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A Plant-Level, Spatial, Bioeconomic Model of Plant Disease Diffusion and Control: Grapevine Leafroll Disease

A Plant-Level, Spatial, Bioeconomic Model of Plant Disease Diffusion and Control: Grapevine Leafroll Disease
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  AP LANT -L EVEL ,S PATIAL ,B IOECONOMIC M ODELOF P LANT D ISEASE D IFFUSIONAND C ONTROL :G RAPEVINE L EAFROLL D ISEASE S HADY  S.A TALLAH ,M IGUEL . I. G ÓMEZ ,J ON  M. C ONRAD , AND  J AN  P. N YROP Grapevine leafroll disease threatens the economic sustainability of the grape and wine industry inthe United States and around the world. This viral disease reduces yield, delays fruit ripening, andaffects wine quality. Although there is new information on the disease spatial-dynamic diffusion,little is known about profit-maximizing control strategies. Using cellular automata, we model thedisease spatial-dynamic diffusion for individual plants in a vineyard, evaluate nonspatial and spa-tial control strategies, and rank them based on vineyard expected net present values. Nonspatialstrategies consist of roguing and replacing symptomatic grapevines. In spatial strategies, symp-tomatic vines are rogued and replaced, and their nonsymptomatic neighbors are virus-tested, thenrogued and replaced if the test is positive. Both nonspatial and spatial classes of strategies areformulated and examined with and without considering vine age. We find that spatial strategiestargeting immediate neighbors of symptomatic vines dominate nonspatial strategies, increasingthe vineyard expected net present value by 18% to 19% relative to the strategy of no diseasecontrol. We also find that age-structured disease control is preferred to non-age-structured controlbut only for nonspatial strategies. Sensitivity analyses show that disease eradication is possible if either the disease transmission rate or the virus undetectability period is substantially reduced. Key words : bioeconomic models, cellular automata, computational methods, disease control,grapevine leafroll disease, spatial-dynamic processes.  JEL codes : C15, C63, D24. Grapevine leafroll disease (GLRD) presentlythreatens grape harvests in the United States(Fuchs et al. 2009; Golino et al. 2008; Martin et al. 2005) and around the world (Cabaleiro et al. 2008; Charles et al. 2009; Martelli and Shady S. Atallah is a PhD candidate, Miguel I. Gómez is theMorgan Assistant Professor, and Jon M. Conrad is a professor,all in the Dyson School of Applied Economics and Manage-ment, Cornell University. Jan P. Nyrop is a Professor in theDepartment of Entomology, Cornell University.This article was previously circulated under the title “AnAgent-Based Computational Bioeconomic Model of Plant Dis-ease Diffusion and Control: Grapevine Leafroll Disease.” Theauthors thank editor Brian Roe and two anonymous review-ers for excellent comments and suggestions. The authors aregrateful to Marc Fuchs (Associate Professor, Department of Plant Pathology and Plant Microbe Biology, New York StateAgricultural Experiment Station, Cornell University) for hisguidance as they explored the literature on grapevine leafrolldisease biology and ecology. The authors thank Nelson L. Bills(Emeritus Professor, Dyson School of Applied Economics andManagement, Cornell University) for suggestions on earlierversions of the manuscript. The authors gratefully acknowl-edge the financial support of the United States Departmentof Agriculture’s National Institute of Food and Agriculturethrough Hatch Multistate Project S1050 and through Viticul-ture Consortium East Grant 2008-34360-19469. Errors remainthe authors’ responsibility. Boudon-Padieu 2006). This viral diseasereduces yield, delays fruit ripening, andnegatively affects wine quality by loweringsoluble solids and increasing fruit juice acid-ity (Goheen and Cook 1959; Martinson et al. 2008). Its economic impact was recently esti-mated at $25,000 to $40,000 per hectare if thedisease is left uncontrolled, which representsmore than 75% of a vineyard’s net presentvalue (Atallah et al. 2012). GLRD is primar-ily introduced to vineyards through infectedplanting material. Once introduced, the dis-ease can be transmitted from vine to vine byseveral species of mealybugs and soft-scaleinsects (Martelli and Boudon-Padieu 2006;Pietersen 2006; Tsai et al. 2010). Mealybugs can transmit GLRD within and across vine-yards in at least three ways (Charles et al.2009; Grasswitz and James 2008). Insects crawling on wires and fruiting canes cancause disease transmission to neighbor-ing vines. Vineyard management activitiescan facilitate mealybug dispersal to fartherneighboring vines within the same vineyard.  