Combined control evaluation for Neospora caninum infection in dairy: Economic point of view coupled with population dynamics

Journal Pre-proof Combined control evaluation for Neospora caninum infection in dairy: Economic point of view coupled with population dynamics Yue Liu, Michael P. Reichel, Wing-Cheong Lo

PII:

S0304-4017(19)30248-1

DOI:

https://doi.org/10.1016/j.vetpar.2019.108967

Reference:

VETPAR 108967

To appear in:

Veterinary Parasitology

Received Date:

4 July 2019

Revised Date:

1 November 2019

Accepted Date:

4 November 2019

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Combined control evaluation for Neospora caninum infection in dairy: economic point of view coupled with population dynamics Yue Liua,∗, Michael P. Reichelb , Wing-Cheong Loa b College

a Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, SAR. of Veterinary Medicine and Life Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, SAR.

Abstract

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Neospora caninum infection is regarded as one of the most important infectious causes of abortion in dairy cattle. To intervene in its spread, four potential controls including test-and-cull, medication, vaccination, and selective breeding are considered and assessed in this study. The cost of each control, together with the inevitable annual

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loss due to population dynamics, is adopted as an assessment criterion from an economic point of view. By performing simulation and sensitivity analysis, our results demonstrate that compared with each single control,

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combined controls are worthwhile with better financial outcomes. For farm affected with significant prevalence (equal to or greater than 30%), vaccine treatment is the most effective and economical option among all control strategies. On the other hand, for farm where prevalence is relatively low (around 10%), combined control, by

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applying vaccination followed with test-and-cull, medication or selective breeding, could be alternative treatment to provide better financial outcome against single control in an observed period.

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1. Introduction

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Keywords: Neospora caninum; dairy cattle; infectious disease; economic considerations; combined control

Neospora caninum (N. caninum) is a coccidian parasite with a wide host range. It is widely recognized as the

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predominant infection and cause of abortion of dairy cattle in many countries (Dubey and Lindsay, 1996; Wouda

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et al., 1997; Dubey, 2003; Wilson et al., 2016). The major transmission route is transplacental invasion of the

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embryo or fetus (Par´e et al., 1996; Davison et al., 1999). Studies in different regions (Schares et al., 1998; Hall

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et al., 2005; Almer´ıa and L´ opez-Gatius, 2013; de Aquino Diniz et al., 2019) have provided strong evidence to show

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that this mode of transmission is highly efficient. Efficiency has been reported to range from 81% to 95% (Lindsay

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et al., 1996; Hall et al., 2005; Schares et al., 1998; Davison et al., 1999). Besides the vertical infection from mother

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to daughter during pregnancy, cattle can also be infected horizontally by the seropositive ones within-herd where

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N. caninum circulates endemically (Davison et al., 1999; Crawshaw and Brocklehurst, 2003; Bartels et al., 2007)

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or other hosts from wildlife (McAllister et al., 1998; Fuehrer et al., 2010; Dubey and Schares, 2011; Dubey et al.,

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2017) by ingestion of food or drinking water contaminated by sporulated oocysts.

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∗ Corresponding

author Email address: [email protected] (Yue Liu)

N. caninum has been associated with high abortion rates (Atkinson et al., 2000; Pfeiffer et al., 2002), low

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milk yields due to adversely affected organ system functions of infected cow, reduced weight gain, and premature

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culling (Hernandez et al., 2001). The abortions are a major root cause of economic loss to dairy management

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(Hernandez et al., 2003; Reichel and Ellis, 2006; Reichel et al., 2013). Preventive control options or treatments

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have been discussed by different methodologies and assessment criteria in geographically distinct areas (Reichel

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and Ellis, 2002; Larson et al., 2004; H¨ asler et al., 2006a,b). The controls intrinsically involve the prevention of

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vertical and horizontal transmission. By now, four main options for the producer to control N. caninum have

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been demonstrated: (i) test-and-cull; (ii) medication; (iii) vaccination; (iv) selective breeding. Mathematical

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models have been used to describe the dynamics of cattle and explore possible control measures (French et al.,

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1999). They proposed that the annual culling of infected cattle would be the most effective control since it could

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reduce the prevalence rapidly. However, a good control strategy should be able to reduce the prevalence and

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simultaneously be affordable. To achieve this aim, models of decision tree analysis were developed to evaluate

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the control options from an economic point of view (Larson et al., 2004; Hall et al., 2005). Larson et al. (2004)

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developed a 5-year simulation model and indicated that testing the herd for N. caninum infection and excluding

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female offspring of seropositive dams as replacements gave the best economic return in the United States. In

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the investigation carried out by Hall et al. (2005) in New South Wales in Australia, the economic benefits of

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controls are quantified by how much the control can reduce the economic loss with respect to the control cost.

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Subsequently, two investigations in Switzerland conducted the stochastic epidemiologic and economic modules to

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assess controls in terms of prevalence and benefits, respectively (H¨asler et al., 2006a,b). The first study (H¨ asler

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et al., 2006a) aimed at investigating the impact of four controls on population dynamics. It used 12 age-groups to

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depict cattle population and revealed that the policy of testing and culling all seropositive animals in cattle was

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the most efficient, which cut down the prevalence rapidly to 0.13% in the 4th year at 12% prevalence. Compared

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with test-and-cull, both chemotherapy and selective breeding have a lower impact on prevalence. What’s more,

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they also have been proved to be economic (H¨asler et al., 2006b). H¨asler et al. (2006b) employed the prevented

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loss and benefit-cost ratio to assess the economic outcomes of control options and released that the chemotherapy

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of all-female offspring had the highest benefit-cost ratio among all options. A control program, which was based

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only on the use of the beef-breed semen in seropositive cows, without culling seropositive animals, was applied in

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a closed dairy herd over 5-year period in northern Italy (Sala et al., 2018). Although eradication of N. caninum

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was not achieved at the end of the study period, it declared a significant reduction in prevalence and incidence

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of neosporosis in the herd and a reduction of the abortion rate was achieved with the application of the control

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plan in five years.

