Optimal design of culling compensation policy under the African swine fever — Based on simulations of typical pig farms in China

GUO Shi-juan ,Lü Xin-ye ,HU Xiang-dong

1 Institute of Agricultural Economics and Development,Chinese Academy of Agricultural Sciences,Beijing 100081,P.R.China

2 Institute of Agricultural Information and Economy,Shandong Academy of Agricultural Sciences,Jinan 250000,P.R.China

Abstract This paper aims to optimize the culling compensation policy from a micro perspective through scenario simulation.Based on an investigation of 273 pig farms in eight regions,four typical pig farms were constructed according to farm size and breeding mode,representing the swine producers in China.Besides,a decision objective function of pig farms facing suspected African swine fever (ASF) outbreaks was constructed.This study used a mathematical programming model to design and simulate scenarios based on compensation standards and local implementation levels,aiming to incentivize pig farms to report epidemics.The results show that the optimal decisions on epidemic reports differed among typical farms and by herd daily age.The results suggest the following adjustments for optimizing culling compensation policies:(1) to set culling compensation standards based on the market value and (2) to maintain a high level of epidemic surveillance capability in the animal husbandry and veterinary sector.

Keywords: culling compensation,African swine fever,epidemic report,mathematical programming model

1.Introduction

In recent years,epidemic animal diseases such as foot-and-mouth disease (FMD),pathogenic porcine reproductive and respiratory syndrome (PRRS),and African swine fever (ASF) frequently occurred,causing severe economic losses (Brownet al.2020).Animal epidemics characterized by fast transmission and strong pathogenicity are the main factors that harm livestock health,cause property loss of farmers,and hinder the sustainable development of the whole industry (Mahul and Durand 2000;Brownet al.2007;Djunaidi and Djunaidi 2007).Culling infected herds is a timely intervention to control the epidemic and avoid greater loss (Kobayashiet al.2007;Fadigaet al.2014).

Accurate identification of infected or latently infected herds is the prerequisite for effective eradication measures,and farmers play a crucial role in the early detection of livestock epidemics (Elberset al.2010).First,farmers hold complete information on livestock health.Changes in herd health,such as reduced feed intake,poor activity,and even unnatural death,can always be first detected by the breeders.The time lag between farmers’finding and reporting directly determines the time interval between the discovery and culling of animal epidemics in this region,eventually affecting the epidemic’s spread (Yanet al.2012).Second,the disposition of infected animals is rested with breeders (Beachet al.2007;Reeling and Horan 2014).Farm-level activities such as stalling herds into groups or selling would spread the virus,which the government wants to avoid in disease control.In addition,farmers’ policy-participation willingness directly affects the effective implementation of prevention and control measures (Delgadoet al.2014).The report willingness of farmers is influenced by many factors,such as the fear of culling losses (Lambrouet al.2020),the cognition of the consequences of animal epidemics (Randrianantoandroet al.2015),the trust in the executive capacity of the livestock and veterinary sector (Heffernanet al.2008;Elberset al.2010),and the knowledge of epidemic reporting procedures (Gateset al.2021).

Countries usually implement financial compensation when culling is carried out.Studies showed that supporting fiscal policies can encourage farmers to adopt proactive epidemic prevention and control practices(Barneset al.2015).Incentives for farmers to actively report outbreaks through budgetary policies are the most effective means of monitoring early attacks (Garneret al.2016).Compensation for culling livestock did increase farmers’ willingness to report epidemics (Hennessy 2007).

However,the implementation of compensation policy faces challenges,especially the lack of an effective compensation standard.Low-level standards cannot cover the livestock value,while high-level ones may increase artificial infected herds.Studies showed that the probability of no-reporting would significantly increase when farmers get a higher return by selling the latent influenced stocks (Kuchler 2000),while farmers would take negative investments in epidemic prevention when facing higher compensation (Randrianantoandroet al.2018).Reasonable standards could motivate farmers to report actively,shortening the time interval from discovery to elimination and minimizing prevalent scope (Gramiget al.2009).Therefore,designing and optimizing culling compensation policy should be an unignorable measure in response to the epidemic.