Amer. J. Agr. Econ.  00(0): 1–20; doi: 10.1093/ajae/aau032© The Author (2014). Published by Oxford University Press on behalf of the Agricultural and Applied EconomicsAssociation. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs licence (, which permits non-commercial reproduction and distribution of the work, in any medium, provided the original work is notaltered or transformed in any way, and that the work is properly cited. For commercial re-use, please contact   American Journal of Agricultural Economics Advance Access published June 18, 2014   b  y g u e  s  t   on J   un e 2 2  ,2  0 1 4 h  t   t   p :  /   /   a  j   a  e  . oxf   or  d  j   o ur n a l   s  . or  g /  D o wnl   o a  d  e  d f  r  om   2  Amer. J. Agr. Econ. Finally, disease spread between neighboringblocks or vineyards can take place throughaerial dispersal of mealybugs (Le Maguetet al. 2013).Vineyard managers are currently advisedto avoid introducing GLRD into their vine-yards by planting certified vines derived fromvirus-tested mother plants (Almeida et al.2013; Fuchs 2007; Golino et al. 2002). How- ever, when GLRD is already present, diseasemanagement consists mainly of minimizingthe source of infection by roguing symp-tomatic vines after harvest, especially theyoung ones and replacing them with virus-tested vines (Maree et al. 2013; Rayapati, O’Neil, and Walsh 2008; Walton et al. 2009). Vector management is recommended toreduce disease transmission (Skinkis et al.2009). Although insecticide sprays can reducemealybug densities, they have not been effec-tive at controlling GLRD spread, mainlybecause of the exceptionally low insectdensity needed for disease transmission(Almeida et al. 2013; Cabaleiro and Segura 2006,2007;Golino et al.,2002,2008). Most GLRD research has focused onstudying the pathogens, with less emphasison disease ecology and disease manage-ment (Almeida et al. 2013). This article usesinformation available in the GLRD diseaseecology literature to develop a computa-tional, spatial bioeconomic model that can beused to identify profit-maximizing strategiesfor GLRD control. Using cellular automata,we model the disease at the plant level in aspatial-dynamic way. In the simulations, thedisease is introduced to an artificial vine-yard through infected plant material at thetime of planting. Subsequently, its diffusionfollows a Markov process that is affectedby each vine’s location, virus detectability,age, own infection state, and infection statesof its neighbors. We then use a vineyardmanager’s profit maximization objectivefunction to evaluate the cost-effectivenessof disease control strategies formulatedbased on these vine-level characteristics.Our model contributes to the literature thatuses nonspatial, compartmental models whenmodeling diseases by relaxing the simplifyingassumptions that individuals are homoge-nous in their attributes and spatially perfectlymixed. 1 1 The perfect-mixing assumption implies that any infectiveindividual can transmit the infection to any healthy individualwith equal probability (Brauer and Castillo-Chavez 2001). We examine the impact of alternative dis-ease control strategies on distributions of bioeconomic outcomes and rank them basedon the vineyard expected net present values(ENPVs). The results highlight the potentialof vine-level, spatial strategies in reducingthe economic cost of GLRD. In addition, ourmodel can be modified to address spatial-dynamic disease diffusion and control issuesin other perennial crops. We are not awareof previous work in agricultural and resourceeconomics that formulates a spatial, plant-level, model of plant disease diffusion andcontrol. Literature Review The unique characteristics of certain insect-transmitted plant diseases restrict the choiceof approaches to model disease diffusion andcontrol. The first characteristic of such dis-eases is that they are simultaneously drivenby integrated dynamic and spatial forces,rather than by dynamic processes alone.When diseased plants are heterogeneouslydistributed in space and the physical environ-ment includes spatial constraints on diseasediffusion, such as a vineyard’s spatial config-uration, the optimality of disease control isaffected not only by its intensity but also byits location.Second, in insect-transmitted plantdiseases, pesticide applications can be inef-fective. This is particularly true in the case of GLRD, where insect vectors can have a shortinfectivity retention period, 2 live in crevicesand underneath the bark of the grapevine(Cabaleiro and Segura 2006, 2007; Daane et al. 