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Infection controls will be taken to inhibit the spread of disease but infection may not be completely eradicated

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among dairy (Sala et al., 2018), which means abortion induced by N. caninum may still bring on loss which is

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inevitable. Therefore, we will adopt the cost of control coupled with annual loss due to population dynamics as

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the evaluation criterion in terms of economic loss, which makes the option more practical over living with the

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disease. Based on this economic principle to guide decision-making, single control is firstly assessed and we will

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extend our study to answer the following interesting questions. Whether a combined control with two methods

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could be more effective and economical than single control? How much is the economical improvement for the

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combined controls? For a combined control, which timing should be decided to initiate the second control during

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an observed period? Our study considers the population dynamics of dairy cattle and economic loss induced by controls simultane-

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ously. A discrete age-structured population model with 5 age-groups is used to describe N. caninum transmission

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process. Subsequently, four potential controls including test-and-cull, medication, vaccination, and selective

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breeding are assessed considering reduction in prevalence and reduced economic loss. The cost of control coupled

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with dynamics of annual loss is conducted as the comparison standard to assess potential control options from an

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economic point of view. Furthermore, we consider different combined controls, vaccination combined with test-

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and-cull, medication or selective breeding, to determine the most effective and economically attractive method

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with regard to varied farm sizes, and then decide at which timing the second control should be initiated during

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an observed period. Finally, sensitivity analysis highlights the robustness of our recommendations.

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2. Materials and methods

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2.1. Model for N. caninum infection in dairy

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Age plays an important role in the dynamical population, especially pregnancy and birth. In this study, the

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cattle are stratified by two categories: the susceptible individuals (S) and the infected individuals (I). Each

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category is divided into 5 classes (Sch¨ arrer et al., 2014), and they represent 0–1, 1–2, 2–3, 3–4, ≥ 4 years old,

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respectively. Hence, the susceptible category and infected category have subclasses: Sk (t) and Ik (t) for k = 1, ..., 5.

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The population distribution may change every year due to transmission of N. caninum, culling of unhealthy ones

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and aging. According to fertility status, animals in age-group 1 are called offspring (O), animals in age-group 2

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are heifers (H) and the remaining animals are cows (C). It should be remarked here that population of whole

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cattle is kept balanced during an observed period and the present model is a one-sex model, namely all changes

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are assumed to occur in females and all animals we referred are female. Overall infection processes among 5

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age-groups are described in Fig. 1, and the time-dependent variables involved in population model are listed in

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Table 1.

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2.1.1. Birth and vertical infection

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Animals with age from 3 to 5 (k = 3, 4, 5) are mature and can contribute to birth. Pregnancy rate αk

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depends on age-class k but not health category. However, abortions occur frequently in dairy by diverse reasons

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and those abortions that are not caused by N. caninum are difficult to identify. The study in New Zealand

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(Mcdougall et al., 2005) has released the total abortion rate of dairy animals is to be 6.4%, and some other

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reports in Australia (Atkinson et al., 2000; Quinn et al., 2004; Hall et al., 2005) estimate the loss ranging from

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2.4% to 21.3%. We assume that overall abortion rate was 3% with an initial seroprevalence of 10%. Accordingly,

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the susceptible individuals and infected individuals have an abortion risk of 2% and 9%, respectively. This

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assumption is consistent with the studies (Moen et al., 1998; Trees et al., 1999) which have reported the abortion

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risk of seropositive animals is more than three times of seronegative ones. βS and βI are defined as the abortion 5 P rates for susceptible and infected animals, respectively. Then for each year, (αk − βS )Sk susceptible animals k=3

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and

5 P

(αk − βI )Ik infected animals will give birth to offspring.

k=3

The calves born from susceptible mother are always susceptible but the calves born from infected mother have

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a possibility to be susceptible without vertical infection. The efficiency of vertical infection is reported to be high

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in different regions. It was concluded to be high in some states like California in the United States with 81%

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(Lindsay et al., 1996) and New South Wales in Australia with 90% (Hall et al., 2005), or even in some countries

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like Germany with 93% (Schares et al., 1998) and the United Kingdom with 95% (Davison et al., 1999). Whereas,

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other studies reported vertical infection rate was as low as 44.4% in Qu´ebec (Santos et al., 2012) and 43.0% in

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Maryland (Dyer et al., 2000).

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2.1.2. Horizontal infection

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Horizontal transmission process includes within herd level and outside herd level. Within the herd level, the

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process depends on the current proportion of mature infected animals (k ≥ 3) in farm with a prevalence dependent

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factor ζ. This mode of spread with infection may via pooled colostrum or milk (Uggla et al., 1998). Cattle can

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also be infected by hosts outside the herd (McAllister et al., 1998; Par´e et al., 1998) and this kind of transmission

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process is modeled by a constant per-capita force parameter σ. Hence the horizontal infection rate, ρh , is defined

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as:

ρh =

ζCI /C | {z }

+

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within herd level

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σ |{z}

outside herd level

2.1.3. Involuntary culling

Culling is the removal of animals from the herd due to sale, slaughter, or death. In general, culling has been

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classified as involuntary (forced) or voluntary (Dohoo and Dijkhuizeu, 1993). Involuntary culling implies that

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animals are culled due to disease, injury, infertility or death. For example, the lameness, metabolic disorder,

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udder disease, and calving problems. Voluntary culling could be departure of animals that are surplus to herd

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requirement or producing low yield. We assume that the culling considered in our model was involuntary culling

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(or forced culling), and to keep a high-quality farm, those animals inferior to genetic qualities would be culled by

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farmers every year.

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The culling rates of infected animals at all age-classes, δI,1 –δI,5 , are set to be constant according to historic

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data (H¨ asler et al., 2006a,b) and especially the culling rate of susceptible animals in age-class 5 is set to 30% to

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prevent the accumulation of animals at old age. For other age-classes, the culling rates for susceptible animals

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are varied since the number of susceptible animals that will be culled is used to balance total population after the 4

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removal of infected animals from dairy. Therefore, the culling rate of susceptible animals of group 1–4 in each

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year are calculated as follows: 5 P

(S1 (t) + I1 (t)) −

δI,k Ik − δS,5 S5

k=1

δS,i =

4 P

, for i = 1, 2, 3, 4.

Sk

k=1

Animals that are not culled or horizontally infected will grow one year old and flow into the next age-group.

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Thus this portion of population of groups Sk−1 and Ik−1 in the current year will be the population of Sk and Ik

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in the next year.

