Simulating the impact of four control strategies on the population dynamics of Neospora caninum infection in Swiss dairy cattle

Preventive Veterinary Medicine 77 (2006) 254–283 www.elsevier.com/locate/prevetmed

Simulating the impact of four control strategies on the population dynamics of Neospora caninum infection in Swiss dairy cattle Barbara Ha¨sler a, Katharina D.C. Sta¨rk a,*, Heinz Sager b,1, Bruno Gottstein b, Martin Reist a,2 a

b

Swiss Federal Veterinary Office, Schwarzenburgstrasse 155, CH-3003 Bern, Switzerland Institute of Parasitology, University of Bern, La¨nggassstrasse 122, CH-3001 Bern, Switzerland Received 23 November 2005; received in revised form 28 July 2006; accepted 31 July 2006

Abstract A dynamic deterministic simulation model was developed to assess the impact of different putative control strategies on the seroprevalence of Neospora caninum in female Swiss dairy cattle. The model structure comprised compartments of ‘‘susceptible’’ and ‘‘infected’’ animals (SI-model) and the cattle population was divided into 12 age classes. A reference model (Model 1) was developed to simulate the current (status quo) situation (present seroprevalence in Switzerland 12%), taking into account available demographic and seroprevalence data of Switzerland. Model 1 was modified to represent four putative control strategies: testing and culling of seropositive animals (Model 2), discontinued breeding with offspring from seropositive cows (Model 3), chemotherapeutic treatment of calves from seropositive cows (Model 4), and vaccination of susceptible and infected animals (Model 5). Models 2–4 considered different sub-scenarios with regard to the frequency of diagnostic testing. Multivariable Monte Carlo sensitivity analysis was used to assess the impact of uncertainty in input parameters. A policy of annual testing and culling of all seropositive cattle in the population reduced the seroprevalence effectively and rapidly from 12% to <1% in the first year of simulation. The control strategies with discontinued breeding with offspring from all seropositive cows, chemotherapy of calves and vaccination of all cattle reduced the prevalence more slowly than culling but were still very effective (reduction of prevalence below 2% within 11, 23 and 3 years of simulation, respectively). * Corresponding author. Tel.: +41 31 323 95 44; fax: +41 31 323 95 43. E-mail address: [email protected] (K.D.C. Sta¨rk). 1 Novartis Centre de Recherche Sante´ Animale SA, CH-1566 St-Aubin FR, Switzerland. 2 Department of Animal Science, Swiss College of Agriculture, CH-3052 Zollikofen, Switzerland. 0167-5877/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.prevetmed.2006.07.007

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However, sensitivity analyses revealed that the effectiveness of these strategies depended strongly on the quality of the input parameters used, such as the horizontal and vertical transmission factors, the sensitivity of the diagnostic test and the efficacy of medication and vaccination. Finally, all models confirmed that it was not possible to completely eradicate N. caninum as long as the horizontal transmission process was not interrupted. # 2006 Elsevier B.V. All rights reserved. Keywords: Neospora caninum; Cattle; SIR-model; Control strategies

1. Introduction Neospora caninum, an apicomplexan protozoan parasite, has been recognized as one of the most important causes of infectious abortion in bovines worldwide (Dubey and Lindsay, 1996). The major route of transmission relies upon reactivation of a persistent infection and subsequent transplacental invasion of the embryo or fetus (=vertical or endogenous infection mode) (Pare et al., 1996; Schares et al., 1998; Davison et al., 1999). The transplacental infection may provoke abortion, although in the majority of the cases a calf without clinical symptoms is born and will harbor the parasite for its whole life (Pare et al., 1996; Thurmond and Hietala, 1997). Cattle can also become postnatally infected by horizontal transmission (=exogenous transmission mode) (McAllister et al., 1996; Hietala and Thurmond, 1999; Dijkstra et al., 2002b). The complete life cycle of N. caninum, more specifically the full range of definitive hosts and respective intestinal gamogony, is not yet fully elucidated, although dogs and coyotes have been found to be end hosts of the parasite (McAllister et al., 1998; Dijkstra et al., 2002a; Gondim et al., 2002, 2004). N. caninum infection in a cattle population can be influenced by four control measures that are either available now or potentially might be available in the future: culling of infected animals, selective breeding in infected herds, vaccination of susceptible and infected animals, and chemotherapeutic treatment of calves. A modeling study demonstrated that a policy of culling or selective breeding in a N. caninum-infected herd can considerably reduce the prevalence of infection (French et al., 1999), although such measures were not effective in eliminating herd infection in the presence of horizontal transmission. In another study, a 5-year dynamic farm probability simulation model was used to test and evaluate three control strategies for N. caninum. It was concluded that testing an entire herd for N. caninum infection and excluding the daughters of seropositive animals from breeding provided the best economic return (Larson et al., 2004). Little information is available on the metaphylactic use of drugs to address the problem. An experimental chemotherapeutic treatment study found that Toltrazuril medication in female C57/BL6 mice could considerably reduce the diaplacental passage of the parasite to the fetal brain (Gottstein et al., 2005). An explorative study to assess Toltrazuril-sulfone (Ponazuril) indicated a basic efficacy of the chemotherapeutic intervention against N. caninum in experimentally infected calves (Kritzner et al., 2002). In North, Central and South America as well as in New Zealand, a commercial, killed protozoa vaccine (NeoGuardTM and Bovilis Neoguard1, http://www.intervet.com/) is available to be applied in cattle. In Costa Rica and New Zealand, field studies were conducted to examine the

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efficacy of the vaccine that indicated that the vaccine reduced the chance of abortion by approximately 39% and 50%, respectively (Heuer et al., 2004; Romero et al., 2004). Conversely, another study reported the failure of the vaccine to protect herds from abortion (Andrianarivo et al., 2000). In the European Union and Switzerland, neither vaccine nor chemotherapy have been reliably assessed and validated for field application. Since 2001, N. caninum has been registered as a notifiable disease in Switzerland, but so far a national control program has not been implemented. As resources for national control programs are limited, it is necessary to fully understand the population dynamics and economic consequences of control options to support the policy decision-making process. Our study aimed to assess the impact of the following control strategies on the seroprevalence of N. caninum infection in the Swiss dairy cattle population: a. b. c. d.

testing and culling of seropositive cattle; discontinued breeding with offspring from seropositive cows; chemotherapeutic treatment of calves from seropositive cows; vaccination of susceptible and infected cattle.