2012), and spread disease rapidly evenif their population is kept at a low density(Charles et al. 2009; Tsai et al. 2008; Walton and Pringle 1999). Instead, insect-transmitteddisease control relies mostly on reducingthe source of infection by roguing (remov-ing) infected plants and replacing them withyoung, healthy ones (Chan and Jeger 1994).Thus, despite the attractive features of pestcontrol models, such as the ability to accountfor product quality in estimating pest con-trol effectiveness (Babcock, Lichtenberg,and Zilberman 1992) or incorporating pestrandomness in pesticide application decision 2 The insect infectivity period is the time in which insect vectorsretain the virus and remain infective (Tsai et al. 2008).   b  y g u e  s  t   on J   un e 2 2  ,2  0 1 4 h  t   t   p :  /   /   a  j   a  e  . oxf   or  d  j   o ur n a l   s  . or  g /  D o wnl   o a  d  e  d f  r  om    Atallah et al. A Plant-Level, Spatial, Bioeconomic Model of Plant Disease Diffusion and Control   3 rules (Saphores 2000), these models are notappropriate for vector-transmitted plantdiseases such as GLRD.Plant heterogeneity is the third charac-teristic of certain diseases. In the case of GLRD, individual vines that are infected butnonsymptomatic are heterogeneous in thetime it takes for their virus population tobe detectable by virus tests (Cabaleiro andSegura 2007; Constable et al. 2012). For some of these vines, the virus may not be detectedand rogued before they transmit the diseaseto neighboring vines, causing disease controlto lag behind disease diffusion and impedingeradication. Taken together, these three char-acteristics call for plant-level, spatial-dynamicmodels of disease diffusion and control. Spatial Bioeconomic Models Spatial-dynamic processes have only recentlybeen studied by economists, and the bioe-conomic literature on agricultural diseasesand invasive species control is mostly non-spatial (see review in Wilen 2007). Sanchirico and Wilen (1999, 2005) show that ignoring spatial processes can lead to suboptimalmanagerial decisions. Space can be incor-porated in bioeconomic disease models byintroducing barriers to disease diffusion (e.g.,Brown, Lynch, and Zilberman 2002), spec-ifying location-dependent, state-transitionprobabilities (e.g., Rich and Winter-Nelson2007), or using partial differential equations(e.g., Holmes et al. 1994). In such models,spatial heterogeneity is exogenous and fixedover time (see review in Smith, Sanchirico,and Wilen 2009). In some diseases, includingGLRD, however, spatial heterogeneity suchas the health status of a plant’s neighborhoodcan be endogenously determined by the dif-fusion process, affect disease diffusion, andbe affected by the implementation of controlstrategies. The challenge of incorporatingsuch spatial feedbacks into state dynamicsis a common thread in resource economicsand not confined to disease dynamic models(Smith, Sanchirico, and Wilen 2009). More-over, spatial bioeconomic models often makerestrictive assumptions such as linear growthand control to achieve tractability or to focuson steady state analyses in simple landscapes(see review in Epanchin-Niell and Wilen2012). Relaxing such assumptions precludesanalytical solutions and calls for numeri-cal methods in most applications (Smith,Sanchirico,andWilen 2009;Wilen 2007). Bioeconomic Models ofAgricultural Diseases Research on the economics of agriculturaldisease control has increasingly movedtoward integrated epidemiological modelsthat incorporate feedbacks between eco-nomic and disease diffusion componentswithin the model (Beach, Poulos, and Pat-tanayak 2007; Fenichel and Horan 2007; Horan and Wolf 2005). These models typi-cally aggregate individuals into disease-state(e.g., Horan et al. 2010) or age-state (e.g.,Tahvonen 2009) compartments (they arethus called compartmental models) anduse differential or difference equations torepresent transitions between states. Theyassume that the population is spatially per-fectly mixed and that the individuals arehomogenous in their attributes within eachcompartment.These assumptions are limiting in dis-ease modeling, especially in the case of GLRD where ( a ) plants are heterogeneousin virus detectability and ( b ) disease dif-fusion follows imperfect mixing processesand is shaped by vineyard spatial configura-tion and location of vines (Constable et al.2012; Pietersen 2006). The homogeneity assumption of aggregate models is partic-ularly restrictive because it precludes theformulation and testing of disease controlstrategies targeting individuals based on theirheterogeneous, spatial-dynamic attributes.Also, the perfect-mixing assumption