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2.1.4. Governing equations

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A series of difference equations can be developed based on above discussion to describe the dynamics of cattle

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population. The age-structured population is modeled by year as a time interval. We summarize the population

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model by the following equations: 5 X k=3

I1 (t + 1) =

5 X

αk (1 − βS )Sk (t) | {z }

births for susceptible in S

+ αk (1 − ρv )(1 − βI )Ik (t)], {z } | births for susceptible in I

[ρv αk (1 − βI )Ik (t)], {z } | births for infected in I

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k=3

[

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S1 (t + 1) =

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Sk (t + 1) = (1 − ρh − δS,k−1 )Sk−1 (t), for k = 2, 3, 4,

S5 (t + 1) =

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Ik (t + 1) = (1 − δI,k−1 )Ik−1 (t) + ρh Sk−1 (t), for k = 2, 3, 4, (1 − ρh − δS,4 )S4 (t) | {z }

+

aging of age-group 4 in last year

I5 (t + 1) = (1 − δI,4 )I4 (t) + ρh S4 (t) + {z } | 122

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aging of age-group 4 in last year

(1 − ρh − δS,5 )S5 (t), {z } |

accumulation of age-group 5 in last year

ρh S5 (t) + (1 − δI,5 )I5 (t). {z } |

accumulation of age-group 5 in last year

2.2. Economy considerations

To prevent the spread of N. caninum in farm, recent works have focused on a number of different control

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strategies by distinct methodologies (French et al., 1999; Larson et al., 2004; H¨asler et al., 2006a). Overall, the

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four most efficient strategies in terms of reduction in prevalence are test-and-cull, medication, vaccination, and

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selective breeding. Fig. 2 provides the schematic representation of changes in population for each control. On the

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basis of the cattle population model, four potential control methods will be evaluated from an economic point of

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view.

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For each control, direct cost arises from control option by the management actions (sampling, laboratory,

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healthy animals replacement, medication, and vaccination) and indirect loss results from cow abortions, reduced

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milk production and farm veterinary services since the N. caninum cannot be eradicated. Therefore, considering

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the cost of control coupled with the inevitable annual loss as the total loss to evaluate control option with regard

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to reduced economic loss is more reasonable and practical. 5

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2.2.1. Basic annual loss without control In a year without intervention, there exists loss incurred due to N. caninum infection. Researchers have

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reported different effects on milk production of N. caninum-infected cows. In two studies conducted in the

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United States (Thurmond and Hietala, 1997; Hernandez et al., 2001), infection is shown to be associated with a

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decrease in milk yield. Each N. caninum seropositive cow produces 1.3/kg/day less milk than the seronegative

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one. Another investigation (Pfeiffer et al., 2002) proposed that infection has a positive effect on milk production

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since each N. caninum seropositive cow produces 0.4/kg/day more milk than seronegative one (Pfeiffer et al.,

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2002). It is generally recognized that milk yield will be negatively affected by N. caninum infection and we also

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assume it is the case in this paper. Altogether, these abortions along with veterinary services and the decreased

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milk production result in basic annual loss for farmer.

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For cows and heifers that aborted, we consider to keep on feeding them and they will be re-inseminated

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to continue into pregnancy by veterinary service. However, when a cow is aborting, its calving interval will be

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extended to 595 days including 305-day of lactating and 290-day of drying. In contrast, a general cow has 305-day

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of lactating and 60-day of drying. Consequently, the abortion loss per cow, denoted as v1 , is the sum of feeding

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expense during the additional dry days (230 days) and average value of an offspring. For an aborting heifer, it

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has additional 230 dry days compared to a general heifer. Therefore, the abortion loss per heifer, denoted as v2 ,

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is the feeding expense during dry days.

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To sum up, the basic annual loss without control consists of abortion loss, veterinary service cost, and loss of

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reduced milk yield. Therefore, annual loss, L0 , due to the disease is defined as:

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L0 = v1 βI CI + v2 βI HI + c1 βI (CI + HI ) + | {z } | {z } abortion loss

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2.2.2. Test-and-cull

veterinary cost

c2 C I | {z }

.

reduced milk yield loss

An efficacious control strategy is to test and then cull N. caninum-infected individual animals from herd (Hall

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et al., 2005). In this study, we test infected animals first and then cull the seropositive ones with replacement

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to keep population balanced (Fig. 2A). With this control strategy, the culling rate of infected animals, δI,k , is

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set to 100%. Considering the sensitivity, rs , of serological test, the culling rate of infected animals should be

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rs δI,k . We assume that only 70% of female offspring were fed for replacement and the remaining offspring were

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for fattening (H¨ asler et al., 2006a,b). The total cost consists of the veterinary service cost p1 (the number of farms

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times the veterinary service price per farm) and the sampling cost of infected animals (the sampling price of each

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individual, p2 , multiplied by the amount of infected animals). The parameters, vc , vh and vo are the differences

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between market values and slaughter values of a cow, heifer and offspring, respectively. The replacement cost

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of test-and-cull depends on the numbers of infected cows (CI ), infected heifers (HI ) and infected offspring (OI ).

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With this control, the corresponding loss, L1 , is the direct cost coupled with annual loss, L0 , and it can be

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calculated as follows: L1 = p1 + p2 I + | {z } testing cost

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+

rs vc CI + rs vh HI + 0.7rs vo OI {z } |

replacement cost of cows, heifers and offspring

L0 |{z}

.

annual loss

2.2.3. Medication

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Among all the medication methods, the most efficient one is treating all calves born from infected mothers

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without previous testing. Since there is no strong evidence of the efficacy of chemotherapy, we assume it was

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around 60% (H¨ asler et al., 2006a,b) although Kritzner et al. (2002) reported that it could be as high as 90%. Here we assume that chemotherapy treatment on neonatal calves from infected dams had a proportion of

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60% to recover and this recovered portion would flow into non-infected category. As for the population structure

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shown in Fig. 2B, only the number of new birth flowing into age-group 1 will change. In this case, the cost is only

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induced by medication which is the multiplication of the number of all offspring and the cost of drugs on each

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calf c. Additionally, when combined with the annual loss, loss in medication option, L2 , is calculated as follows: L2 = cOI + |{z}

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L0 |{z}

.

annual loss

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2.2.4. Vaccination

Vaccines have been discussed in some studies and appear to be the favored control strategy (Liddell et al., 1999;

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Miller et al., 2005). In the scenario, whole cattle were vaccinated without previous testing and the accompanied

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cost induced includes veterinary service cost a1 and vaccination injection cost N a2 where N is the total number

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of animals in dairy. Nevertheless, only one vaccine has been demonstrated to have more than 60% efficacy (H¨ asler

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et al., 2006b) and others may be as low as 25% (Weston et al., 2012).

