Modeling alternative mitigation strategies for a hypothetical outbreak of foot-and-mouth disease in the United States

Preventive Veterinary Medicine 58 (2003) 25–52

Modeling alternative mitigation strategies for a hypothetical outbreak of foot-and-mouth disease in the United States Mark A. Schoenbaum*, W. Terry Disney United States Department of Agriculture, Animal Plant Health Inspection Service, Veterinary Services, Center of Epidemiology and Animal Health; Mail Stop 2W4; 2150 Centre Ave., Bldg. B, Fort Collins, CO 80526-8117, USA Received 18 October 2001; accepted 19 November 2002

Abstract Alternative mitigation strategies were compared during hypothetical outbreaks of foot-and-mouth disease (FMD) in the USA using a computer-simulation model. The epidemiologic and economic consequences were compared during these simulated outbreaks. Three vaccination and four slaughter strategies were studied along with two speeds of FMD virus spread among three susceptible populations of animals. The populations represented typical animal demographics in the United States. The best strategy depended on the speed of spread of FMD virus and the demographics of the susceptible population. Slaughter of herds in contact with known contagious herds was less costly than slaughtering only contagious herds. Slaughtering in 3 km rings around contagious herds was consistently more costly than other slaughter strategies. Ring vaccination in 10 km rings was judged more costly than slaughter alone in most situations. Although early ring vaccination resulted in lower government costs and duration in fast-spread scenarios, it was more costly when vaccinated animals were slaughtered with indemnity and other related slaughter costs. Published by Elsevier Science B.V. Keywords: Computer simulation; Foot-and-mouth disease (FMD); Economic consequences; Producer surplus; Consumer surplus

1. Introduction Traditional thinking dictates that foot-and-mouth disease (FMD; with its rapid spread and the need to protect the long-term health and profitability of United States (US) animal * Corresponding author. Tel.: þ1-970-494-7314; fax: þ1-970-494-7294. E-mail address: [email protected] (M.A. Schoenbaum).

0167-5877/03/$ – see front matter. Published by Elsevier Science B.V. doi:10.1016/S0167-5877(03)00004-7

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agriculture) must be controlled rapidly. Control usually has meant eradication. The total cost of an FMD outbreak would be the sum of eradication costs, production losses, and the most-immediate and -severe consequence of any animal-disease occurrence in the United States—the potential loss of export markets. Indirect costs, such as impacts on other sectors of the economy (tourism restrictions, etc.), also could be important. As we move into the 21st century, economic considerations have become an increasingly more-important tool in animal-disease prevention, control, management, and recovery. Newly emerging considerations such as worldwide free-trade agreements, the increasing acceptance of regionalization concepts for trade in animals and animal products, intensification of animal production, and the uncertain impact of biotechnology and bioterrorism add complexity to animal-health decisions. Economics-based decision criteria will be key to establishing future guidelines in the area of animal-disease risk management and control. Simulation and mathematical models have been used to explain or predict various epidemiologic and economic consequences of FMD and other animal-disease outbreaks (Berentsen et al., 1992; Sanson and Morris, 1994; Garner and Lack, 1995; Nielen et al., 1996; Jalvingh et al., 1999; Morris et al., 2001). In agricultural economics, quantitative models occasionally have been used to compare the economic consequences of alternative mitigation strategies in the event of an FMD outbreak (Disney et al., 2001). Models have the distinct advantage of being relatively inexpensive (versus actual disease outbreaks) when built to simulate an actual outbreak. It can be difficult to extrapolate the experience of one country with an outbreak of FMD to another. The overall consequences of an outbreak depend on factors such as the reaction of trading partners, extent of export of livestock and their products, livestock-population demographics, livestock-movement patterns, disease-control policies and their costs, reaction of the general public, value of the livestock, and even the strain of the virus. These dependencies link the consequences closely with each individual government and country. We present in this report a way to model theoretical outbreaks of FMD (and potentially, other contagious diseases) using input parameters to account for these countryspecific factors. Our purpose was to compare the epidemiologic and economic consequences of different slaughter and vaccination strategies based on hypothetical FMD outbreaks in the US. The consequences of four specific stamping-out and three vaccination strategies were compared under varying conditions of herd density/sizes and rates of disease spread. Economic consequences—including government cost of control and eradication, production losses, trade losses, and trade recovery—were estimated.

2. Materials and methods A stochastic simulation model was constructed to simulate outbreaks of FMD. This model incorporates both epidemiologic and economic modules. The model design is flexible enough to allow for incorporation of outbreaks of other contagious diseases by adjusting certain input parameters. Outputs of the epidemiological module are linked to an economic module that tracks various cost and price values. This linkage allows

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for tracking and comparing the costs of hypothetical FMD outbreaks and related mitigation strategies. 2.1. Epidemiologic framework A simulation model was written based on a previously designed stochastic statetransition model (Garner and Lack, 1995). The model was written in Delphi 4.0 for Windows (Borland International, Scotts Valley, CA, USA) with Diamond Access components (Timur Islamov, Memphis, Tennessee, USA; http://www.islamov.com) for database operations. The model runs on most microcomputers with the Windows 95, 98, 2000, NT operating systems and is available free upon request from the first author. Chance occurrences such as the spread of infection were simulated with Monte-Carlo methods to maintain a stochastic basis. Daily time steps were used. The results of multiple replications of outbreak runs (iterations) were stored in a database and could be summarized by replication or on a day-to-day basis. 2.1.1. Charts to define input parameters Some of the input parameters correspond to charts in the software that can be modified based on field data or expert opinions about a certain parameter. Some of the charts represent density (probability-density) functions for input parameters. The area under the curve of a density curve is compared to a random number from 0 to 1 to simulate a stochastic process. Other charts represent an input parameter and its relationship with the number of days since an event in the simulation. For example, to represent the capacity of the veterinary service to slaughter herds, the chart depicts the number of herds that can be slaughtered on the y-axis and the days since starting the slaughter program on the x-axis. During the running of the simulations, the specific input value represented by the y-axis is obtained depending on the x-axis value. The charts modeled in this study are described in the appropriate subsection, and are also available upon request from the first author. 2.1.2. Population dataset Generating a population of herds was the initial step in supplying some of the input parameters to the model. Two options were available in the model framework: (1) importing actual field data, with numbers of animals in the herds and their locations (latitude/longitude) or (2) simulating a hypothetical population of herds based on herd density patterns and typical numbers of animals per herd. We used the second option. Each geographic area containing the simulated herds was circular. The study populations were intended to represent typical US animal demographics. Due to the demographic diversity of livestock populations in the USA by regions, three representative animal populations from different geographic areas were considered: (1) a county in the south-central US (31,308 km2 area, 0.36 herd per km2, mean of 33 animals per herd); (2) a county in the north-central US (44,096 km2 area, 0.157 herd per km2, mean 1875 animals per herd); and (3) a county in the western US (60,391 km2 area, 0.069 herd per km2, mean 670 animals per herd). Simulated outbreaks did not extend beyond the borders of the study areas because susceptible herds were not modeled outside of these borders.