hasbeen shown to underestimate the rate of spread in the early stages of a disease andto overestimate it in the later stages (Caneand McNamee 1982). These assumptions canbe relaxed in difference equation models torepresent distinct groups where individualsare heterogeneous by increasing the numberof subpopulations or dividing the subpop-ulations into smaller stocks (e.g., Medlockand Galvani 2009). Depending on the levelof heterogeneity desired, however, this pro-cess can lead to a combinatorial explosionin the number of state variables, equations,parameters, and data requirements (Teoseet al. 2011). Moreover, in aggregate bioe-conomic models of diseases, transmissionrates are imposed on individuals exogenouslydepending on membership in a specificsubpopulation. In reality, however, theserates are determined in a spatial-dynamicfashion as a result of the spatial-dynamicfeedbacks between disease diffusion anddisease control.   b  y g u e  s  t   on J   un e 2 2  ,2  0 1 4 h  t   t   p :  /   /   a  j   a  e  . oxf   or  d  j   o ur n a l   s  . or  g /  D o wnl   o a  d  e  d f  r  om   4  Amer. J. Agr. Econ. Table 1. Overview of the Modeling Process Modeling Step Tool1.  Formal model. Define bioeconomic model. None2.  Computational model. 2a.  Model specification.  Java,AnyLogic- Specify cellular automata model by defining: ◦  Space and time ◦  States and state transitions- Define model parameters and variables.2b.  Model verification.  Java,AnyLogic- Conduct simulation and collect simulated data.- Debug to ensure consistency in model behavior betweencomputational model and formal model.2c.  Model calibration Define optimization experiment that aims to find the optimal transmissionparameter values using field data from the literature.OptQuest,AnyLogic2d.  Model validation Validate calibrated model by testing that the expected time to 50%disease prevalence (expected half-life) and expected time to 100%disease prevalence measures fall within intervals reported in theliterature.Java,AnyLogic3.  Simulation experiments Define and conduct Monte Carlo experiments: scenarios of “no disease,”“no disease control,” eight nonspatial and ten spatial disease controlstrategies.Java,AnyLogic4.  Statistical analyses Conduct statistical tests on the differences between expected net presentvalues.Stata5.  Sensitivity analyses Repeat steps 3 and 4 for each parameter considered in the sensitivityanalysis. CellularAutomata Models With dramatic decreases in computationalcosts, cellular automata and agent-basedmodels have emerged as a preferred method-ological framework to study complex systems(Miller and Page 2007) such as diseases.Cellular automata are dynamic models thatoperate in discrete space and time on a uni-form and regular lattice of cells. Each cell isin one of a finite number of states that getupdated according to mathematical func-tions and algorithms that constitute statetransition rules. At each time step, a cellcomputes its new state given its own oldstate and the old state of its neighborhoodaccording to the transition rules (Tesfatsionand Judd 2006; Wolfram 1986). The spatial- dynamic structure is especially relevantwhen modeling processes that face physicalconstraints (Gilbert and Terna 2000) suchas boundaries and geometry, as in the caseof managed agricultural systems. In con-trast with compartmental models, cellularautomata and agent-based models do notaggregate individuals in compartments, thusallowing each individual to be heterogeneousin any finite number of attributes (Rahman-dad and Sterman 2008). Although cellularautomata models have been extensively usedto model spatial-dynamic processes (e.g., Sunet al. 2010; Yassemi, Dragi´ cevi´ c, and Schmidt 2008), their use in the agricultural economicsliterature has been rare. The few examplesinclude one application to foot-and-mouthdisease control (Rich, Winter-Nelson, andBrozovi´ c 2005) and land use change stud-ies (Balmann 1997; Kaye-Blake et al. 2009; Marshall and Homans 2004;Roth et al. 2009). We contribute to the disease control bioe-conomic literature by using cellular automatato offer a model that is inherently spatial anddynamic.We formally define the bioeconomicmodel, then build the computational model,verify its behavior, calibrate it, and validateit using GLRD disease ecology literaturefield data. Using simulation experiments,we generate distributions of bioeconomic   b  y g u e  s  t   on J   un e 2 2  ,2  0 1 4 h  t   t   p :  /   /   a  j   a  e  . oxf   or  d  j   o ur n a l   s  . or  g /  D o wnl   o a  d  e  d f  r  om    Atallah et al. A Plant-Level, Spatial, Bioeconomic Model of Plant Disease Diffusion