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Vaccinated animals also had a possibility of losing immunity within each year and this proportion was assumed

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to be 10%. We assume that when infected animals were vaccinated successfully, dams would be protected from

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the abortion caused by N. caninum and also give birth to calves with a lower vertical transmission rate. When

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susceptible animals were vaccinated successfully, they would be protected from the horizontal infection. In this

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case, there were two more categories, the vaccinated susceptible (VS ) and the vaccinated infected (VI ). The

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changes in population structure are described in Fig. 2C. The vaccination loss, L3 , is the veterinary cost and

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injection cost coupled with the annual loss:

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L3 =

a1 |{z}

veterinary cost

+

a2 N |{z}

injection cost

+

L0 |{z}

.

annual loss

2.2.5. Selective breeding

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Discontinuing breeding offspring born from seropositive dams is also an efficient way to control N. caninum

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transmission. We consider testing all infected cows yearly and discontinuing breeding offspring born from seropos-

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itive mothers (Fig. 2D). Hence only the offspring born from cows that are not correctly tested by serological test

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would flow into cattle, specifically the first age-group. 7

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In the first year, offspring born from seropositive cows are discontinued feeding in farm. To keep cattle popu-

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lation in balance, equivalent amount of dairy offspring bought from market will be put into cattle. Replacement

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cost per offspring, vo , is the difference between the market value and the slaughter value of dairy offspring. During

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the second to the fourth year, seropositive cows will be inseminated with a beef breed. Therefore, replacement

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cost is the difference between the market value of a dairy calf and the slaughter value of a breeding calf. In the

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subsequent years, farm management will only inseminate seropositive cows and not replace the offspring anymore.

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Thus, there is no replacement cost but only testing cost. Finally, testing cost and replacement cost coupled with

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annual loss contribute to the loss of selective breeding, L4 , which is defined as follows:

testing cost

replacement cost of offspring

L0 |{z}

.

annual loss

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L4 = p1 + p2 CI + vo rs OI + (1 − rp )OS + | {z } | {z }

where rs and rp are the sensitivity and specificity of the serological test, respectively.

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3. Results

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Numerical simulations are developed in MATLAB to analyze the factors driving changes in prevalence and

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economic loss. All parameters used for our model are shown in Table 2 and Table 3. To access the uncertainty

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of input parameters, a probability distribution is assigned to each parameter according to studies (Schares et al.,

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1998; Davison et al., 1999; Atkinson et al., 2000; Quinn et al., 2004; Mcdougall et al., 2005; Hall et al., 2005;

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H¨ asler et al., 2006a,b; Sch¨ arrer et al., 2014) and Monte Carlo simulations are used to obtain the median and range

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of outputs with 1000 simulation runs. Detailed descriptions of the uncertain parameters and the corresponding

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probability distributions are referred in Table B.2 in the supplementary material.

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3.1. Comparison of reduction in prevalence under the four controls

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3.1.1. Infection rates

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Transmission of N. caninum in dairy can occur through vertical and horizontal infection routes. Vertical

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infection mainly accounts for N. caninum transmission with its efficiency varying from 81% to 95% according

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to studies (Lindsay et al., 1996; Schares et al., 1998; Davison et al., 1999; Hall et al., 2005). In addition, the

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horizontal infection rate, especially the unknown transmission factor from wildlife, also varies since hosts outside

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herd are uncontrollable. Therefore, reduction in prevalence under varied infection rates is evaluated to provide

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us an insight on how controls take effect on the prevention of N. caninum transmission.

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All controls except medication show no difference on reduction in prevalence as vertical infection rate varies

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(Fig. 3). This can be well explained that test-and-cull, vaccination, and selective breeding are able to effectively

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block the vertical infection route of N. caninum in cattle. Nevertheless, medication and selective breeding show

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less effect on horizontal transmission route since prevalence outcome varies substantially as horizontal transmission

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factor changes. Therefore, it can be concluded that test-and-cull and selective breeding mainly prevent the vertical

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infection route while medication and vaccination take effect on both vertical and horizontal transmission routes. 8

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Furthermore, to access the uncertainty, pregnancy rate, abortion rate, and some unknown transmission factors

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are varied in Fig. 3A. Results show that medication and selective breeding are more sensitive to the changes against

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test-and-cull and vaccination. For example, with 81% vertical infection rate, the prevalence in year 25 is between

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1.06% and 2.16% in medication but is between 0.12% and 0.26% in test-and-cull. Similar conclusion is obtained

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from Fig. 3B which shows that medication and selective breeding vary significantly towards uncertain pregnancy,

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abortion and vertical infection rates.

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3.1.2. Initial prevalence Seroprevalence of N. caninum is considerably different among countries, within countries, and between regions

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(Otranto et al., 2003; Schares et al., 2003; Hall et al., 2005). Effects of four controls on prevalence are evaluated

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over a 25-year period with initial prevalence of 10%, 30%, 50% and 70% since prevalence larger than 70% is

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rare to be observed in dairy cattle (French et al., 1999). A comparison of median prevalence across 25 years is

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presented in Fig. 4 and results of reduction in prevalence for model years 5, 15 and 25 are illustrated in Table 4.

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With the initial prevalence of 10%, control of test-and-cull reduces the prevalence rapidly to 0.22% in year 5

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and then prevalence keeps at 0.17% in the subsequent period which is consistent with result from H¨asler et al.

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(2006a). In the strategy, a large number of infected animals are removed from cattle, and this leads to a smaller

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horizontal infection rate and less infected birth. Vaccination, which is less effective than test-and-cull, reduces the

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prevalence from 10% to 0.24% in year 25. While the efficiency of medication and selective breeding is much less

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substantial and the prevalence values of the two controls at the end are 1.72% and 1.61%. Nevertheless, similar

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conclusions can be made from the case with prevalence of 70%. Although starting with varied prevalence, four

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controls still possess a similar decreasing tendency over 25 years (Fig. 4). With a higher prevalence rate, more

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time is needed to reduce the prevalence to an acceptable level. However, the control of test-and-cull is always

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most efficient among all strategies aimed at reducing prevalence.

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The ranges of prevalence in test-and-cull (0.12%–0.22%) and vaccination (0.15%–0.37%) are narrower in

247

comparison to medication (0.68%–3.54%) and selective breeding (0.57%–2.64%) at 10% prevalence. This property

248

does not change with a high prevalence rate at 70%. These results demonstrate that medication and selective

249

breeding are more sensitive to the uncertainty in parameters that are assessed. Thus, test-and-cull and vaccination

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are the most efficient and reliable control options with regard to reduction in prevalence.

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3.2. Comparison of economic outcomes in the four controls

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3.2.1. Initial prevalence

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A comparison of median economic loss across 25 years is presented in Fig. 5 and economic outcomes of four

254

controls for model years 1, 15 and 25 with prevalence of 10% and 70% are illustrated in Table 5. Four control

255

strategies have positive effects on both the reduction in prevalence and the reduced economic loss against baseline

256

case (dashed line in Figs. 4 and 5).