The culling strategy is also adopted in China to eradicate foreign animal epidemics.The outbreak and prevalence of ASF in 2018 have attracted the attention of the Chinese animal epidemic prevention departments.Motivating pig farmers to report is a concern of the Chinese government.Based on the outbreak of ASF and the survey on pig farms in China,this paper explores the compensation policy design from the micro perspective through a scenario simulation.Although the prevalence situation of ASF has been controlled since 2020,the prevention and control of animal epidemics is still a research topic to protect animal health and stabilize the development of animal husbandry.Besides,animal epidemics such as FMD and PRRS have been threatening the production returns of livestock farms.The results of this study are expected to provide a reference for the optimization and adjustment of animal disease prevention and control policies.

The following parts of the paper are arranged as follows.The second part introduces the research background of this paper: the situation and impact of ASF in China and the according prevention and control strategies.The third part introduces the framework of this paper,including data sources,the construction of typical farms,mathematical programming methods and the scenario design.The fourth part presents the simulation results.Finally,the fifth part concludes the paper and provides policy recommendations.

2.Research background

2.1.The prevalence of ASF in China

ASF is a severe infectious disease caused by the African swine fever virus (ASFV) infecting domestic pigs and wild boars.All pigs at different ages are susceptible,and the morbidity and mortality are up to 100%.It is not a danger to human health but has devastating effects on pig populations and the farming economy.There is currently no effective vaccine to prevent and treat this disease(https://www.oie.int/en/disease/african-swine-fever/).

China’s first ASF case was reported in Liaoning Province in August 2018,and as of March 2019,31 provinces,municipalities and autonomous regions in mainland China had experienced the ASF outbreak.By August 2020,167 cases of epidemic diseases had been reported in China,involving 14 390 deaths and 339 164 pigs at epidemic sites,according to data released by the Ministry of Agriculture and Rural Affairs (MARA).The prevalence of ASF in China has seriously damaged the pig market,leading to a 21.3 and 24.6% decrease in pork in 2019 and 2020,respectively,according to the National Bureau of Statistics of China (NBSC 2020,2021).The inadequate pig supply induces significant fluctuation in market prices.The average market price of pigs increased from 13.43 CNY in August 2018 to 37.71 CNY in October 2019,and the average cost of piglets increased from 19.93 to 81.93 CNY in December 2019 (MARA 2020).

The prevalence of ASF in China is characterized by fast transmission speed,wide distribution,and severe market damage,which can be attributed to the following pig industry factors.First,the pig farms are large in quantity but small in size.China has a long history of pig breeding which has always been an essential part of household income.In 2019,there were 22.74 million pig farms in China,and 94.31% had fewer than 50 pigs(Editorial Committee of China Animal Husbandry and Veterinary Yearbook 2020).Second,pig production is separated from the market.In China,consumers have a dietary habit of preferring fresh meat.The fattened pigs enter the consumption link directly after slaughter without cooling,freezing,or processing.Thus,slaughterhouses are generally distributed around cities with large pork consumption,while pig farms are usually located in rural areas.In this context,the long-distance transportation of live pigs has become inevitable.The transregional and frequent transportation of pigs provided conditions for the spread and diffusion of the virus.

2.2.Cull compensation policy of ASF in China

The MARA has implemented a series of emergency measures to prevent the outbreak.(1) Cull pig herds at infection points.The only way to eradicate the ASF is to cull infected or latent infected hogs when no vaccines are available.According to the distance to infected pigs,the locations are classified into three: infection points(farms or villages where the infected pigs were located),infection areas (within 3 km from the infection point),and threatened areas (within 10 km from the infection area).All pigs in the infection points need to be culled with safety disposition.Besides,the MARA issued the Notice on Strengthening Supervision over the Transportation of Pigs and Products on August 31,2018,to strengthen product exit control in both infection areas and threatened areas.(2) Compensate for culled pigs.To lighten the loss of pig farms and ensure the implementation of prevention measures,the Ministry of Finance and MARA jointly issued the Notice on Subsidies for the Compulsory Culling of the ASF on September 13,2018.The notice includes ASF in the culling compensation scope and practices the standard at 1 200 CNY per head (including artificially raised wild boars).The central government would provide 40,60,and 80% of subsidies to the eastern,middle,and western regions,respectively,and the local finance made up for the rest.The compensation was settled based on the number of hogs culled.