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2.1.3. Transition state Each simulated herd was assigned one ‘‘state’’ (i.e. health condition): susceptible, latent, contagious, naturally immune, vaccine immune, or dead. During the running of the model, the herds shifted (made transitions) among these states. The factors considered in these transitions and the definition of the states are summarized in Table 1 and were incorporated into the input parameters of the model. At the start of each iteration in the current study, one herd was in the latent and the rest were in the susceptible state (Table 2). A latently infected herd was chosen that was located in the geographic center of the circle containing the other herds. The center was chosen to provide susceptible herds in all directions for secondary spread of FMD. This selection also modeled the potential chance introduction of the virus by mechanical transfer in contaminated meat, boots, or clothing into a livestock area in the US. Time periods of transition states for FMD were modeled with triangular density functions. The modeling of these time periods was based on the studies of Garner and Lack (1995). These density distributions could be directly modified to represent essentially any density distribution for input into the model. For this analysis, density distributions were chosen to represent an aggregate of both cattle and swine herds in the US and the proportions thereof, because the model does not distinguish herds by species of animals. The latent period for a given herd was assumed to be a triangular density with minimum, most likely, and maximum of 5, 7, and 10 days. We assumed that every herd vaccinated became immune after a specified delay for immunity to develop; 4 days was used based on Ferguson et al. (2001), to model a highly effective vaccine. The herd remained immune for 84–364 days depending on a stochastic (Monte-Carlo) selection of the time period from the triangular distribution (parameters 84, 128, 364). A slightly longer time period was chosen for the immune period from infection. 2.1.4. Simulation of animal movement, contact, and infection spread Simulating spread of contagious infections often has been based on the Reed–Frost algorithm (Thrushfield, 1995). This algorithm does not provide for spatial spread of infection—the typical phenomenon seen in spread of contagious agents—because it assumes that each herd is equally likely to contact every other herd. In our model, a spatial pattern of spread was simulated. We simulated three simultaneous spread mechanisms: direct contact, indirect contact and airborne. Spread of infection by direct and indirect contact was based on simulated contact/ movements among infected and susceptible herds. Two input parameters quantified the rates of direct (e.g. movement of animals or other direct contact of animals) and indirect (e.g. movement of vehicles and people) movement among herds. The direction of the movements was random. The distances of movements were based on two probabilitydensity charts (one for direct and the other for indirect). The most-recent exposures of each susceptible herd to infected herds were tracked along with the time of exposure. Probabilities (input parameters) determined whether or not disease transmission occurred from simulated contact among infected and susceptible herds. At the start of the simulations, a single herd, geographically in the center of the county, was in the latent state for the infection. Two different levels of infection spread (slow and fast) were simulated (Table 2). The direct and indirect-contact rates of 0.15, 1 per day (slow

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Table 1 Health (transition) states and factors considered for transition from one health state to another by a contagiousdisease model Health (transition) state of the herd

Definition of the health state

Factors considered before transition to this health state

Susceptible

All animals in the herd are not infected and are able to contract the infection

Current state (only naturally and vaccine immune considered) Number of days remaining in current statea

Latent

Some animals in the herd are infected during the time before they shed the virus

Current state (only susceptible considered) Rate of direct or indirect contactb Probability of infection transfer if contact occurredb Distance from exposing herd(s) Number of animals in this herd and in exposing herd(s) Movement-control restrictionsb Probability of airborne spread at 1 km distanceb Maximum distance of airborne spreadb Wind directionb

Contagious

Some animals in the herd are infected and are shedding the virus

Current state (only latent considered) Number of days remaining in latent statea

Naturally immune

Animals in the herd have recovered recently from the infection and the herd is not susceptible

Current state (only contagious considered) Number of days remaining in contagious statea

Vaccine immune

Animals in the herd have vaccine-induced active immunity toward the disease and the herd is not susceptible

Current state (only susceptible considered) Vaccination schemeb Lag time before beginning vaccination campaignb Lag time from vaccination to transition to immuneb Distance from detected contagious herd (within ring or notb) Capacity of veterinary services to vaccinateb

Dead

All animals in the herd were slaughtered via a stamping-out program to control the disease

Current state (all except those already in dead considered) Slaughtering schemeb Lag time before beginning slaughter campaignb Type of contact (direct, indirect, within ringb) Capacity of veterinary services to slaughterb

a With a herd transition to a new health state, a value for the number of days to remain in this state is assigned randomly based on a probability distribution (which may be modified in the input parameters prior to running the model). Each day of simulation decreases this variable 1 day. When this variable equals zero, the herd makes a transition to the new state. This does not apply to susceptible or dead states, because herds in these states do not automatically transition in a stepwise fashion to another state. b Can be modified directly in the input parameters of the model.

spread), and 0.4, 2 (fast spread) have been described together as a single contact rate (Garner and Lack, 1995). We used contact-rate parameters based on studies of Bates et al. (2001) in California. Probabilities of 0.8 (direct) and 0.05 (indirect) for contact-transfer of the virus from contagious to susceptible herds were based on the first-author’s impression

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Primary input

Secondary input

Value/distribution type

Value/distribution used

Justification/basis of assumptions

Infection

Number of initial cases

Scalar

1

We assumed one incubating herd with 4 days left in the latent period in the center of the population to simulate virus introduction via mechanical transmission to a livestock area

Disease

Incubation period (days) Contagious period (days) Immune period infection (months)

PDFa PDF PDF

Triangular, 5, 7.5, 10 Triangular, 0, 21, 81 Triangular, 6, 9, 12

Garner and Lack (1995) Garner and Lack (1995) A distribution greater than the immunity from vaccination was chosen

Contact

Rate of direct movement of exposed animals (movements/day) Distance distribution of direct movements Direct movement—probability of infection transfer Rate of indirect movement of exposed animals (movements/day) Distance distribution of indirect movements Indirect movement—probability of infection transfer Effect of movement control after detection

Scalar

Slow: 0.15, fast: 0.4

Bates et al. (2001)

PDF Scalar Scalar

Triangular, 0, 0.9, 100 km Bates et al. (2001) 0.8 Considered high, given that these are movements of animals from herds in the contagious stage to susceptible herds Slow: 1, fast: 2 Bates et al. (2001)

PDF Scalar

Triangular, 0, 0.9, 30 km 0.05

Bates et al. (2001) Considered low probability of spread via indirect means

Relational chart

Reduced to 1/6 original rates in 6 weeks

1967–1968 outbreak in the UK, Garner and Lack (1995)

Probability of spread/day, at 1 km

Scalar

0.0001

Maximum distance spread (km) Wind direction

Scalar Scalar range

Slow: 2, fast: 4 0–3608

Preliminary runs indicated a small proportion of new infected herds could be produced with this low probability value Morris et al. (2001) A low rate of airborne infection was desired to simulate short-distance airborne and mechanical transfer by wild animals/pets in any direction

Airborne

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Table 2 Description of major epidemiologic input parameters for FMD model

Detection

Relational chart

Probability of reporting versus days since first confirmation of the infection

Relational chart

Preliminary studies with these surveillance settings indicated that the first of 20 infected herds was detected 6–7 days after introduction and all 20 were detected in 25 days. This simulates a rapid detection system for FMD. The same settings were used in all scenarios Sigmoid-shaped line from See above 1, 0.15 to 50, 1 (where 1 and 50 are days)

Straight line from 1, 0.2 to 5, 1.0 (where 1 and 5 are days)

Surveillance Size of surveillance area Visits per herd in the surveillance area Laboratory-diagnostic examinations

Scalar Scalar Scalar

15 km Twice weekly 1 per herd in surveillance area/outbreak

USDA-APHIS-VS (1991) USDA-APHIS-VS (1991) Visits would generate suspects that would require diagnostic or serological examinations; no published reports were available in the US; therefore, a simple assumption was made

Slaughter

Scalar

5 days

Ferguson et al. (2001)

Scalar

1 day

Morris et al. (2001)

Scalar

0–14 days

Scalar

0–14 days

Scalar Scalar Relational

1 3 km Up to 250 herds/day, sensitivity study

Assumed a maximum incubation period, Garner and Lack (1995) Assumed a maximum incubation period, Garner and Lack (1995) Considered ideal conditions Ferguson et al. (2001) The study compares ideal slaughtering conditions where capacity is unlimited. A follow-up study is done of the sensitivity of this capacity on costs

Scalar PDF Scalar

4 Triangular, 4, 5, 6 10 Early: 2, late: 50

Relational

Up to 650 herds/day, sensitivity study

Delay in beginning a slaughter program after first confirmation in an outbreak Delay in slaughter after detection of positive herd Direct-contact slaughter, days exposed and traced Indirect-contact slaughter, days exposed and traced Tracing probability of success Ring slaughter, diameter of the ring Slaughter capacity

Vaccination Delay in herd immunity (days) Immune period vaccine (months) Vaccination radius Ring vaccination begins after a prescribed number of detected herds Vaccination capacity

Probability-density function.