9

In year 1, the control of test-and-cull brings on the biggest loss with initial prevalence of 10% (e 61,690)

258

and 70% (e 430,970)(Table 5). It is mainly because of the substantial control cost (e 43,600 at 10% prevalence

259

and e 350,410 at 70% prevalence, respectively) caused by replacing seropositive cattle with seronegative ones at

260

the beginning. This also accounts for the rapid reduction in prevalence (Fig. 4). Subsequently, economic loss

261

increases slightly after year 1 (Fig. 5) as its prevalence keeps almost constant which reveals that loss is highly

262

depending on the dynamics of infected animals. With a slight increase, test-and-cull behaves most economically

263

(e 76,770 in year 15 and e 81,570 in year 25, respectively) with the prevalence as low as 10%. However, when the

264

prevalence rate is as high as 70%, vaccination yields the lowest loss (e 328,270 in year 15 and e 373,360 in year

265

25, respectively). This is different from the economic outcome reported by H¨asler et al. (2006a) which concluded

266

medication was the most economically attractive option of all intervention strategies with 12% prevalence. The

267

main reason is that the latter one considered prevented loss as benefit, but we employ the costs coupled with the

268

dynamics of annual loss to access control from an economic point of view.

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With 10% prevalence, test-and-cull leads to the lowest loss in year 25 (Fig. 5A). Yet with prevalence equal to

270

or greater than 30%, vaccination is becoming the best control over the entire period (Fig. 5B–5D). Therefore, for

271

countries affected with high prevalence, such as New Zealand (6.8%–73.0%) (Thornton et al., 1991; Reichel, 1998;

272

Reichel and Ellis, 2002; Mcdougall et al., 2005), Mexico (42.0%–59.0%) (Morales et al., 2001a,b) and the United

273

States (16.1%–89.2%) (Thurmond and Hietala, 1997), vaccination among all single controls will be a favored

274

choice for farmer.

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Since the results of sensitivity analysis with different prevalence rates do not differ substantially, only the

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case with 30% prevalence is shown in Fig. 6. Each graph for baseline, test-and-cull, medication, vaccination and

277

selective breeding shows the median and range of economic loss obtained by 1000 simulation runs.

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The economic loss varies over a narrow range at the beginning of medication (e 0.042–0.083 million), vacci-

279

nation (e 0.026–0.045 million) and selective breeding (e 0.039–0.086 million) and then the ranges become wider

280

steadily in medication (e 0.366–0.691 million) and selective breeding (e 0.280–0.518 million) (Fig. 6). Although

281

the range in test-and-cull and vaccination keeps almost unchanged until the end, it is much wider in test-and-cull

282

(e 0.089–0.312 million) than that in vaccination (e 0.186–0.257 million). Large variation in test-and-cull is a

283

result of various management actions such as the culling of unhealthy cows and replacements of healthy ones,

284

and those behaviours are closely depending on parameters associated with market. Thus, for a farm with equal

285

to or greater than 30% prevalence, vaccination would be the most economical as well as stable decision to make

286

considering reduced economic loss.

287

3.2.2. Farm sizes

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288

To evaluate the effect of farm size on the decision option, two farm sizes are considered: 50 head and 1000

289

head. With the same initial prevalence, the population of farm with 50 cattle multiplied by 20 is the population

290

of farm with 1000 cattle. Table 6 shows the economic results by varying farm sizes and initial prevalence with

291

1000 simulation runs. 10

292

Economic losses of test-and-cull, medication, vaccination, and selective breeding are calculated over 25 years.

293

Results suggest that test-and-cull is the economically best option at 10% prevalence and it reduces the loss to e

294

4,160 for farm with 50 cattle and e 77,500 for farm with 1000 cattle, respectively. However, vaccination is the

295

optimal economic control at 70% prevalence and its economic loss declines to e 19,200 for farm with 50 cattle

296

and e 361,690 for farm with 1000 cattle, respectively. The present model indicates that the optimal economic

297

decision will not change with varied farm sizes.

298

3.3. Comparison of economic outcomes in combined controls For long time running of dairy affected with N. caninum, single control may not be more effective compared

300

to combined control. In this section, we will try exploring a potential combination of these measures, and more

301

specifically, we will verify whether combined measures perform more economically in comparison with single

302

control, and further study at which timing the second treatment should be initiated and how it depends on farm

303

size if the combined case worked better.

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As discussed above, vaccination is the most economical option when the farm is affected with a prevalence rate

305

equal to or greater than 30%. Hence combined control strategies will be necessarily evaluated for farm where the

306

prevalence is low. Since taking vaccines leads to the lowest loss at the beginning (Fig. 5A), combination will start

307

with vaccination and then work with remaining alternative treatments. Therefore, three combined scenarios will

308

be considered: vaccination combined with test-and-cull, vaccination combined with medication, and vaccination

309

combined with selective breeding. Recommendation for initiating the second control (and probability over 1000

310

runs) in three combined controls over 25 years with varied farm sizes (50 head and 1000 head) are shown in Table

311

7.

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For a farm with 1000 cattle, control of taking vaccines combined with test-and-cull may have more economical

313

outcomes in comparison to two single controls, vaccination and test-and-cull, for the whole period (Fig. 7). This

314

is only available by implementing the control of test-and-cull in the 2nd–5th year (the corresponding economic

315

outcomes lie in the shaded region in Fig. 7A). Moreover, the prevalence in this combined case declines to 0.15%

316

in year 25 which is less than that in test-and-cull (0.17%) and vaccination (0.24%). If the control of test-and-cull

317

was taken later than the 5th year, i.e. carrying out the test-and-cull in the 6th–24th year, combined control would

318

not behave economically anymore concerning single control. Test-and-cull brings much cost at the initiation, and

319

economical response is in a later period. Therefore, earlier initiation of this measure in a combined case will bring

320

preferred finance outcomes. In order to verify the reliability of the recommendation, we run the program 1000

321

times with randomly generated sets of parameters chosen within the ranges provided before. Simulation results

322

demonstrate that this recommendation has the biggest possibility of 72.9% compared to 2nd–6th with 13.8% and

323

2nd–4th with 12.7%.

