The Economics of Managing Infectious Wildlife Diseases when Livestock are at Risk: Preliminary Results Richard D. Horan and Christopher A. Wolf Department.

The Economics of Managing The Economics of Managing Infectious Wildlife Diseases when Infectious Wildlife Diseases when

Livestock are at Risk:Livestock are at Risk:Preliminary ResultsPreliminary Results

Richard D. Horan and Christopher A. WolfRichard D. Horan and Christopher A. WolfDepartment of Agricultural EconomicsDepartment of Agricultural Economics

Michigan State UniversityMichigan State University

Kenneth H. Matthews, Jr.Kenneth H. Matthews, Jr.ERS – USDAERS – USDA

Concern over risks toConcern over risks to

Human health Human health

LivestockLivestock

Recreation/huntingRecreation/hunting

Conservation of biodiversityConservation of biodiversity

Diseases transmitted via a Diseases transmitted via a wildlife population are a growing wildlife population are a growing

problem worldwideproblem worldwide

Bovine Tuberculosis (TB) in Bovine Tuberculosis (TB) in Michigan DeerMichigan Deer

• Only known area in North America where Only known area in North America where bovine TB is established in wild deerbovine TB is established in wild deer

• Deer have infected a number of cattle herds.Deer have infected a number of cattle herds.– Agricultural damages estimated at $12 million/yearAgricultural damages estimated at $12 million/year

• Policy responsesPolicy responses– Reduce deer herdReduce deer herd– Stop supplemental feedingStop supplemental feeding

Model of optimal Model of optimal managementmanagement

Bioeconomic model of deer and cattle, incorporating disease transmission

Decentralized modelDecentralized model

Analyze private incentives and impacts in unregulated case

Analyze incentives created by existing policy

approaches, and impacts

First-best and second-best policy options

Prior research on wildlife transmitted diseasePrior research on wildlife transmitted disease

• Little regard given to wildlife dimensionLittle regard given to wildlife dimension• Estimates of costs to farmers and consumers from diff’t control Estimates of costs to farmers and consumers from diff’t control

strategies strategies (e.g., depopulation, test and remove) and resulting trade (e.g., depopulation, test and remove) and resulting trade and market effectsand market effects

• Bicknell et al. (Bicknell et al. (Aus. J. Agr. Res. Econ. Aus. J. Agr. Res. Econ. 1999)1999)• Bioeconomic model of possum and dairy cow populationsBioeconomic model of possum and dairy cow populations

• Optimal disease control strategies from a single farmer’s Optimal disease control strategies from a single farmer’s perspectiveperspective

• Selective harvesting of diseased possums possibleSelective harvesting of diseased possums possible

• Possums have no real value (other than nuisance)Possums have no real value (other than nuisance)

(Some) Research gaps(Some) Research gaps

• Social optimumSocial optimum– Most problems faced jointly by many farmersMost problems faced jointly by many farmers

– Wildlife-related benefits also importantWildlife-related benefits also important• High recreational values (hunting)High recreational values (hunting)• Threatened and endangered speciesThreatened and endangered species• Wildlife eradication policies may be expensiveWildlife eradication policies may be expensive

• Non-selective harvesting of infected wildlifeNon-selective harvesting of infected wildlife– Offtake accompanied by healthy and valuable animalsOfftake accompanied by healthy and valuable animals

– Increases disease control costsIncreases disease control costs• More difficult to exterminate diseased animalsMore difficult to exterminate diseased animals• Alters disease dynamics in a sub-optimal fashion.Alters disease dynamics in a sub-optimal fashion.

Outline of basic modelOutline of basic model• Two state variablesTwo state variables

– Deer population, Deer population, NN– Prevalence rate in deer, Prevalence rate in deer,

• Two control variablesTwo control variables– Aggregate harvest, Aggregate harvest, hh

• Non-selective with respect to diseaseNon-selective with respect to disease• By itself, harvesting cannot eliminate a persistent disease (without By itself, harvesting cannot eliminate a persistent disease (without

eradicating all wildlife in the area)eradicating all wildlife in the area)

– Supplemental feeding, Supplemental feeding, ff• Increases Increases in situin situ productivity (diminishes density-dependence) productivity (diminishes density-dependence)• Non-selective with respect to diseaseNon-selective with respect to disease

– Increases transmissionIncreases transmission– Decreases disease-related mortalityDecreases disease-related mortality

Social planner’s problemSocial planner’s problem

• NB(NB(tt) = ) = value of hunting – value of hunting – costs of hunting – costs of hunting – costs of feeding –costs of feeding –

damages to livestock sectordamages to livestock sector

• Objective function:Objective function:

subject to the equations of motionsubject to the equations of motion

• Linear control modelLinear control model

0

)( dtetNBMax t

h,f

Double singular solutionDouble singular solution• Adjoint equations for Adjoint equations for NN and and yield “golden rule” equations yield “golden rule” equations

(in implicit form):(in implicit form):

• Solve for nonlinear feedback laws for controls, Solve for nonlinear feedback laws for controls, ff((NN,,) and ) and hh((NN,,) )

• Plug Plug ff((NN,,) and ) and hh((NN,,) into the equations of motion for ) into the equations of motion for N N andand , and , and solve the differential equationssolve the differential equations

• Note: solution depends on initial states, Note: solution depends on initial states, NN00 andand 00