However,local animal epidemic prevention departments lack sufficient funds to control ASF,resulting in unfulfilled compensation for farms.Moreover,the accuracy and timeliness of ASFV detection techniques are limited.These restraining factors cause unguaranteed payments to farms for reporting.On the one hand,pig farms are worried about the property loss caused by the pathogen infection of pigs.On the other hand,farmers are also concerned about compensation after culling.Thus,many farms sell the hogs because of panic,even in the latently infected stage.These problems resulted in the delayed identification and forced culling of infected and potentially infected pigs.The early stage of ASF in China was not timely identified and controlled,expanding the spread of ASFV in mainland China.

This work explores the optimization of prevention and control strategy through a micro-decision simulation,in which compensation policies could motivate farmers to report voluntarily.

2.3.How the compensation policies incentivize farms to report

The farm’s report decision on outbreaks is considered a kind of “profit-seeking” process (Lupoet al.2014).The influencing mechanism of epidemic report decisionmaking is described in Fig.1.Based on the perceived policies,market environment,and the characteristics of pig herds,farmers comprehensively compare the benefits between decisions.In controlling ASF,the state has issued relevant documents on compensation for epidemic culling,called “document policy”.However,the document policy cannot be ultimately implemented.On the one hand,local animal husbandry departments might have insufficient personnel,materials,or funds when taking culling measures.On the other hand,the lack of detection probability would induce inaccurate identification when facing this new and exotic attack.Therefore,farms would decide on disease reporting according to their perceived compensation policy,called “perceived policy”.The perceived policy can be seen as a combination of the culling compensation policy (document policy),the policy implementation level,and the detection probability in regions.In addition,the market environment and the characteristics of pig herds also affect the cost-benefit of pigs.For example,the market price and weight directly determine the sales income of hogs,and the daily age of pigs is also directly related to the feeding cost.Thus,this study attempts to address the difficulty in implementing culling compensation on the farm level,the basic unit of epidemic control.

Fig.1 Influencing mechanism of epidemic reporting decision in farms.

3.Data and methods

3.1.Data

To fully understand the prevention and control behavior on the farm level for ASF,we carried out a large-scale field survey across eight regions in China from June to December 2020.The samples covered eight regions across six regions: northeast,north,east,central,south,and southwest China.Two countries were selected from each province.In addition,the opinions of the local animal husbandry and veterinary departments were fully considered when selecting the type of pig farms for investigation in each county.Thus,the sample farms could represent the local breeding characteristics in terms of size and mode.This survey obtained information on 273 pig farms,including (1) basic farm information (e.g.,farmers’personal information,breeding mode,herd size,and farm location),(2) the pig-feeding costs (e.g.,labor cost,feed,water,and electricity),(3) disease prevention and control(e.g.,the input of vaccines and veterinary medicine),and (4)understanding on ASF controlling (e.g.,epidemic reporting and prevention tools in pens).The regional distribution of these surveyed farms is shown in Table 1.

Table 1 Distribution of surveyed farms

Among these surveyed farms,47.53% of farms experienced suspected ASF1Suspected ASF cases are different from those confirmed by the Ministry of Agriculture and Rural Affairs.in which only 34.91% had actively reported the unnatural death of pigs to the local animal husbandry and veterinary departments.Since the first case of the suspected outbreak was found,61.46% of farms had immediately sold the rest of the latent affected hogs to avoid more severe damage.The finding might explain the prevalence of ASF during the initial period.In other words,the practiced culling compensation policy lacked sufficient incentive to report the epidemic on farms.Here,the following conditions should be met for the suspected ASF epidemic in the sample farms: (1)there is abnormal death of pigs with symptoms similar to ASF;(2) the ASF pathogen is positive in the farm;(3) the surrounding farms have been infected with ASF or tested positive for ASF virus antigen.

3.2.Theoretical framework

Mathematical programming modelThe mathematical programming (MP) model has become an essential and widely used tool in agricultural economic analysis.The essential motivation of mathematical planning in agricultural economic analysis is to solve the problem of how to make better use of limited resources (Mills 1984).The MP model can easily simulate the effect of different policy tools,such as prices,subsidies,taxes,and technologies at the farm level (Mahyet al.2015).Usually,the MP model is more suitable for analyzing the policy responses of farmers (Buysseet al.2007).The model can effectively promote communication between stakeholders,especially farmers and policymakers.Compared with the analysis method of econometrics,mathematical programming can better simulate the interaction between policy adjustment and micro-decisionmaking,which has been proven to be a very effective method in policy optimization simulation (Manoset al.2013;Cortignani and Dono 2019;Guoet al.2021).