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For combination with medication, the initiation of medication can be at any time in the 3rd–24th year

325

with prevalence ranging from 0.30% to 1.01% (the corresponding economic outcomes lie in the shaded region in

11

Fig. 7B). Simulation results conclude the top three recommendations for initiating medication are in the 3rd–

327

24th (38.7%), 4th–24th (29.9%) and 2nd–24th (26.5%), respectively. For combination with selective breeding of

328

offspring, the control of selective breeding should be initiated in the 2nd–24th year with prevalence ranging from

329

0.30% to 0.64% (the corresponding economic outcomes lie in the shaded region in Fig. 7C). In contrast, the

330

initiation of medication in the 9th–24th year brings less loss compared to its initiation in the 2nd–8th year. Later

331

initiation of medication in the combined case will provide a better economic response. Simulation results indicate

332

that the recommendation is most reliable with the possibility of 75.6% comparing against 2nd–23rd with 24.4%.

333

For a small farm with 50 cattle, similar conclusions are made and the recommendations of combination with

334

test-and-cull and medication are the same. Nevertheless, the recommendation of combination with selective

335

breeding differs. The optimal initiation points are the 2nd–22nd (59.7%) and 2nd–23rd (40.3%) which suggest

336

that the initiation of selective breeding is a little earlier than it in farm with 1000 head.

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This analysis provides evidence that combined options are worthwhile in terms of reduction in prevalence and

338

economic loss and by adopting vaccination and then applying one of the other three controls may provide better

339

economic outcomes than single control methods. Moreover, the optimal point to initiate the second option of

340

test-and-cull or medication will not change with varied farm sizes.

341

4. Discussion

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Neospora caninum infection is one of the most important infectious causes of abortion in dairy cattle. These

343

abortions give rise to a major loss to dairy management. To intervene in its transmission, preventive control

344

options with different methodologies and assessment criteria in geographically distinct areas have been discussed

345

and studied. However, the economic considerations coupled with population dynamics are not well studied and

346

the combined controls have not been explored yet.

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In our study, four single controls including test-and-cull (testing infected animals and then culling seropos-

348

itive ones), medication (treating newborn offspring from infected category with medicine), vaccination (doing

349

vaccination for whole cattle), and selective breeding (discontinuing breeding offspring born from seropositive cow

350

mothers after testing) have been assessed with regard to reduction in prevalence and economic loss. Cost of each

351

control, together with the inevitable annual loss due to population dynamics is adopted as an assessment criterion

352

from an economic point of view. In the single control cases, with 10% initial prevalence, control of test-and-cull

353

appreciably reduced prevalence in the first five years and then prevalence is keeping at 0.17% in the subsequent

354

period. This is in agreement with study (H¨ asler et al., 2006a) even which started with prevalence of 12%. Con-

355

sidering the overall loss throughout the 25 years, vaccination is the most favored method. Moreover, optimal

356

decision options will not change with varied farm sizes. This is different from the results obtained in a previous

357

study (H¨ asler et al., 2006b) which concluded the medication was the most economical among all interventions.

358

Main reason is that they considered prevented loss to evaluate controls, but we conduct the costs coupled with

359

annual loss as a control evaluation criterion.

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12

For the farm affected with significant prevalence (equal to or greater than 30%), vaccine treatment is the

361

most economical option compared to the other three. Therefore, taking vaccines could be the favored choice

362

for management. On the other hand, in the farm where the lower prevalence of infection (around 10%) occurs,

363

combined controls could be alternative treatments to provide better financial outcomes against single control in

364

the observed period. This is only available by implementing the test-and-cull control after vaccine treatment

365

from the 2nd to the 5th year. For combination with the other two cases, medication and selective breeding, the

366

initiation of medication can be at any time in the 3rd–24th year for varied farm sizes but the initiation of selective

367

breeding should be in the 2nd–24th year for a large farm (with 1000 cattle) and in the 2nd–22nd for a small

368

farm (with 50 cattle). In combined scenarios, earlier initiation of test-and-cull would bring less loss but later

369

implementation of medication could give rise to better financial performance. Analysis of our model discovers

370

that combined options are worthwhile and by adopting vaccine therapy and then doing test-and-cull, medication

371

or selective breeding respectively are alternative ways to carry out so far available measures.

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In summary, our study has revealed that a combination of control strategies could be effective and economic

373

treatments to intervene in N. caninum transmission among diary affected with low prevalence (around 10%).

374

However, in dairy where prevalence is high (equal to or greater than 30%), vaccination is always the most

375

economical treatment with an effective reduction in prevalence throughout the observed period. Moreover, it also

376

demonstrates the timing that the second treatment should be initiated in combined case is vital for providing

377

better finance results. This study helps us gain an insight into the potential combined control strategies from

378

an economic point of view. However, a fixed initial age distribution is considered throughout all the simulations.

379

Thus, further studies including analysis of different initial age distributions from different geographical locations

380

are needed to explore the performance of the combination of controls.

381

Conflict of interest statement

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The authors declare no conflicts of interest.

Acknowledgements

Y. Liu would like to thank the University Grants Committee (UGC) in Hong Kong for the financial support.

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17

Table 1. List of variables included in the model. Variable

Description

Sk

number of susceptible animals in age-class k

Ik

number of infected animals in age-class k

O

number of offspring, S1 + I1

H C

number of heifers, S2 + I2 P number of cows, 5k=3 (Sk + Ik )

OI

number of infected offspring, I1

HI

number of infected heifers, I2 P number of infected cows, 5k=3 Ik

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CI

18

Table 2. Parameters used in the population model of N. caninum transmission. Definition

Value

Sources

N

total number of animals in dairy

1000

this work

Sk (1)

initial susceptible population distribution

[180 135 117 99 369]∗

referencea

Ik (1)

initial infected population distribution

[20 15 13 11 41]∗

referencea

αk

pregnancy rate at age k

[0 0 0.34 0.37 0.27]∗

estimationb

βS

abortion rate of susceptible animals

2%

estimationc

βI

abortion rate of infected animals

9%

estimationd

ζ

prevalence dependent factor

0.028

referencee

δI,k

culling rate of the infected at age k

[0.20 0.08 0.18 0.19 0.26]∗

referencee

ρv

vertical infection rate

81%–95%

referencef

σ

unknown infection factor from wildlife

0.0025

of

Parameter

ro

estimationg

the value of the 5th age-class is estimated from referred literature by the weighted mean value.

a

H¨ asler et al. (2006a); Sch¨ arrer et al. (2014).

b

mean value of each uniform distributed pregnancy rate, [0 0 uniform(0.28,0.40) uniform(0.31,0.43) uniform(0.21,

-p

∗

0.33))] (H¨ asler et al. (2006a)).

mean value of a uniform distribution, uniform(0.01,0.03) (H¨ asler et al. (2006a)).

d

mean value of a uniform distribution, uniform(0.06,0.12) (H¨ asler et al. (2006a)).

e

H¨ asler et al. (2006a).

f

uniform distribution, uniform(0.81, 0.95) (Davison et al. (1999); Hall et al. (2005); Lindsay et al. (1996); Schares

uniform distribution, uniform(0.01, 0.05).