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a

Ferguson et al. (2001) Ferguson et al. (2001) Garner and Lack (1995) Comparing nearly immediate institution of a vaccination program with one after the outbreak is established Compares ideal vaccinating conditions where capacity is unlimited. A follow-up study was done of the sensitivity of capacity on the cost

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Probability of reporting versus number of days the herd has been in the contagious state

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from available literature (Morris et al., 2001; Ferguson et al., 2001; Nielen et al., 1996). Direct contact of a susceptible herd with another that is actively shedding virus has a high likelihood of infection transfer. Indirect contact is much less likely to transfer the infection. Airborne spread of the contagious disease was simulated based on input parameters for wind direction, probability of infection transfer at 1 km, the size of the herds, and the maximum distance the virus is thought to be able to spread by aerosol. In the current study, wind direction was assumed to be random. Airborne spread of FMD virus was not considered to be a major method of spread in this study. Probability of spread/day at 1 km distance was set at 0.0001 over distances <2 km for slow-spread scenarios and 4 km for fast (distances based on Morris et al., 2001). Based on previous work with these settings, airborne-origin infection was expected to occur at 0.3–0.4% of new infections. 2.1.5. Simulation of movement controls Disease-control measures such as movement controls influence the rates of direct and indirect contacts. Simulated movements were decreased with time after the initial detection of the infection. A chart in the input parameters modeled the amount of decrease. A decrease to 1/6 of the original rates after 6 weeks was chosen based on earlier studies of the 1967–1968 outbreak of FMD in the United Kingdom (Garner and Lack, 1995). Movement controls might be different from those modeled here in the event of an actual FMD outbreak in the US Current USDA regulations call for an immediate 72 h halt to animal movements following confirmed diagnosis of FMD. Additionally, most state plans call for a quarantine area (within which, and from which, movement will be limited strictly). Our input chart for movement controls was intended to simulate a more conservative gradual implementation of movement controls. 2.1.6. Detection Detection of contagious herds was based on two charts in the input parameters. The charts corresponded to two factors thought to be critical to the detection of clinical signs of FMD. The first factor was the stage of infection of a herd based on the number of days in the contagious state. The corresponding chart represented the probability that the farmer or the attending veterinarian would report suspicious signs of FMD to regulatory authorities given that infection had been present in the herd for a given number of days. It is assumed that signs would worsen over the first 5 days due to additional animals showing signs of infection and worsening manifestations of already existing lesions. The function represented in the chart yielded the daily probability of detection, d1. This chart featured a line starting at 20% probability at day 1 and reaching 100% probability of detection by day 5. The second factor was community awareness based on the days since the first case of FMD was diagnosed. The chart corresponding to this factor represented the probability that the herd would be reported to animal-health authorities based on the awareness of farmers and attending veterinarians of a recent outbreak of FMD. The function represented in the chart started at 15% probability from days 1–14 and then progressed linearly to 100% at day 50. The daily probability of detection from the second chart is termed d2. To model detection, the probabilities from the charts were treated as independent. On each simulation day, detection was modeled for each undetected herd in the contagious

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state by multiplying together probability values obtained from the two charts (d1 and d2) and then stochastically determining whether the herd was detected. In preliminary studies of these chart settings, the first of 20 infected herds was detected 6–7 days after introduction and all 20 were detected in most iterations by 25 days. This simulated a rapid detection system for FMD. These same settings were used in all scenarios. 2.1.7. Surveillance To determine surveillance costs during simulated FMD outbreaks, twice-weekly surveillance visits to farms within 15 km of detected herds were assumed per USDA guidelines (1991). These visits continued on susceptible herds until 30 days after the last case-herd of the outbreak was detected. One laboratory-diagnostic examination of each unique herd that fell within these surveillance rings also was assumed per outbreak. 2.1.8. Slaughter The model simulated the slaughter of herds detected with FMD. Herds in direct contact with detected herds, those in indirect contact with them, and/or within a specified distance could be included in the slaughtering strategy of the input parameters; these herds have been referred to as ‘‘dangerous contacts’’ and their slaughter as ‘‘pre-emptive slaughter’’. During daily time steps for the newly detected herds, the model determined which herds met the input criteria for slaughter by exposure history and the distances among the herds. We simulated four slaughter strategies. One strategy was to slaughter only contagious herds detected with clinical signs of FMD (the slaughter baseline strategy; S0). The other strategies added different ways of slaughtering some herds pre-emptively to this baseline: S1 added herds with direct contact with the contagious herd in the 14 days prior to the detection of the infection; S2 (ring slaughter) added slaughtering herds within 3 km of the detected herd; S3 added slaughtering both the direct and indirect-contact herds. The 3 km distance for S2 corresponded to the work of Ferguson et al. (2001) and to the high-risk zone described in USDA procedures (USDA-APHIS-VS, 1991). We chose 14 days as the number of days to trace direct and indirect-contact herds. Fourteen days was a conservative estimate of the maximum incubation period (Garner and Lack, 1995). We assumed that tracing direct and indirect-contact herds for slaughter was 100% accurate for all scenarios. A delay of 5 days from time of FMD confirmation and executing a slaughter (stampingout) program was assumed based on Ferguson et al. (2001) and USDA procedures (USDAAPHIS-VS, 1991). After the slaughter program was initiated, slaughter of the herds was assumed to occur within 24 h. Capacity of the veterinary services to slaughter herds was assumed to be up to 250 per day in comparing mitigation strategies. Although appearing unrealistic, the high capacity figure allowed comparison of the different mitigations under optimal conditions. A separate study of the impact of different slaughter capacities was also conducted and is described later. 2.1.9. Vaccination Three different strategies for vaccination were studied. The first was not to vaccinate (vaccination baseline; V0). Other strategies vaccinated all herds within 10 km of herds