Establishment of the typical farmsThe idea of “typical farm” has drawn the attention of researchers in agricultural economic analysis in recent years (Chibandaet al.2020).The “typical farm” method was applied to collecting farmlevel information by many research institutes,such as the Center for Agriculture and Food Policy (AFPC) at Texas A&M University (TAMU),Brazil’s National Commodity Supply Corporation (CONAB),the International Agricultural Comparison Network (IFCN),and Thunen Institute’s Agri-Benchmark Agricultural Network.The “typical farm” has been used to understand the agricultural production system(Ndambiet al.2007;Ndambi and Hemme 2008;Siqueira and Duru 2016),establish observation benchmark (Lasneret al.2016),analyze changes in production practices(Kress and Verhaagh 2019),and conduct policy evaluation(Guoet al.2021).Usually,farmers with similar production conditions and agricultural production systems were similar in production decisions (Dillon and Melvin 1992).By constructing typical farms,behaviors in the same region and the same type of farm can be well represented.This abstract data processing method avoids the particularity caused by individual observation and thus could accurately simulate and predict the micro producers’ decision changes in this region.

In order to analyze farms’ reporting decisions for ASF,four typical farms were constructed according to breeding size and breeding mode based on our farm-level survey,representing pig farms in China (Table 2).Farm 1 and Farm 2 represent full-scale pig farms with over 500 hogs2This is the Ministry of Agriculture and Rural Affairs of the number of full-scale pig farms demarcated standard.fattened annually,while Farm 3 and Farm 4 represent pig households with less than 500 heads.The full-scale pig farms usually have a large quantity of pig herds with professional and technical personnel in breeding,operation,and management.On the other hand,the households have small-scale pig herds with backyard breeding and family-operating mode.Farm 1 and Farm 3 are self-supporting farms,and Farm 2 and Farm 4 are pigfattening farms.The feeding costs and related breeding parameters of the four typical farms are shown in Table 2.

For the convenience of comparison,fattening pig herds were focused on both self-supportive and pig-fattening farms.The main cost and benefit data of the four typical farms are shown in Table 2,which are determined by the average data of sampled farms,representing the general level of this kind of farm.The main difference between the two feed modes was the source of piglets and the associated costs.In self-supportive farms,fattening piglets were provided by sows,and the cost of piglets was called “l(fā)anding cost”,which was the cost of feeding sows.In contrast,the pig-fattening farms purchased the piglets from the market,and the market price was seen as piglet cost.There is a difference in the initial weight of piglets in the two modes.The piglets in the pig-fattening farm were purchased from the breeding farm and fed with feed for a period of time after weaning.Their weight was usually higher than 10 kg.The weight of self-breeding piglets was the weight of weaned piglets.In addition,due to the differences in feeding management,the full-scale farms have a slightly higher investment in labor and vaccine than the household.

Table 2 Feeding costs and related parameters of fattening pigs in typical farms1)

3.3.Behavior decision process and objective function

The programming model usually includes assumptions when simulating farm decisions.(1) Farmers actrationally.The objective of decision-making in disposing of epidemic pigs is to maximize the economic benefit based on the farm’s expected income for each decision.(2) Single production cycle hypothesis.Breeders’behavioral decisions aim to maximize the economic benefit of fattening pigs in a single production period.(3)Complete information.Farmers can obtain timely and comprehensive information on prevention and control policies and market information.

Report decision process in farmsDo farms voluntarily report the unusual deaths or clinical symptoms of ASF to local animal health authorities? How to deal with the dead hogs if farmers do not report them? What should be done about pigs that may be carrying the virus but have not yet shown clinical symptoms? Effective post-epidemic control of animals can prevent and slow down the epidemic spreading and lower the threat to the ecological environment.The farms make the balance based on the comprehensive analysis and judgment of factors such as culling compensation policy,market information,and pig characteristics,aiming to maximize the benefits of the expected decision.