and Control   5 Table 2. Vine Revenue Age ( a i ,  j  , t  ) and Yield Quality Vine RevenueInfection (  s i ,  j  , t  ) States Reduction (%) a Penalty (%) b ($/vine/month) c a i ,  j  , t   ≤ 36months N/A N/A 0.00 a i ,  j  , t   ≥ 48months and  H   0 0 0.43 a i ,  j  , t   ≥ 48months and  E u  or  E d  30 10 0.27 a i ,  j  , t   ≥ 48months and  I  m  50 10 0.19 a i ,  j  , t   ≥ 48months and  I  h  75 10 0.09 Note:  N/A indicates not applicable (a vine is not productive before the age of 36months). a Goheen and Cook (1959); Martinson et al. (2008) b Atallah et al. 2012. c Vine revenue calculations are based on the Cabernet franc grape yield of 3.3tons per acre, per year (White 2008), a planting density of 1,096 vines per acre (Wolf 2008), and a grape price of $1,700/ton (White 2008). outcomes for the scenario of no disease, thestrategy of no disease control, and eighteenalternative nonspatial and spatial diseasecontrol strategies. We then conduct statisticalanalyses to rank the ENPVs generated ineach experiment and find the optimal diseasecontrol strategy. Finally, we conduct sensi-tivity analyses to key bioeconomic modelparameters. We synthesize our modelingprocess in table 1. Bioeconomic Model The spatial geometry of disease diffusion isrepresented by a two-dimensional grid  G representing a vineyard plot.  G  is the set of   I   ×  J   cells where  I   and  J   are the number of rows and columns, respectively. In our model,there are 5,720 cells  ( i ,  j  ) ∈ G , each holdingone grapevine. Vineyard rows are orientednorth to south with  I   = 44 vines per grid rowand  J   = 130 vines per grid column resulting ina vineyard area of approximately 5.2 acres. 3 Each cell  ( i ,  j  )  has an age state and aninfection state. Time  t   progresses in discretemonthly steps up to 600months.  a i ,  j  , t   is a 600 × 1  vector holding a  1  for a vine’s agein months and zeros for the other possibleages. A vine can be  Infective  or  Noninfective .  Infective  (  I  ) and  Noninfective  ( NI  ) vines dif-fer by whether or not they exhibit symptomsand have the ability to transmit the infec-tion to their neighbors.  Noninfective  vines,in turn, can be in the following infectionstates:  Healthy  ( H  ),  Exposed-undetectable 3 This configuration is considered representative of a typicalvineyard in the Northeastern United States (Wolf 2008). Therepresented vineyard dimensions are 350 ′ × 650 ′ with an areaof 227,500ft 2 or 5.22acres. Vine and column spacing are 5 and8feet, respectively. ( E u ), and  Exposed-detectable  ( E d ). Subdi-viding the  Noninfective  states allows us toseparate healthy vines from those that havebeen exposed to the virus and have thereforelower grape yield and quality. The distinctionbetween the states  Exposed-undetectable  ( E u )and  Exposed-detectable  ( E d ) is importantto separate the vines whose virus popula-tions have not reached detectable levels( Exposed-undetectable ),from those with viruspopulations high enough to be detectablethrough a virus test ( Exposed-detectable ).  Infective  vines, for their part, can exhibittwo states, namely  Infective-moderate  (  I  m )or  Infective-high  (  I  h ). Separating the twostates allows us to model the decrease invine economic value as GLRD symptomsseverity increases over time from the mod-erate to the high level.  s i ,  j  , t   is the infectionstate vector at time  t   of dimension  5 × 1 . Thevector holds a  1  for the state that describesa vine’s infection state and zeros for theremaining four states.  w i ,  j  , t   is an age-infectioncomposite state defined as the combinationof a vine’s age state  a i ,  j  , t   and its infectionstate  s i ,  j  , t  .A vine’s infection and age states map intoa third dynamic state variable, its economicvalue, or per-vine revenue  r  ( w i ,  j  , t  ) . Per-vinerevenue equals zero if the vine’s age  a i ,  j  , t  is below  τ max . Beyond that age,  r  ( w i ,  j  , t  )  is afunction of the vine infection state. Grapesfrom GLRD-affected vines are subject toa penalty imposed on the price paid forgrapes harvested from healthy vines. Fur-thermore, GLRD reduces grapevine yieldby 30%, 50%, and 75% for vines in states Exposed  (both  Exposed-undetectable  and Exposed-detectable ),  Infective-moderate , and  Infective-high , respectively (table 2). A vine’srevenue is known to a vineyard manager attime  t  . Nevertheless, the per-vine revenue   b  y g u e  s  t   on J   un e 2 2  ,2  0 1 4 h  t   t   p :  /   /   a  j   a  e  . oxf   or  d  j   o ur n a l   s  . or  g /  D o wnl   o a  d  e  d f  r  om 
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