle, sheep, goats, and camels. The objectives of this study were to describe the distributions of the 44 reported FMD outbreaks in Mongolia and to assess their spatial clustering and directions of movement. Official reports were collected to obtain the number and species of animals both affected and at risk, and the date and geographical coordinates of each outbreak. Significant global and local spatial clusters of reported FMD outbreaks were identified. Disease spread during the second epidemic moved 76° northeast and the spread of the disease during the third epidemic moved 110° northwest. FMD outbreaks were clustered intensely close to other FMD-positive counties. These findings can be used in the future to help plan prevention and control measures in high risk areas.     

Effectiveness of movement-prevention regulations to reduce the spread of foot-and-mouth disease in The Netherlands

After the foot-and-mouth disease (FMD) outbreak in 2001 the Dutch government implemented movement-prevention regulations to reduce the number of contacts between farms and consequently the risk of spread of highly contagious animal infections in the future. We studied the efficacy of these regulations by comparing registered cattle-movement data from 2000 to those from 2002. We also used the spatial and stochastic simulation model InterFMD to evaluate the consequences of the observed alterations in cattle-contact structure on the spread and control of a FMD epidemic.

There was a significant decrease in the number of cattle movements “for live use”, no difference in the number of group movements “for live use” and a distinct change in the overall contact structure. The most important structure changes were a decrease in the number of group movements from dairy farms to cattle-collection centres (−44%), and an increase in the number of group movements from dairy farms to beef farms (111%).

Our simulations demonstrated that the implemented regulations result in a concentration of the FMD-affected area and therefore in a reduction in size of the epidemics. Based on the intended Dutch strategy to control future FMD outbreaks, the decrease in extreme epidemics (95th percentiles) went from 31 infected farms in an epidemic-length of 65 days to 8 infected farms in an epidemic-length of 53 days in sparsely populated areas. In densely populated areas this decrease went from 135 infected farms to 103, while the duration reduced from 88 days to 81.     

Metapopulation dynamics and determinants of H5N1 highly pathogenic avian influenza outbreaks in Indonesian poultry

In 2008, the Indonesian Government implemented a revised village-level Participatory Disease Surveillance and Response (PDSR) program to gain a better understanding of both the magnitude and spatial distribution of H5N1 highly pathogenic avian influenza (HPAI) outbreaks in backyard poultry. To date, there has been considerable collection of data, but limited publically available analysis. This study utilizes data collected by the PDSR program between April 2008 and September 2010 for Java, Bali and the Lampung Province of Sumatra. The analysis employs hierarchical Bayesian occurrence models to quantify spatial and temporal dynamics in backyard HPAI infection reports at the District level in 90 day time periods, and relates the probability of HPAI occurrence to PDSR-reported village HPAI infection status and human and poultry density. The probability of infection in a District was assumed to be dependent on the status of the District in the previous 90 day time period, and described by either a colonization probability (the probability of HPAI infection in a District given there had not been infection in the previous 90 day time period) or a persistence probability (the probability of HPAI infection being maintained in the District from the previous to current 90 day period). Results suggest that the number of surveillance activities in a district had little relationship to outbreak occurrence probabilities, but human and poultry densities were found to have non-linear relationships to outbreak occurrence probabilities. We found significant spatial dependency among neighboring districts, indicating that there are latent spatial processes that are not captured by the covariates available for this study, but which nonetheless impact outbreak dynamics. The results of this work may help improve understanding of the seasonal nature of H5N1 in poultry and the potential role of poultry density in enabling endemicity to occur, as well as to assist the Government of Indonesia target scarce resources to regions and time periods when outbreaks of HPAI in poultry are most likely to occur.     

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

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.     

The local threshold for geographical spread of infectious diseases between farms

We investigated the influence of the spatial pattern of farms on the geographical spread of infectious livestock diseases, such as classical swine fever, foot-and-mouth disease and avian influenza in a combined analytical-numerical approach. Our purpose of this paper is to develop a method to identify the areas in which an infection has the potential to spread in an outbreak. In our model, each infected farm can infect neighbouring farms and the probability of transmission is a function of the inter-farm distance (spatial kernel). Therefore, the density of farms in an area is a good indicator for the probability of a major outbreak. In the epidemiological nomenclature, such density corresponds to a local reproduction ratio and we studied the critical behaviour of both the local density and the local reproduction ratio. We found that a threshold can be defined above which major outbreaks can occur, and the threshold value depends on the spatial kernel. Our expression for the threshold value is derived based on scaling arguments and contains two parameters in the exponents of the equation. We estimated these parameters from numerical results for the spatial spread using one particular mathematical function for the form of the spatial kernel. Subsequently, we show that our expression for the threshold using these estimated parameters agrees very well with numerical results for a number of different other functional forms of the spatial kernel (thus suggesting that we are dealing with universal parameters). As an illustration of the practical relevance of the presented method, we calculated the threshold value for avian influenza in the Netherlands and use it to produce a risk map for this disease.