Jo

ur na

g

lP

et al. (1998)).

re

c

19

Table 3. Parameters (and range) used in the economic model of N. caninum transmission. Definition

Value (range)

Sources

v1

abortion loss per cow

2337.50 (86.80, 3371.70)

estimation

v2

abortion loss per heifer

524.43 (484.63, 539.09)

estimation

c1

average veterinary cost per cow

159.11 (131.44, 186.92)

estimation

c2

reduced milk production loss per cow

65.74 (5.89, 157.07)

estimation

vc

replacement cost per cow

658.61 (82.20, 1077.80)

estimation

vh

replacement cost per heifer

228.90 (21.55, 508.17)

estimation

vo

replacement cost per offspring

-24.55 (-244.53, 136.99)

estimation

c

cost of drugs on each calf

7.60

a1

veterinary service cost each year

40

a2

vaccination injection cost per animal

9.50

rs

sensitivity of serological test

0.96 (0.93, 0.99)

estimation

rp

specificity of serological test

0.98 (0.96, 1.00)

estimation

p1

veterinary cost of per farm

18

H¨asler et al. (2006b)

p2

sampling price per animal

23.50

r

discount rate

of

Parameter

H¨asler et al. (2006b)

ro

H¨asler et al. (2006a,b)

re

-p

H¨asler et al. (2006a,b)

Jo

ur na

lP

0.03

20

H¨asler et al. (2006b) this work

Table 4. Median and range of N. caninum prevalence (in %) across time in four controls with initial prevalence of 10% and 70%.

Prevalence

Year 5

Year 15

Year 25

Median (range)

Median (range)

Median (range)

test-and-cull

0.22 (0.12, 0.31)

0.17 (0.12, 0.22)

0.17 (0.12, 0.22)

medication

6.62 (5.30, 8.44)

2.81 (1.24, 5.15)

1.72 (0.68, 3.54)

vaccination

1.82 (1.62, 2.05)

0.59 (0.42, 0.81)

0.24 (0.15, 0.37)

selective breeding

5.39 (4.81, 6.02)

1.93 (0.95, 2.95)

1.58 (0.56, 2.64)

test-and-cull

0.22 (0.12, 0.31)

0.17 (0.12, 0.22)

0.17 (0.12, 0.22)

medication

43.19 (37.48, 47.80)

15.73 (7.78, 21.03)

7.55 (2.17, 12.79)

vaccination

11.20 (9.95, 12.68)

3.03 (2.14, 4.27)

1.00 (0.61, 1.62)

selective breeding

29.98 (29.40, 30.59)

4.28 (3.22, 5.29)

Control

Jo

ur na

lP

re

-p

ro

70%

21

of

10%

1.86 (0.80, 2.89)

Table 5. Median and range of economic loss (103 e) across time in four controls with initial prevalence of 10% and 70%. Control cost and annual loss of four controls are only presented in year 1 in particular. Year 1 Prevalence

Year 15

Year 25

Control Control cost

Annual loss

Median (range)

Median (range)

Median (range)

test-and-cull

43.60

18.09

61.69 (29.28, 93.63)

76.77 (31.76, 116.23)

81.57 (33.78, 123.48)

medication

0.15

19.25

19.40 (14.36, 27.97)

159.70 (121.53, 226.41)

182.99 (139.39, 259.26)

vaccination

5.02

9.47

14.49 (12.29, 17.89)

100.79 (91.58, 115.08)

131.66 (121.69, 147.13)

selective breeding

0.91

19.23

20.14 (13.18, 30.25)

127.78 (96.49, 178.63)

138.29 (104.65, 193.15)

test-and-cull

305.41

125.55

430.97 (169.60, 650.53)

469.76 (186.55, 707.70)

474.56 (188.49, 714.89)

medication

0.46

134.31

135.36 (107.23, 182.49)

968.40 (776.20, 1284.90)

1053.00 (844.40, 1396.50)

vaccination

5.02

67.45

72.47 (56.26, 98.06)

328.27 (264.54, 428.92)

373.36 (305.47, 480.57)

selective breeding

7.37

134.85

142.22 (96.79, 189.09)

777.51 (592.39, 994.07)

799.50 (609.60, 1021.90)

10%

Jo

ur na

lP

re

-p

ro

of

70%

22

Table 6. Median and range of economic loss (103 e) in four controls over 25 years with varied farm sizes (50 head and 1000 head) and initial prevalence (10% and 70%). 50 Head Control

1000 Head

70% Prevalence

10% Prevalence

70% Prevalence

Median (range)

Median (range)

Median (range)

Median (range)

test-and-cull

4.16 (1.26, 6.06)

22.68 (8.30, 38.01)

77.50 (46.73, 111.76)

444.53 (161.10, 724.44)

medication

9.34 (7.23, 12.61)

53.71 (41.98, 71.26)

181.42 (138.37, 244.16)

1076.10 (850.30, 1388.70)

vaccination

6.97 (6.42, 7.84)

19.20 (15.94, 23.98)

130.41 (119.81, 146.40)

361.69 (288.12, 448.56)

selective breeding

7.07 (5.38, 9.67)

39.63 (28.41, 55.80)

135.67 (95.11, 184.17)

of

10% Prevalence

Jo

ur na

lP

re

-p

ro

788.60 (572.10, 1050.80)

23

Table 7. Recommendation for initiating the second control (combined with the first control, vaccination) in three types of combinations over 25 years with varied farm sizes (50 head and 1000 head). In order to verify the reliability of the recommendation, we run the program 1000 times with randomly generated sets of parameters chosen within the ranges provided in Tables 2 and 3. 50 Head

1000 Head

combination 2b

combination 3c

combination 1a

combination 2b

combination 3c

2nd–5th (60.8%)

3rd–24th (50.8%)

2nd–22nd (59.7%)

2nd–5th (72.9%)

3rd–24th (38.7%)

2nd–24th (75.6%)

2nd–6th (31.2%)

4th–24th (31.3%)

2nd–23rd (40.3%)

2nd–6th (13.8%)

4th–24th (29.9%)

2nd–23rd (24.4%)

2nd–4th (5.2%)

2nd–24th (15.5%)

2nd–4th (12.7%)

2nd–24th (26.5%)

a

vaccination combined with test-and-cull;

b

of

combination 1a

vaccination combined with medication;

vaccination combined

Jo

ur na

lP

re

-p

ro

with selective breeding.

c

24

Offspring O

Cow C

Heifer H

Birth

S S1 1
v


v

S2

S3

S4

S5

horizontal infection
h

I1

Culling

I2

I3

I4

I5

vertical infection

I

of

Birth

ro

aging

Jo

ur na

lP

re

-p

Fig. 1. Schematic representation of population dynamics. O represents offspring; H represents heifer; C represents cow.