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detected positive for FMD. The 10 km zone corresponded to buffer zones in USDA procedures (USDA-APHIS-VS, 1991) and another study (Garner and Lack, 1995). A delay of 4 days was assumed between vaccination and transition to the vaccine immune state (based on Ferguson et al., 2001). See earlier transition state assumptions about the vaccine immune state. Early vaccination (V1) began vaccination after 2 herds were detected; V2 (late vaccination) began after 50 herds were detected. Once the vaccination strategy had begun, herds were vaccinated within 24 h of detection of the positive herd at the center of the ring. Capacity to vaccinate herds was assumed to be up to 650 per day in comparing mitigation strategies. Although appearing unrealistic, the high capacity figure allowed comparison of the different mitigations under optimal conditions. A separate study of the impact of different vaccination capacities was also conducted and is described later. All vaccinated animals were slaughtered within 30 days of the slaughter of the last detected case-herd of FMD. 2.1.10. Scenarios and output In all, 72 different scenarios were studied: combinations of three demographic populations of herds, two rates of FMD spread, four slaughter strategies, and three vaccination strategies. One hundred iterations of each scenario were modeled. Preliminary studies indicated that 100 iterations yielded mean-output values within 3% of the mean values when 5000 iterations were run. Output variables of primary interest included the number of herds and animals slaughtered, number of herds and animals vaccinated, and duration of the outbreaks in days. The outbreak is considered over when slaughter and vaccination are complete in addition to there being no more latent or contagious herds. 2.1.11. Capacity for mitigations The effect of capacity of the veterinary services to slaughter animal herds also was modeled. A comparison of a huge capacity (maximum of 250 herds per day), moderate (maximum of 20 herds per day), and low (maximum of five herds per day) slaughter capabilities was completed for a single selected scenario (population 2, fast-spread rate, slaughtering contagious/direct/indirect (S3), and early vaccination (V1)). Five hundred iterations were run per capacity scenario. The effect of the capacity of the veterinary services to vaccinate herds also was modeled. A comparison of a huge capacity (maximum 650 herds per day), moderate (maximum of 40 herds per day), and low (maximum of 10 herds per day) vaccination capabilities was completed for the same single selected scenario. Again, 500 iterations were run per scenario. On each simulation day, the number of herds that can be slaughtered and vaccinated is determined from the corresponding probability chart (in input parameters) based on the day since beginning slaughter or vaccination. Once this capacity for the day is exceeded, herds are designated as holding for slaughter or vaccination (yet retain their transition state). While holding for slaughter, they are assumed not to be contacting other herds directly. On subsequent days (as daily capacity allows), these herds are slaughtered based on the length of time they have been holding and the following priority list: detected contagious,

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direct-contact, ring-slaughter, and indirect-contact herds. Capacity for vaccination is modeled in a similar way. The priority for vaccinating herds that are holding for vaccination is based on the length of time they have been holding. Low-capacity settings can lead to protracted outbreaks because of the large caches of herds that might be holding for slaughter or vaccination even after containment of the last infected herd. 2.2. Economic framework Cost-minimization techniques were used to compare alternative mitigation strategies in the various outbreak situations described in the epidemiological framework above. Welfare economic criteria were used to measure changes in private benefits and costs to producers (producer surplus, PS) and consumers (consumer surplus, CS) (Just et al., 1982). The total cost of an FMD outbreak was defined by the following equation: Cij ¼ Gij þ ðPSij þ CSij Þ;

(1)

where Cij is the total cost of an FMD outbreak for the ith mitigation strategy in the jth outbreak situation, and Gij is the government cost of control and eradication. PSij represents the net change in PS in FMD-affected product markets (cattle, hogs, sheep, dairy, beef, pork) due to the supply effect of an FMD outbreak, combined with the change in PS in FMD-affected product markets due to the loss of export markets, and the indirect change in PS in all related markets (poultry meat, feed grains, etc.). Similarly, CSij represents the net change in CS in FMD-affected product markets due to the supply effect of an FMD outbreak, combined with the change in CS in FMD-affected product markets due to the loss of export markets, and the indirect change in CS in all related markets. Projected annual changes in CS þ PS were converted to daily changes assuming homogeneous volume throughout the year (annual change/365 ¼ daily change) to determine overall change in CS and PS for each of the ith mitigation strategies in each of the jth outbreak situations. 2.2.1. Determination of government cost of FMD outbreak Assumptions about the parameters involved in the government control and eradication of disease outbreaks are shown in Table 3. These assumptions were developed based on unpublished partial budgets developed for the various aspects of control and eradication during the 1998 US READEO ‘‘NIMBY’’ FMD test exercises (USDA-APHIS-VS, 1998). Costs were linked directly to epidemiological output variables (number of herds, number of animals removed, number of vaccinated animals, etc.) to determine the government costs of control and eradication for each mitigation (i)/outbreak situation (j) combination. When vaccination strategies were deployed, an assumption was made that all vaccinated animals were destroyed within 30 days after the last case was found. Government costs in these cases included all the economic parameters for the vaccinated animals described in Table 3 except for the cleaning and disinfection charges. 2.2.2. Determination of domestic-loss impacts due to FMD outbreak Animals that were destroyed in the simulated FMD outbreaks were removed from the market system, thus reducing supply available to meet demand. Additional production

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Table 3 Description of major economic input parameters for FMD model Primary input

Secondary input

Slaughter

Cost Cost Cost Cost Cost Cost Cost Cost Cost Cost Cost

of of of of of of of of of of of

Surveillance

Cost Cost Cost Cost Cost Cost

of testing per herd: small herds of testing per herd: medium herds of testing per herd: large herds per surveillance visit: small herds per surveillance visit: medium herds per surveillance visit: large herds

Vaccination

Vaccination cost per herd: small herds Vaccination cost per herd: medium herds Vaccination cost per herd: large herds Vaccination cost per animal Baseline vaccination capacity Additional per animal cost when exceed baseline

Scalar Scalar Scalar Scalar Scalar Scalar

Trade

Daily net impact (change in PS þ CS) Number of months to destroy vaccinated animals

Scalar Scalar

appraisal per herd: small herdsb appraisal per herd: medium herdsc appraisal per herd: large herdsd euthanasia per animal indemnification per animal carcass disposal per animal: small herds carcass disposal per animal: medium herds carcass disposal per animal: large herds cleaning/disinfecting per herd: small herds cleaning/disinfecting per herd: medium herds cleaning/disinfecting per herd: large herds

Value/distribution type

Valuea/distribution used (US$)

Scalar Scalar Scalar Scalar Scalar Scalar Scalar Scalar Scalar Scalar Scalar

300 400 500 5.5 250 11 11 12 5000 7000 10000

Scalar Scalar Scalar Scalar Scalar Scalar

150 200 400 50 75 100 300 500 800 6 2000000 0.50 2.16 million 1

a

Values for all scalar economic inputs except daily trade loss were derived by the authors from activity budgets developed from the 1998 NIMBY test exercises (USDA-APHIS-VS, 1998). Daily net trade impact calculated by the authors using exogenous economic model, USMP (House et al., 1999). b A small farm contains <100 head of animals of multiple species. c A medium farm contains 100–450 head of animals of multiple species. d A large farm contains >450 head of animals of multiple species.

impacts included losses due to downtime required after a herd is removed, the recovery time associated with resuming pre-outbreak production efficiency levels, and losses in efficiency due to quarantines and animal-movement restrictions. At the aggregate national level, the production impact is small relative to the overall costs of FMD-susceptible livestock production. Although FMD poses little or no threat to humans, the psychological effect could be important. Shifts in consumer demand have in the past been associated with FMD and other animal-disease outbreaks (McCauley et al., 1979; Paarlberg and Lee, 1998). Additionally, consumers are faced with higher prices for meat products as supply is reduced—offsetting the positive (lower domestic price) impact from closed export markets. The impact of production losses due to an FMD outbreak was represented by the reduction in supply shown in Fig. 1. The area (ABCD) under the demand curve between the

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Fig. 1. Production consequence for domestic FMD-affected markets.

original equilibrium price (P) and the post-outbreak equilibrium price (P0 ) was defined as the loss in CS due to the FMD outbreak. Similarly, the integral of the difference between the area above the original supply curve and below P (DCE) and the area above the new supply curve and below P0 (ABF) was defined as the change in PS due to the FMD outbreak. (Please note that the impact of export trade loss due to the FMD outbreak was not considered here. Later in this discussion, the impact of loss of export markets is described separately in Fig. 2.) For simplicity in this analysis, the assumption was made that consumer demand (could be represented by a downward shift in D in Fig. 1) was not affected by an FMD outbreak. This simplifying assumption was made because anecdotally, it seemed that none of the mitigation strategies being compared in the analysis would significantly affect the marginal modeling of shift in consumer demand. This uncertain shift in consumer demand is a candidate for future research.