As shown in Fig.2,reporting suspected outbreaks to local animal husbandry and veterinary authorities is the farmers’ primary decision.The departments will carry out epidemic confirmation procedures,culling with compensation when farms choose to report.The infected or latent infected pigs will be culled and treated with professional inoculation subsequently,minimizing the risk of the spread of ASF.When not to report,farmers would face the second decision on dealing with infected or potentially infected herds.Sell immediately to avoid more pig death? Or quarantine the surviving pigs?

Fig.2 The decision process of pig farms.ASF,African swine fever.

For quarantining,raisers usually remove the pigs with abnormal characteristics,such as abnormal body temperature,and reduce the infection of the remaining pigs in time.This process is vividly called “tooth extraction”.However,due to the high transmissibility of ASFV,farmers may face quarantine failure.What are the chances of a herd surviving quarantine? For selling,producers need to consider several factors affecting pig sales: Do pig herds meet the slaughtered weight? Is the market price attractive? Does the local animal quarantine department detect the sold pigs for ASFV?

For farmers,the decision process is a personal rational behavior to seek profit,whose decision to report is what the government wants to see.Thus,policy design aims to combine farms’ rational decision process with the macro purpose of controlling the epidemic to give full play to the incentive role of the culling compensation policy.

Objective functionEq.(1) is the decision objective function of the typical farms,in whichxandyrepresent the report decision and disposal choice,respectively,whileUandVindicate the expected profit under different decisions,respectively;x1andx2can be regarded as the decisions of reporting and non-reporting,andU1andU2indicate the expected profit when reporting and not reporting the epidemic,respectively;y1andy2represent decisions of selling and quarantining of pig herd disposition,andV1andV2are the expected profit under the two decisions,respectively.

The expected net income of typical farms in different scenarios could be calculated by eq.(2).The feeding cost was the input in the breeding process of hogs.As rational individuals,the epidemic reporting and disposal choices of typical farms are all based on maximizing the farm-level production profit -the decisions ground on the farms’ judgment on the market,policy,and epidemic situation.

Eqs.(3) to (5) describe the process ofU1,V1andV2in detail,wheretrepresents the daily age of the hogs at the time of decision making,andcfeedis the feeding cost of pigs at the time oft;pandweightindicate the price and weight of fattened pigs,respectively;βis the implementing level of compensation level;Subindicates the compensation level;γandαrepresent the price adjustment coefficient for selling and quarantining,respectively.Besides,θandκrepresent the possibility of detection for selling and quarantining when farmers decide not to report,andζis the rate of increase in feeding cost when deciding to quarantine.

3.4.Scenario design

Benchmark scenarioThe benchmark scenario is the situation with no intervention.The animal husbandry and veterinary department carry out no relevant control measures.The decision to sell or quarantine depends entirely on the judgment of farmers.The benchmark scenario can also be expressed as an extreme situation with only a documented policy but no policy implementation (β=0).All the scenario designs and parameters are shown in Tables 3 and 4.

Scenario design of compensation standard(1)Scenario simulation of document policy.The standard was fixed at 1 200 CNY per head,which was based on the Notice on Subsidies for Compulsory ASF Culling issued by the Ministry of Finance and the Ministry of Agriculture and Rural Affairs on September 13,2018.The notice was the first national guidance on culling compensation in the wake of the ASF outbreak,and subsequent documents have been guided by the circular.Besides,the document policy would also simulate the design of one size fits all compensation for culling (Scenario 1).

(2) Scenario simulation of modified standards.Although the fixed standard is simple to enforce,it may overlook the feeding cost variance between farms,thus being incapable of identifying the differences between farmers’ decisions.

In Scenario 2,the standard was designed nearly to cover the feeding cost based on the surveyed farm data(Table 4).Besides,the hogs were divided into four age periods to distinguish the cost difference between pig herds.The division of T1 and T2 refers to the slaughtering age of pigs.According to the investigation,the 110-dayold was taken as the dividing line of whether it could be slaughtered.The average weight of a healthy lean finishing pig could reach 60 kg at that age.The 110-dayold pig herds were further divided into 55-day-old pigs(T1-1) and 85-day-old pigs (T1-2).Moreover,pigs over 110 days old were split into 115-day-age pigs (T2-1) and sold-age pigs (T2-2).The feeding cost is calculated by the average data of four typical farms at different ages.Thus,the compensation standards for culling in Scenario 2 for the four age period herds were designed as 600,800,1 000,and 1 200 CNY,respectively.