),,,( ),,,( hfNGfNF

, ),,( , ),( 00 NNBNAN

Figure 1. Solution of the benchmark numerical example

2000 4000 6000 8000 10000 12000 14000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

a 1

N

maxff

2 b

f=0

3

4

c c

d e

5

Some results of basic modelSome results of basic model• Disease eradication may not be optimalDisease eradication may not be optimal

• Feeding bans to quickly reduce/eliminate the Feeding bans to quickly reduce/eliminate the disease may be too costlydisease may be too costly– Opportunity cost of forgoing productivity investments Opportunity cost of forgoing productivity investments

(via feeding) may be too large(via feeding) may be too large

– Feeding is an investment in deer productivityFeeding is an investment in deer productivity• Intermittent investments create opportunities for near-term Intermittent investments create opportunities for near-term

gainsgains– Similar to Clark, Clarke, and Munro (1979), although investment Similar to Clark, Clarke, and Munro (1979), although investment

in our model produces adverse affects on resource dynamicsin our model produces adverse affects on resource dynamics

Adding the livestock (cattle) sectorAdding the livestock (cattle) sector• On-farm biosecurity and stocking decisions affect damagesOn-farm biosecurity and stocking decisions affect damages

ResultsResults• Cost-effective to target cattle sector for risk-reductionCost-effective to target cattle sector for risk-reduction

• Direct cattle risk controls vs. non-selective dDirect cattle risk controls vs. non-selective deer-related controlseer-related controls• Cattle sector is not highly profitableCattle sector is not highly profitable

• Reduce risk of transmission to livestock to zeroReduce risk of transmission to livestock to zero• Fully invest in biosecurity or permanently remove all cattle from infected Fully invest in biosecurity or permanently remove all cattle from infected

regionregion• Deer are managed independentlyDeer are managed independently

– Deer are highly valued whereas cattle sector is not valuableDeer are highly valued whereas cattle sector is not valuable– Only damages are to hunters; can support greater prevalence in deerOnly damages are to hunters; can support greater prevalence in deer

• Only have cattle sector if profitability exceeds investment cost Only have cattle sector if profitability exceeds investment cost

Targeting risk by sex of deerTargeting risk by sex of deer

• Prevalence in deer varies by sexPrevalence in deer varies by sex– Male/female behavioral differences affect Male/female behavioral differences affect

transmissiontransmission

• Sex-based harvests target important risk factorSex-based harvests target important risk factor– Reduces wildlife disease control costsReduces wildlife disease control costs– Disease eradication might be optimalDisease eradication might be optimal

(assumed no adjustments in the cattle sector)(assumed no adjustments in the cattle sector)

Summary of results from Summary of results from expanded modelsexpanded models

• Better risk targeting in wildlife sector increases likelihood that it will be optimal to– eradicate disease in wildlife– preserve cattle sector

• Better risk targeting in livestock sector increases likelihood that it will be optimal to– eliminate inter-species transmission

• Possibly eliminate cattle sector

– allow endemic disease in wildlife

Research outputsResearch outputs• Horan, R.D. and C.A. Wolf, “The Economics of Managing Wildlife Disease”. Under

2nd round review at American Journal of Agricultural Economics

• Horan, R.D., C.A. Wolf, E.P. Fenichel, and K.H. Matthews, Jr., “Wildlife and Livestock Disease Control with Inter-and Intra-Specific Transmission and Endogenous On-Farm Biosecurity”, Selected paper, the annual meetings of the American Agricultural Economics Association, Denver, CO, August 1-4, 2004.

• Fenichel, E.P., R.D. Horan, and C.A. Wolf, “The Role of Sexual Dimorphism in the Economics of Wildlife Disease Management”, Selected paper, the annual meetings of the American Agricultural Economics Association, Denver, CO, August 1-4, 2004.

• Fenichel, E.P., R.D. Horan, and C.A. Wolf, “Wildlife Disease Management Policies Based on Sexual Dimorphism: An Economic Argument” Selected paper, the annual conference of The Wildlife Society, Calgary, AB, Canada, September 18-23, 2004.

Future workFuture work

• Spatial managementSpatial management– Opportunities to better target risksOpportunities to better target risks– Consideration of additional risks of spreadConsideration of additional risks of spread

• Decentralized model of farmer/hunter Decentralized model of farmer/hunter behaviorbehavior– Examine economic incentives faced by Examine economic incentives faced by

individualsindividuals– Role of policyRole of policy

2000 4000 6000 8000 10000 12000

0.02

0.04

0.06

0.08

0.1

0.12After transforming the problem in terms of femalesAfter transforming the problem in terms of females

Path description

1.Original path- feeding unconstrained, 0 < harvests < all , 0 < f < max (optimal) (t = 0.5, at b)

2. Original path- feeding unconstrained, 0 < harvests < all , 0 < f < max (sub -optimal)

3. Feeding constrained at max, 1, 0 < harvests < all , f = max (t = 1.5, at c )

4. Unconstrained feeding path reemerges, 0 < harvests < all , 0 < f < max (t = 2, at d)

5. Feeding constrained at zero path 2, 0 < harvests < all , f = 0 (t = 22, at e)

6. Bang - bang solution harvests = 0, harvests = 0, f = max (t = 30, t = 45 at g )

F

NF

a

*

Feed max constraint

b

c

ee

d, f = 0 constraint *

Premature switching principle