Fig. 2. Loss of trade consequence for domestic FMD-affected markets.

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M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

The impact of supply reductions due to an FMD outbreak was estimated by calculating changes in PS and CS. Exogenous calculation of changes in the sum of PS þ CS (across all major agricultural commodity production and consumption) was accomplished using a comparative static, multi-commodity, price-endogenous spatial-equilibrium programming model of the US agriculture sector (USMP). Animal production represented in USMP (House et al., 1999) includes poultry (eggs, broilers, turkeys), dairy cattle, swine and beef cattle. Major crops also are represented (including major livestock-feed sources). Processed and retail products represented include eggs, broiler meat, turkey meat, dairy products (milk, nonfat dried milk, cheese and butter), pork, beef (both feedlot and grass-fed), and soybean meal. Market-clearing equilibrium is maintained for animal feed, food, seed and industrial uses, import and export, and domestic stocks. The final output captures the interactions of supply and demand across major commodities and agricultural markets and reports the effects on prices, net returns to producers, PS, and CS. USMP was calibrated to supply, demand, production, and government-program predicted conditions for 2005 as reported in the USDA Long-Term Agricultural Baseline (USDA, 1998a). Crop and livestock costs were based on USDA cost of production estimates (USDA, 1998b) and were indexed to baseline projection for variable costs for 2005. 2.2.3. Determination of trade losses due to FMD outbreak Historically, export losses represent the largest economic consequence to a country undergoing an FMD outbreak. This is especially true for an export-oriented economy such as US agriculture. The gross value of US exports in potentially FMD-affected product was in excess of US$ 4.3 billion in 2000 (USDA-NASS (2000) Agricultural Statistics 2000). This translates into a daily gross trade impact of some US$ 12 million per day. In the event of an FMD outbreak in the US, most if not all importers would restrict US exports of FMDaffected animals and product, and that product would be absorbed back on the US domestic market. Thus (at least conceptually), every day that an outbreak continues costs >$ 12 million in lost gross value of trade. The net trade effects of the loss of export markets are depicted in Fig. 2. Export markets had originally caused domestic production to expand from Q to QE (domestic consumption falling to QDE as price increased from P to PE). Restriction of export markets forces the previously exported quantity (QE—QDE) back on the domestic market (dragging the market-clearing price down from PE to PFMD). Gains in CS from the loss of export market are represented in Fig. 2 by the integral of the area ABCD, as domestic demanders now pay less (PFMD). PS losses were represented by the integral of the area AEGD, as producers receive the lower price (PFMD). Disney et al. (2001) outlined a modeling procedure for determining trade loss based on length of outbreak, OIE-required trade suspension, and ensuing market recovery. These techniques were employed in this analysis. 2.2.4. Calculation of net US economic impact due to FMD outbreak As input into this analysis, USMP was used to model exogenously annual net trade loss simultaneously with shifts in production of FMD-affected products as described in the

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

39

previous section. Small shifts in supply (could be represented by extremely small leftward shifts to the supply curve in Figs. 1 and 2)—typically <0.1% of US national production— occur in simulated FMD outbreaks in this study. Estimates of the net changes in (PS þ CS) are calculated exogenously at US$ 789.9 million annually. This translates into a daily impact of a US$ 2.16 million decline in (PS þ CS). Please note that these changes in (PS þ CS) are the result of simultaneously shutting off export markets for FMD-affected products and imposing the small supply shift to cattle and hog supplies. The exogenously calculated daily economic impact was used in this analysis to calculate effectiveness of alternative mitigations. Daily economic impacts were input directly into the previously referenced trade-loss modeling procedure by Disney et al. (2001) to determine changes in trade-loss impact between the base scenario and the alternative mitigation scenarios. 2.2.5. Scenarios and output Output from the epidemiologic simulations was used to generate economic output. Variables of primary interest included government cost, and government cost plus net welfare change. 2.3. Analysis aids Differences in main effects and interactions of vaccine strategy, slaughter strategy, population, and spread level on length of the outbreaks, and costs were assessed using analysis of variance (ANOVA) techniques. We first ran a multivariable ANOVA model to account for the high correlations among the following five responses: duration of the outbreak (in days), government cost without the government cost of slaughtering vaccinated animals, government cost with the government cost of slaughtering vaccinated animals, government cost plus net welfare changes with the government cost of slaughtering vaccinated animals, and government cost plus net welfare change without the government cost of slaughtering vaccinated animals. The model was highly significant—indicating that a univariate ANOVA was appropriate for each of the responses separately. One-way ANOVA then was conducted for each of the five responses separately. Residual analysis to examine the model assumptions of homoscedasticity and normality associated with the ANOVA models revealed that assumptions were violated for each response (i.e. there was a gross deviation from normality and severe heteroscedasticity). Appropriate power transformations of the responses were applied as suggested by Malaeb’s Box-Cox SAS program (Malaeb, 1997) to stabilize the variances and achieve approximate normality. One response (government cost plus net welfare change with government cost of slaughtering vaccinated animals) required an inverse transformation (i.e. y ¼ 1=y). The rest of the responses required a fourth-root transformation (i.e. y ¼ y1=4 ). Homoscedasticity and approximate normality were achieved and model assumptions were satisfied for the five responses. With the large sample size of N ¼ 7200, the F-statistic tests in the ANOVA models declared most effects and interactions to be statistically significant. After examining the relative magnitude of the F-statistics, we only considered values of 100 and over to be important for the purposes of this study.

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M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 4 Lengths of 7200 simulated outbreaks of FMD, in days, categorized on speed of spread and vaccination-slaughter strategies (n ¼ 300 simulated outbreaks/scenario) Mitigation strategya,b

Slow spreadc P5

d

Fast spread P50

P95

P5

P50

P95

V0 S0 S1 S2 S3

12 12 13 12

40 33 40 30

60 52 62 50

70 47 61 41

109 66 96 62

151 87 128 84

V1 S0 S1 S2 S3

13 12 13 11

40 34 39 30

62 52 58 50

55 39 54 37

68 57 66 56

86 71 86 68

V2 S0 S1 S2 S3

13 12 12 11

40 32 39 31

63 53 63 50

57 50 56 43

68 59 68 57

84 71 85 68

a

V0: no vaccine; V1: early vaccination, begun after 2 herds detected; V2: late vaccination, begun after 50 herds detected. b S0: slaughter contagious herds only; S1: slaughter contagious and direct-contact herds; S2: slaughter contagious and 3 km circle herds; S3: slaughter contagious, direct, and indirect-contact herds. c Slow spread: 0.15 direct movement contacts per herd per day, one indirect contacts per herd per day; fast: 0.4 direct movement contacts per herd per day, two indirect contacts per herd per day. d P5: 5th percentile; P50: 50th percentile (i.e. median); P95: 95th percentile.

Matrices comparing the outbreak circumstances (population and speed of spread) and mitigation (slaughter and vaccination strategies) were constructed for the following output variables: duration of outbreaks (Table 4), government cost (Table 5), and government cost plus net welfare change (Table 6). Because output data were often skewed, percentiles (P5, P50—median, and P95) were used to summarize output.