Table 3 Scenario design

Table 4 Parameter value

Scenario 3 takes the market price as a reference,and the compensation standard was designed at 70% of the market value.The market price referred to the average price of live hogs in the whole country before the ASF outbreak in China.

Scenario design of implementation and detection(1)Full implementation of compensation with fine.Farmers do not have to pay for concealing outbreaks or selling infectedor latently infected herds in previous scenarios,which is usually the fact.Scenario 4 was designed to charge a penalty on farms when the behaviors of concealing or selling infected pigs were detected.The fine was set at 40 CNY per head,referring to China’s subsidy standard for the harmless disposal of dead livestock.Besides,the compensation standard was cut down in Scenario 4,which was carried out at 50% of the market price.

(2) Different levels of implementation and detection.Scenario 1 to Scenario 4 is based on the full implementation of the compensation policy (β=100%).However,in reality,local departments’ implementation ability and detection probability may not be fully effective.Three levels 90,60,and 30% were designed for Scenarios 5,6,and 7,respectively,reflected in the implementation ability to cull compensation policy and the identification probability of infected herds.The higher the value of these parameters,the higher the implementation level of local departments and the higher the detection probability of infected pigs.Specifically,the implementation level (β) was valued at 90,60,and 30%,and the detection probability of selling (θ) was assigned 72,48,and 24%.Similarly,the probability of quarantining(κ) was referred to as 18,12,and 6% (Table 4).

4.Results and discussion

This section presents the results of the model’s application in simulating scenarios (Table 5).

4.1.Decisions on epidemic reports differed among herd daily-age

The results of the Benchmark Scenario showed that the disposal decision was closely related to the daily age of herds.With no intervention,farmers would quarantine the pigs that have not reached the market age or weight (T1),while for pigs qualified the slaughtered weight (T2),the farm would sell immediately to avoid severe loss.

4.2.Scenarios on compensation standards showed the following

The document compensation standard can encourage farms to reportResults of Scenario 1 showed that the optimal decision for all typical farms was to report.However,the problem under the fixed compensation standard was that the profit from the epidemic report of all-age pig herds under 115 days was higher than the“pre-epidemic” (Table 2).The “excess” income from active reporting would induce farms to reduce investment in epidemic control or deliberately expose pigs,thus increasing the risk of infection with the ASFV.However,animal husbandry and veterinary departments cannot detect “malicious” arbitrage activities effectively.

Table 5 Optimal decision and income of typical farms1)

The compensation standard based on breeding cost played an incentive role in reportingResults of Scenario 5 showed that the optimal decision of all typical farms was to report the outbreak.The decision incomeof the self-breeding farms was positive,with similar income levels among different herds.The decision income in pig-fattening mode was relatively low,with a significant difference among pig groups.Taking Farm 4 as an example,the profit of the reporting decision for four types of day-old pigs was -32,12,42,and -158 CNY,respectively.However,the field culling staff needs to classify pigs first in this compensation scenario,resulting in a large amount of work on-site,especially for farms in self-breeding mode.

The compensation standard based on market value played an incentive role and simplified executionIn Scenario 3,the decision income of pigs at any daily age was negative.The expected income level reported by typical farms decreased compared with Scenario 2,resulting in a net loss.However,reporting outbreaks could still reduce losses compared with selling and quarantining infected pigs after “concealing”.Furthermore,the culling compensation that the government needs to pay in this scenario decreased.Take Farm 1 as an example,the average head compensation standards paid to four types of daily-age pigs were 324,464,619,and 859 CNY,respectively,lower than Scenario 1 and Scenario 2.For the local department,the scenario designed based on market value could reduce financial pressure and incentivize farms to report voluntarily.Moreover,in the field culling work,this scenario allowed weighing the pig herd without classification uniformly,thus lightening the workload in the culling site.