25

Test-and-cull

of

Selective breeding

Fig. 2. Schematic representation of population dynamics in the four controls. (A): test-and-cull; (B): medication; (C):

Jo

ur na

lP

re

-p

ro

vaccination; (D): selective breeding.

26

test-and-cull v v

selective breeding

0.12

=81% =90%

0.1

0.08

0.08

0.08

0.08

0.06

0.06

0.06

0.06

0.04

0.04

0.04

0.04

0.02

0.02

0.02

0.02

=93% =95%

0

0 5 10 15 20 25

0 5 10 15 20 25

Year

0.12

Year

test-and-cull

0.12

=0.001 =0.002 =0.003 =0.004

medication

0.12

0.08

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.1

0.08

0.06

0.04

0.04

0.02

0.02

0

5 10 15 20 25

ur na

Year

selective breeding

0.12

0.06

0

5 10 15 20 25

vaccination

Year

re

0.1

0

5 10 15 20 25

Year

0.1

0.02

0 5 10 15 20 25

lP

0.1

prevalence

vaccination

0.1

v

B

0.12

0.1

v

prevalence

medication

ro

0.1

0.12

of

0.12

-p

A

Year

0 5 10 15 20 25

Year

5 10 15 20 25

Year

Fig. 3. Dynamics of prevalence in test-and-cull, medication, vaccination, and selective breeding under varied vertical infection rates ρv (shown in panel A) and unknown transmission factor σ from wildlife (shown in panel B) with 10% initial prevalence. (A): 81% (blue line) (Lindsay et al., 1996), 90% (red line) (Hall et al., 2005), 93% (yellow line) (Schares et al., 1998) and 95% (purple line) (Davison et al., 1999); (B): 0.001 (blue line), 0.002 (red line), 0.003 (yellow line) and 0.004

Jo

(purple line).

27

A 0.7 0.6 0.5

B 0.7 baseline test-and-cull medication vaccination selective breeding

0.08

0.08 0.06

0.6

0.06

0.04

0.04

0.5 0.02

Prevalence

0.02 0

0.4

15

20

0.3 0.2

0.2

0.1

0.1 0

0

10

15

15

25

0.3

5

0

0.4

20

25

C

5

10

15

20

20

25

25

D 0.7

0.7 0.1

of

0.6

0.6 0.05

0.5

0.5 20

25

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1 0

0

5

10

15

20

25

ro

15

-p

Prevalence

0

5

10

15

20

25

Year

re

Year

Fig. 4. Dynamics of prevalence in the baseline scenario and four controls with different initial prevalence over a 25-year period with different initial prevalence. The initial prevalence is (A): 10%, (B): 30%, (C): 50% and (D): 70%. Dashed

lP

line denotes the baseline scenario and solid line denotes the case of four controls. Red line: test-and-cull; Brown line:

Jo

ur na

medication; Blue line: vaccination; Black line: selective breeding.

28

A 4

baseline test-and-cull medication vaccination selective breeding

3.5 3

accumulated loss

B

105

8 7 6

2.5 5 2 4 1.5

3

1

2

0.5

1

0

0 5

C

105

16

10

15

20

25

105

5

D

2

10

15

20

25

106

1.8

14

1.6

of

1.4 10

1.2

8

1

6

0.8 0.6

ro

accumulated loss

12

4 0.4 2

0.2

0 5

10

15

20

0

25

5

106

2

baseline test-and-cull medication vaccination selective breeding

20

25

re

1.5

1

lP

accumulated loss

15

-p

E

10

Year

Year

0.5

0

20

ur na

10

30

40

50

60

70

initial prevalence (%)

Fig. 5. Dynamics of accumulated loss in the baseline scenario and four controls over a 25-year period with different initial prevalence. The initial prevalence is (A): 10%, (B): 30%, (C): 50% and (D): 70%; (E): accumulated loss of four controls and baseline scenario in the 25th year over different initial prevalence of 10%, 30%, 50% or 70%. Dashed line denotes the baseline scenario and solid line with markers denotes the case of four controls. Red line with diamonds: test-and-cull;

Jo

Brown line with circles: medication; Blue line with crosses: vaccination; Black line with asterisks: selective breeding.

29

accumulated loss

baseline

Year 10

6

5

5

4

4

3

3

2

2

1

1

0 5 10

10

15

20

0

25

5

Year vaccination

5

8

7

10

15

20

25

Year selective breeding

105

re

7

6

6

5

5

4

4

3

lP

accum ulated loss

of

7

6

ro

accum ulated loss

7

8

medication

105 8

-p

8

test-and-cull

5

3

2

2

1

1

0

0

5

10

15

20

25

ur na

Year

5

10

15

20

25

Year

Fig. 6. Sensitivity graph of accumulated loss in baseline scenario, test-and-cull, medication, vaccination, and selective breeding over a 25-year period with initial prevalence of 30%. (- - -): maximum value and minimum value; (—): mean

Jo

value.

30

A

15

104

B vaccination test-and-cull start from 2nd year start from 5th year

vaccination medication start from 3rd year start from 9th year start from 24th year

1.8 1.6 1.4

10

accumulated loss

105

2

1.2 1 0.8

5

0.6 0.4 0.2

0

0

C

20

18 16

accumulated loss

14

5

25

10

15

20

25

of

15 104

vaccination selective breeding start from 2nd year start from 24th year

ro

10

12 10

-p

5

8 6

2 0 5

re

4

10

15

20

25

lP

Year

Fig. 7. Vaccination combined with different controls over a 25-year period. (A): combination with test-and-cull. Dashed line and dash-dotted line indicate the initiation of test-and-cull in the 2nd and 5th year, respectively; (B): combination

ur na

with medication; Dashed line, solid line, and dash-dotted line indicate the initiation of medication in the 3rd, 9th, and 24th year, respectively. The solid line is covered by shadow area in the front part. (C): combination with selective breeding. Dashed line and dash-dotted line indicate the initiation of selective breeding in the 2nd and 24th year, respectively; The

Jo

shaded region represent the economic results that feasible combined controls give rise to.

31