3. Results The median duration of outbreaks varied among scenarios from 30 to 109 days. Significant decreases in the duration of outbreaks were noted for all mitigation strategies in the fast-spread scenarios and almost all of the slow-spread scenarios (Table 4) as compared to baseline strategies. In the slow-spread scenarios, the few slightly larger-thanbaseline values were attributed to chance occurrences. The ANOVA indicated significant main effects of vaccine strategy, slaughter strategy, and spread level. Significant vaccine strategy and speed-of-spread interaction was evident (Table 7). This interaction was attributed to vaccination being associated with reduction in duration of outbreaks in

Mitigation strategya,b

Population 1c

Population 2

Slow spreadd P5

e

P50

Fast spread P95

P5

P50

Population 3

Slow spread P95

Without government cost of slaughtering vaccinated animals V0 S0 0.1 1 2 1 20 40 S1 0.1 0.3 2 1 7 29 0.2 2 8 5 72 141 S2 S3 0.2 1 2 1 8 30

P5

Fast spread

P50

P95

P5

1 1 0 3

9 5 26 14

38 28 86 72

89 30 123 59

P50

Slow spread

Fast spread

P95

P5

P50

P95

553 304 945 503

1080 959 1974 1307

0.2 0.2 0.2 1

2 2 5 4

8 9 21 14

P5

P50

P95

19 9 42 7

118 82 206 109

307 224 472 371

V1 S0 S1 S2 S3

0.1 0.1 0.2 0.2

1 0.5 2 1

5 3 7 3

4 2 7 1

17 15 50 15

29 28 101 37

1 1 3 3

9 9 27 17

41 41 100 74

75 4 240 48

349 344 775 491

667 820 1592 1185

0.2 0 0.2 0.0

3 2 5 6

10 10 17 21

9 7 34 8

97 106 172 96

193 210 371 285

V2 S0 S1 S2 S3

0.1 0.1 0.2 0.2

0.5 0.3 2 1

2 2 6 3

6 1 15 1

19 10 57 17

34 29 119 35

1 1 3 4

6 6 27 15

55 27 135 62

59 60 135 89

360 322 823 411

840 878 1683 1223

0.2 0.2 0.2 1

2 2 5 4

17 9 24 17

2 9 42 16

97 82 184 113

214 246 373 293

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 5 Government cost of control and eradication (in US$ millions) for 7200 simulated outbreaks of FMD categorized on three different herd populations, two rates of spread, three vaccination strategies, and four slaughter strategies (n ¼ 100 simulated outbreaks/scenario)

41

42

Mitigation strategya,b

Population 1c

Population 2

Slow spreadd P5

e

P50

Fast spread P95

With government cost of slaughtering V1 S0 0.1 11 46 S1 0.1 5 27 S2 0.2 8 35 S3 0.2 5 26 V2 S0 S1 S2 S3 a

0.1 0.1 0.2 0.2

0.5 0.3 2 1

2 2 6 3

P5

P50

Population 3

Slow spread P95

Fast spread

Slow spread

P5

P50

P95

P5

P50

P95

P5

P50

Fast spread P95

P5

P50

P95

vaccinated animals 40 16 35 9

167 117 190 119

214 196 269 202

1 1 3 3

146 97 178 81

492 420 493 361

857 4 1166 232

2730 1987 2860 1941

3884 3463 4530 3624

0.2 0 0.2 0

27 17 25 19

95 56 76 75

79 35 143 26

541 406 558 284

819 667 973 678

52 1 63 1

172 117 182 131

214 195 262 186

1 1 3 4

6 6 27 15

619 27 135 62

620 60 135 89

2772 1858 2829 1660

4040 3566 4472 3542

0.2 0.2 0.2 1

2 2 5 4

122 9 24 17

2 9 154 16

521 313 573 300

836 715 941 645

V0: no vaccine; V1: early vaccination, begun after 2 herds detected; V2: late vaccination, begun after 50 herds detected. S0: slaughter contagious herds only; S1: slaughter contagious and direct-contact herds; S2: slaughter contagious and 3 km circle herds; S3: slaughter contagious, direct, and indirect-contact herds. c Population 1: 0.36 herds per km2, mean of 33 animals per herd; population 2: 0.157 herds per km2, mean of 1875 animals per herd; and population 3: 0.069 herds per km2, mean of 670 animals per herd. d Slow spread: 0.15 direct movement contacts per herd per day, one indirect contacts per herd per day; fast: 0.4 direct movement contacts per herd per day, two indirect contacts per herd per day. e P5: 5th percentile; P50: 50th percentile (i.e. median); P95: 95th percentile. b

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 5 (Continued )

Mitigation strategya,b

Population 1c

Population 2

Slow spreadd P5

e

P50

Fast spread P95

P5

P50

Population 3

Slow spread P95

Without government cost of slaughtering vaccinated animals V0 S0 204 290 345 332 536 703 207 260 326 297 380 452 S1 S2 210 289 361 342 535 688 S3 207 260 326 276 374 450

P5

P50

207 208 210 212

309 276 322 279

Fast spread P95

Slow spread

Fast spread

P5

P50

P95

P5

P50

P95

P5

P50

P95

390 348 445 404

471 352 513 362

1114 699 1421 864

1670 1425 2594 1737

207 207 213 211

285 279 304 260

354 333 374 327

419 308 418 297

645 461 709 463

864 628 1013 759

V1 S0 S1 S2 S3

234 234 237 231

322 298 306 284

392 352 375 350

369 331 381 309

413 387 444 389

469 435 514 431

242 237 245 242

331 314 348 309

420 392 472 415

453 249 645 389

764 731 1210 866

1109 1210 1988 1553

239 237 234 237

326 305 325 298

407 377 392 371

386 332 424 333

525 484 594 468

636 617 804 676

V2 S0 S1 S2 S3

234 236 234 231

312 289 317 290

386 356 401 353

381 343 383 327

422 392 465 391

469 432 518 430

240 234 236 240

326 291 356 309

460 378 510 414

484 423 538 437

795 695 1231 801

1260 1273 2093 1607

242 237 239 235

328 308 318 297

419 371 410 357

353 355 429 345

541 474 618 495

651 657 811 672

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 6 Government cost of control and eradication plus net welfare change (in US$ millions) for 7200 simulated outbreaks of FMD categorized on three different herd populations, two rates of spread, three vaccination strategies, and four slaughter strategies (n ¼ 100 simulated outbreaks/scenario)

43

44

Mitigation strategya,b

Population 1c

Population 2

d

Slow spread P5

e

P50

Fast spread P95

With government cost of slaughtering V1 S0 234 332 431 234 302 372 S1 S2 237 315 397 S3 231 286 369 V2 S0 S1 S2 S3 a

234 236 234 231

312 289 317 290

402 356 401 353

P5

P50

Population 3

Slow spread P95

P5

P50

Fast spread P95

Slow spread

Fast spread

P5

P50

P95

P5

P50

P95

P5

P50

P95

vaccinated animals 422 350 413 320

567 503 591 499

631 589 676 589

242 237 245 242

463 398 487 375

853 752 880 697

122 249 160 590

3134 2371 3270 2317

4303 3865 4924 3991

242 237 234 237

356 323 350 316

481 418 446 435

458 361 533 348

977 788 986 669

1263 1073 1406 1055

452 343 436 327

581 500 591 501

623 587 657 583

240 234 236 240

326 291 356 309

1028 378 510 414

105 423 538 437

3173 2227 3237 2064

4444 3943 4859 3926

242 237 239 235

328 308 318 297

506 371 412 357

353 355 553 345

955 700 1003 675

1262 1105 1370 1026

V0: no vaccine; V1: early vaccination, begun after 2 herds detected; V2: late vaccination, begun after 50 herds detected. S0: slaughter contagious herds only; S1: slaughter contagious and direct-contact herds; S2: slaughter contagious and 3 km circle herds; S3: slaughter contagious, direct, and indirect-contact herds. c Population 1: 0.36 herds per km2, mean of 33 animals per herd; population 2: 0.157 herds per km2, mean of 1875 animals per herd; and population 3: 0.069 herds per km2, mean of 670 animals per herd. d Slow spread: 0.15 direct movement contacts per herd per day, one indirect contacts per herd per day; fast: 0.4 direct movement contacts per herd per day, two indirect contacts per herd per day. e P5: 5th percentile; P50: 50th percentile (i.e. median); P95: 95th percentile. b