The compensation design with penalty could still give full play to the policy advantages,but farmers mightbe seriously frustratedExcept for the 85-day-old pigs in Farm 1,all the other optimal decisions were to report the epidemic actively.Compared with the above scenarios,the financial compensation pressure in Scenario 4 was further reduced.Taking Farm 1 as an example,the average head compensation at four age stages was 232,331,442,and 614 CNY,respectively,lower than the above scenarios.Compensation with penalty measures increased the opportunity cost of concealing,and the drive to report was to avoid severe punishment and prevent further losses.Taking Farm 1 as an example,the head losses of four pig groups were 170,203,243,and 316 CNY,respectively,higher than those in Scenario 2 and Benchmark Scenario.The scenario designed with penalty forced producers to report outbreaks helped control outbreaks and reduce financial pressure.Still,the expected losses were more weighted than the no-intervention scenario on the farm level.In other words,instead of making up for the loss in disease,the culling compensation multiplied the economic loss in farms,which might discourage the enthusiasm of pig farms for “supplementation” and lead to an insufficient supply of hogs.

4.3.High-level implementation and detection helped compensation policy play effectively

The low implementation level directly weakened the effect of compensation policiesWhen the implementation level was 90% (Scenario 5),the optimal disposal decisions for all pig herds were to report positively.When the regulatory enforcement level was 60% (Scenario 6),the optimal decision for Farm 1 and Farm 3 under the slaughter age was to quarantine.The decrease in the implementation level led to a drop in the expected benefits for farmers,while the reduced probability in the detection of infected pigs indicated a decrease in the opportunity cost,leading to non-reporting as the optimal decision.

The optimal disposal decisions differed from pig herds under the same detection levelIn Scenario 6,Farm 1 and Farm 3 would choose not to report and continue to raise the pigs of 55 and 85 daily age.The optimal decision of older pigs over 115 daily age was to report immediately,under the medium level of detection.In Scenario 7,when the implementation was at a low level,the optimal decision was to conceal and quarantine the infected pigs at 55 and 85 days.The optimal disposal decision for the pigs over 115 daily age was to sell immediately.

The optimal disposal decisions differed from the breeding mode under the same detection levelFarms of simply fattening mode were more inclined to report.In Scenario 6,the optimal disposal decisions of pig fattening farms represented by Farm 2 and Farm 4 were to report the epidemic actively.In contrast,the self-breeding farms represented by Farm 1 and Farm 3 would report the outbreaks only for old-age pigs.

5.Conclusion and policy implications

Under the outbreak of ASF in China,this paper designed and simulated the culling compensation policy from a micro perspective.Scenarios were designed and simulated from the perspective of compensation standards and the level of implication and detection,aiming to incentivize pig farms to report epidemics using a mathematical programming model.The results could be concluded as follows: (1) The “document policy” provided incentives for voluntary reporting.However,it would not only create financial pressure but also encourage activities of deliberately exposing infected herds to seek profit,as the compensation exceeds the cost of feeding.Such policies would not avoid “moral hazard” in the implementation and cause an excessive financial burden on local governments,thus ineffective in epidemic control.(2) The culling compensation standard designed with coverage costs could still motivate the farms to report actively while cumbersome in the actual confirmation.(3) The design of compensation standards based on market value played an incentive role in policy,reducing local financial pressure and saving the on-site workload.(4) Punitive measures forced the farms to report by increasing the opportunity cost of “concealing” but might discourage the farms’ enthusiasm for re-breeding due to increased losses.(5) A high level of detection and policy implementation would promote policy effects.

This study provides the direction of adjustment based on compensation policies to encourage farmers to report actively.First,the compensation standard should be set based on the market value.Based on 70% of the pre-epidemic market price,the compensation standard considered the difference in feeding cost and the compliance of the husbandry and veterinary departments.Compared with the current “one-size-fits-all” fixed policy,it could reduce local financial pressure and simplify complicated confirmation procedures.Second,animal husbandry and veterinary departments should maintain a high epidemic surveillance capacity.Improving the detection and technical means of ASFV would help identify the “profit-seeking” behavior of concealing epidemic timely.

Acknowledgements

This work was supported by the the Science and Technology Innovation Program of the Chinese Academy of Agricultural Sciences (21-2060302-034).

Declaration of competing interest

The authors declare that they have no conflict of interest.