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 6 (Continued )

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

45

Table 7 ANOVA table with days of duration of the FMD epidemic as the dependent variable Source

DF

Type III SS

Mean square

F

P

Vaccine strategy (A) Slaughter strategy (B) AB Population (C) AC BC ABC Spread level (D) AD BD ABD CD ACD BCD ABCD

2 3 6 2 4 6 12 1 2 3 6 2 4 6 12

16.24 50.90 5.30 1.74 0.057 0.57 0.52 431.80 11.48 2.42 5.41 0.0010 0.20 0.58 0.52

8.12 16.97 0.88 0.87 0.014 0.095 0.043 431.80 5.74 0.81 0.90 0.00050 0.050 0.097 0.044

154.83 323.59 16.85 16.58 0.27 1.80 0.82 8234.51 109.50 15.42 17.20 0.01 0.95 1.85 0.83

<0.0001 <0.0001 <0.0001 <0.0001 0.90 0.09 0.63 <0.0001 <0.0001 <0.0001 <0.0001 0.99 0.43 0.09 0.62

the fast-spread scenarios and with less impact in slow-spread scenarios. There were no significant interactions involving population density (all P  0:09). Although most mitigation strategies decreased the duration of outbreaks, the costs of outbreaks varied widely among the scenarios depending on the circumstances and mitigation strategy as compared to baseline. The median government cost (Table 5) varied from US$ 0.3 to US$ 2860 million depending on scenario. In Table 6, the median government cost plus net welfare change varied from US$ 260 to US$ 3270 million depending on scenario. ANOVA indicated population, and slaughter strategy had significant main effects on cost. The analysis that included the government costs of slaughtering vaccinated animals indicated significant vaccine effects. Two-way interactions of population and spread level were significant in these ANOVA tables. This interaction was attributed to the higher-animal-density populations being associated with larger costs during fast-spread scenarios. In slow-spread scenarios, costs were more similar among the populations. There were no significant three- or four-way interactions. The costs and duration of outbreaks for each slaughter strategy are summarized in Table 8. Two slaughter strategies (S1: direct-contact, S3: direct and indirect contact) significantly reduced the duration of outbreaks as compared to the baseline of slaughtering only affected herds. More herds were slaughtered as a result of using ring-slaughter and direct- and indirect-contact slaughter strategies. Slaughtering direct-contact herds resulted in fewer total herds slaughtered (median of 37) than the baseline (median of 48). This difference was attributed to the effectiveness of the strategy in reducing secondary spread of the infection. In terms of government cost and government cost plus net welfare change, adding ring slaughter (at 3 km distance) significantly increased costs of outbreaks (median values were 1.02–2.9 times the baseline). A significant decrease in costs when directcontact herds were slaughtered was noted (median costs were 64 and 90% of baseline). Slaughtering both direct- and indirect-contact herds slightly increased the 95th percentile

46

Slaughter strategy (n ¼ 1800/strategy) Contagious herdsa only (S0)

Contagious and herds in direct contactb (S1)

Contagious and ring herdsc (S2)

Contagious and herds in direct or indirect contactb (S3)

P5d

P50

P5

P5

P5

14 1

59 48

121 1029

Without government cost of slaughtering vaccinated animals Government cost (US$ millions) 0.2 14 Government cost plus net welfare change (US$ millions) 239 392 With government cost of slaughtering vaccinated animals Government cost (US$ millions) Government cost plus net welfare change (US$ millions)

Length of the outbreak in days Number of herds slaughtered during the outbreaks

a

0.2 43 239 466

P95

13 1

P50

P95

P95

58 236

104 4999

49 37

74 941

573 1015

0.1 9 234 351

518 894

0.2 40 237 415

2932 3349

0.1 21 234 370

1997 2383

0.2 81 237 474

Herds with clinical signs of FMD detected by government officials. Evidence of direct or indirect contact with a detected contagious herd within the previous 14 days. c Herds within a 3 km ring around detected contagious herds. d P5: 5th percentile; P50: 50th percentile (i.e. median); P95: 95th percentile. b

14 3

P50

13 6

P50

P95

46 73

70 1339

1183 1629

0.2 14 227 351

693 1084

3100 3502

0.2 27 227 365

2037 2418

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 8 Summary of 7200 computer-simulated outbreaks of FMD in the US, with control and eradication based on four slaughter (stamping-out) strategies

Vaccination strategy (n ¼ 2400/strategy) No vaccination (V0) P5 Length of the outbreak in days Number of herds vaccinated during the outbreaks

c

P50

P95

Early vaccinationa (V1)

Late vaccinationb (V2)

All scenarios

P5

P5

P5

P50

P95

P50

P95

P50

P95

14 0

53 0

121 0

13 0

51 870

76 10761

13 0

53 0

77 10214

13 0

52 0

97 9367

Without government cost of slaughtering vaccinated animals Government cost (US$ millions) Government cost plus net welfare change (US$ millions)

0.2 213

13 352

816 1309

0.2 242

16 377

641 1034

0.2 241

16 383

703 1108

0.2 234

15 373

726 1140

With government cost of slaughtering vaccinated animals Government cost (US$ millions) Government cost plus net welfare change (US$ millions)

0.2 213

13 352

816 1309

0.2 242

122 479

3030 3443

0.2 241

35 401

3007 3404

0.2 234

39 403

2540 2956

a

Vaccination beginning after detecting the 2nd FMD-positive herd, vaccinating a 10 km ring around detected herds. Vaccination beginning after detecting the 50th FMD-positive herd, vaccinating a 10 km ring around detected herds. c P5: 5th percentile; P50: 50th percentile (i.e. median); P95: 95th percentile. b

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

Table 9 Summary of 7200 computer-simulated outbreaks of FMD in the US, with control and eradication based on three vaccination strategies

47

48

M.A. Schoenbaum, W. Terry Disney / Preventive Veterinary Medicine 58 (2003) 25–52

of government costs (from US$ 573 to US$ 693 millions); however, government cost plus net welfare change was lower (90% of the median of baseline). The first set of cost results considered that vaccinated animals would be slaughtered through normal market channels without incurring government or extra private expense. In the lower part of Table 8, we considered government costs for slaughtering vaccinated animals (in vaccination scenarios) similarly to herds with FMD (with appraisal, euthanasia, indemnity, and disposal expenses). Considering these extra expenses in vaccinated scenarios increased overall median cost of simulated outbreaks by 1.1 (government cost plus net welfare change) to 2.6 (government cost) times. In summarizing ring-vaccination strategies in Table 9, lowered duration of outbreaks were noted in vaccination scenarios as compared with a baseline scenario of no vaccination. Median duration was lowered 2 days for early vaccination compared to baseline. Ninety-fifth percentiles were reduced from a baseline of 121 days to 76 (early vaccination) and 77 (late vaccination) days. Given the interaction between vaccination strategy and spread in ANOVA, the main effect of vaccine was masked. In the presence of higher-order interaction, the interpretation of lower-order effects becomes more difficult. In fast-spread scenarios, early vaccination reduced the median duration of baseline from 77 to 61 days, and late vaccination reduced it to 63 days. In slow-spread scenarios, vaccination had little effect on duration of the outbreaks. The median costs of outbreaks were increased by vaccination; however, the variation of costs (from 5th to 95th percentiles) was lowered. Adding the additional expense of slaughtering vaccinated animals in the lower part of Table 9 increased the median costs of outbreaks when vaccination was used (from 1.05 to 7.6 times the baseline). The number of herds that the veterinary service was capable of slaughtering was related to the cost of the outbreak. Compared to a baseline capacity of 5 herds per day, 20 herds per day decreased the median government cost plus net welfare change of outbreaks by 42% (from US$ 1477 million to US$ 860 million, without government cost of slaughtering vaccinated animals), and a capacity of 250 herds per day decreased it by 44% (to US$ 826 million). Median duration of simulated outbreaks were reduced from 186 (5 herds per day), to 62 (20 herds per day), to 57 days (250 herds per day). The costs of increasing the capacity to slaughter were not determined. The number of herds that the veterinary service was capable of vaccinating also was related to the cost of the outbreak. Compared to a baseline capacity of 10 herds per day, 40 herds per day decreased government cost plus net welfare change by 42% (from US$ 1775 million to US$ 1025 million, without government cost of slaughtering vaccinated animals), and a capacity of 650 herds per day decreased it by 53% (to US$ 826). Median duration of simulated outbreaks were reduced from 304 (5 herds per day), to 95 (20 herds per day), to 57 days (250 herds per day). The costs of increasing the capacity to vaccinate were not determined.

4. Discussion In deciding a mitigation strategy, it is best to consider both the susceptible population and the rate of contact among the herds. Both of these were important factors in the length

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49

and cost of our simulated outbreaks. Care in generalizing about the best mitigation strategy must be exercised given the significant two-way interactions found among the mitigations and the population-specific factors. We used the triangular distribution to model the uncertainty associated with some input variables in the model. Other distributions (e.g. the Pert distribution) also could have been appropriate, and the model can be modified accordingly via the input charts of the software. Slaughter (stamping-out) is implemented in many countries to eradicate FMD. We compared a slaughter strategy where only FMD-positive herds are slaughtered with three methods that added pre-emptive slaughter. The herds involved with pre-emptive slaughter are generally healthy; thus, this practice can be controversial. We attempted to simulate the consequences, costs and relative benefits of the three pre-emptive strategies. Slaughter of herds in direct contact with herds diagnosed with FMD resulted in lesscostly outbreaks of shorter duration. Overall, almost 17% fewer herds were slaughtered with this strategy versus the baseline. Median cost was reduced by 10–49% as compared with baseline. The lower number of herds slaughtered was attributed to identifying and removing incubating herds before they could become contagious and spread the infection to other herds. This strategy appeared the most beneficial of all the mitigations to control FMD infection. The assumption of 100% tracing success might have led us to overestimate the benefits of this strategy. We expected a high level of tracing success (approaching 100%) in such a serious matter as FMD in the US. Ring slaughter (at 3 km) resulted in more-costly outcomes than the other slaughter strategies when studied across all situations. Although this strategy reduced the median length of outbreaks from 59 to 58 days as compared to baseline, the costs increased 1.02 to 2.9 times. Based on cost, ring slaughter was not the preferred strategy for any of the demographic and contact-rate situations. The higher costs were attributed to the higher number of herds slaughtered in the ring-slaughter scenarios (4.9 times the baseline number of herds slaughtered). Because the input disease-spread parameters had distances up to 100 (direct contact) and 25 km (indirect contact), it was expected that 3 km rings would not contain the spread of FMD virus. Based on these results and the assumptions made, ring slaughter cannot be recommended for an outbreak of FMD. Although this strategy does eliminate some herds incubating the infection, it seems to slaughter and remove from the market many more that would not develop FMD. Slaughter of herds in direct and indirect contact (i.e. full pre-emptive slaughter) resulted in outbreaks of shorter duration. This most-aggressive slaughter strategy appeared to increase government cost in slow-spread scenarios. We attributed this to the higher government cost of slaughtering higher numbers of herds (þ52% over baseline) in these scenarios without a corresponding benefit in reducing additional spread. Decreased costs were found in fast-spread scenarios and for government costs plus net welfare change. These data suggest that some pre-emptive slaughter is cost-effective; however, the selection of herds appeared to be crucial to the cost savings of the strategy. Those herds at highest risk of developing FMD must be targeted (e.g. those in direct and indirect contact with infected herds). Pre-emptive slaughter was thought to be more beneficial in fastversus slow-spread scenarios in a prior Australian study (Garner and Lack, 1995). Our study is consistent with this concept.

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Ring vaccination (at 10 km) was studied as implemented early (after 2 positive herds) and later (after 50 positive herds) in an outbreak. Early vaccination decreased the duration of outbreaks. Both early and late vaccination decreased the 95th percentile—indicating a reduction in the number of longer duration outbreaks. This was expected, because herds in geographic areas around positive herds were vaccinated immune resulting in less spread of the infection. This immunity limited relatively longer-duration outbreaks found in the baseline scenarios. Two methods of accounting for vaccination costs were studied. In the first method, the vaccinated animals went to slaughter through normal market channels with no additional cost to producers or the government assumed. Early ring vaccination resulted in lower government costs (2–11% reduction from baseline) and government costs plus net welfare change (11–13% reduction) in the fast-spread scenarios only. Costs were higher in slowspread scenarios (10–15%). The second method of tracking vaccination costs involved slaughtering the vaccinated animals with a similar cost as in a positive herd. As expected, this increased costs of an outbreak greatly. Both late and early vaccination resulted in outbreaks costing 2.7 and 9.4 times baseline (government cost); and 1.1 and 1.4 times baseline (government cost plus net welfare cost). We expect that as the number of animals vaccinated goes up, this option becomes less attractive—since the supply effect of those animals being removed from the market becomes more pronounced. Ring vaccination was judged not to be cost effective except under specific circumstances. These circumstances would be a fast-spread rate and the ability to slaughter vaccinated animals at low cost. Other vaccination strategies such as vaccination of animals in larger geographic areas or herds awaiting depopulation were not evaluated. Vaccination and slaughter infrastructure (capacity) had an effect on the cost of these simulated outbreaks of FMD. The scenarios with higher capacity to slaughter or vaccinate resulted in lowered the costs and duration of outbreaks. This begins to address the issue not only of the availability of personnel to man vaccination crews—but also, the availability of the vaccine itself. Another missing piece is the cost of increasing the vaccination and slaughter capacities. Environmental considerations (that might limit ability or increase costs of carcass disposal) also are not considered in this analysis. A potential future expansion of this study might contribute to determining a cost-optimal infrastructure of a veterinary service in preparation for outbreaks of FMD.

5. Conclusions

The choice of best mitigation strategy depended on herd demographics and the rate of contact among the herds. Ring slaughter was consistently more costly than other slaughter strategies. The slaughter of in-contact herds (pre-emptive slaughter) reduced costs of controlling an FMD outbreak as compared to slaughtering contagious herds alone. Early ring vaccination decreased the duration of outbreaks. Ring vaccination was generally more costly than controlling with slaughter alone.

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Ring vaccination was less costly in fast-spread scenarios if vaccinated animals were slaughtered without additional cost (marketed through normal terminal market channels). Increases in vaccination-and-slaughter infrastructure (capacity) decreased duration and costs of simulated outbreaks.

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