The results were used as inputs in a financial analysis that is presented in a separate publication (Ha¨sler et al., 2006).

2. Materials and methods 2.1. General approach A dynamic deterministic simulation model with time steps of 1 year was developed. The number of susceptible and infected animals per time step was simulated taking into account four control strategies: (1) testing and culling of seropositive cattle, (2) discontinued breeding with offspring from seropositive cows, (3) chemotherapeutic treatment of calves from seropositive cows and (4) vaccination of susceptible and infected cattle. For this purpose, a simulation model of the status quo situation, i.e. without application of control strategies, was established as a baseline scenario. This baseline model was then modified to represent each of the control strategies, resulting in a set of four specific models with various sub-scenarios. Once the mathematical model was developed, Monte Carlo sensitivity simulations were run to assess the impact of uncertainty of parameters on the model output. 2.2. Study population and data collection The study population included all female Swiss cattle of the dairy breeds Simmental, Red and White, Brown Swiss, Holstein and Montbe´liard. Livestock demographic data was obtained from the Swiss Animal Movement Database (TVD), which stores data on each individual animal of the bovine species in Switzerland, including individual cattle movements from birth to slaughter. The TVD applies a quality assurance system to ensure high data quality. The farmers are offered a relevant financial incentive for notification of animal movements. Furthermore, a plausible TVD history is important in order to slaughter

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cattle. By such means a reliability of TVD data could be achieved and maintained. From TVD data, figures on the total number of female dairy cows in Switzerland, number of births and culled animals in the specified population and the age structure of the cattle under consideration were derived. Twelve different age classes were set up: 0 to <1, 1 to <2, 2 to <3, . . ., 10 to <11, 11 years. Cows in age classes 3 were considered to be used for breeding and were called ‘‘mature’’. Culling rates and birth rates in the 12 age classes were calculated using the raw data from the TVD. The pregnancy rates were obtained by adding abortion rates to the birth rates (Table 1). It is very important to note that all data Table 1 Constants used in the baseline model for the simulation of Neospora caninum infection dynamics in the Swiss dairy cattle population (females only) Parameter

Notation

Value

Source

Pregnancy and abortion ratesa Pregnancy rate 3 Pregnancy rate 4 Pregnancy rate 5 Pregnancy rate 6 Pregnancy rate 7 Pregnancy rate 8 Pregnancy rate 9 Pregnancy rate 10 Pregnancy rate 11 Pregnancy rate 12 Overall abortion rate of female fetuses

pr3 pr4 pr5 pr6 pr7 pr8 pr9 pr10 pr11 pr12 arTOT

0.34 0.37 0.37 0.33 0.28 0.22 0.22 0.20 0.18 0.17 0.01

TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb Hassig (2000)

Culling ratesa Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate Culling rate

crI1 crI2 crI3 crI4 crI5 crI6 crI7 crI8 crI9 crI10 crI11 crI12 crS12

0.20 0.08 0.18 0.19 0.22 0.23 0.24 0.22 0.27 0.29 0.29 0.45 0.60

TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb TVDb

Transmission factors Vertical transmission factorc

vtf

0.9

Prevalence dependent factora Unknown factora

pf uf

0.028 0.001181

Pare et al. (1996), Schares et al. (1998), Davison et al. (1999) and Hietala and Thurmond (1999) Assumption Assumption

a b c

I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 S12

Unit = 1/year. TVD = Swiss Animal Movement Database. Values were derived from there as described in Section 2. Unit = dimensionless.

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used in the model only refer to female dairy cattle and do neither include male animals nor beef breeds or cross breeds. The seroprevalence of N. caninum in Swiss dairy cattle appeared to remain stable over the past 30 years (B. Gottstein, Institute of Parasitology, Bern, pers. commun.). Moreover, in two studies conducted on N. caninum in Switzerland in 1996 and from 1998 to 2000, respectively, no differences were found in the seroprevalences among adult dairy cattle (Gottstein et al., 1998; Sager et al., 2001). Therefore, the N. caninum baseline seroprevalence in the model was set to the endemic equilibrium seroprevalence of 12% (Gottstein et al., 1998; Sager et al., 2001). 2.3. Model structure 2.3.1. General settings All models were built and run with the modeling software Vensim# Professional32 Version 5.4a (Ventana Systems, Inc., Harvard, USA) in time steps of 1 year and with a constant population size over a time period of 25 years. The key output was the seroprevalence of N. caninum-infected cows by age class and over time. 2.3.2. Model 1: the baseline scenario (status quo without control measures) Fig. 1 shows the structure of Model 1. Because evidence for a recovered or immune class is missing, the model is restricted to susceptible (S) and infected animals (I). The boxes S1–S12 (Fig. 1) represent the compartments of the susceptible animals by age class. The boxes I1–I12 (Fig. 1) represent the compartments of the infected animals by age class. Every age class was defined by its own set of pregnancy and culling rates. All equations and constants used in Model 1 are described below or summarized in Table 1. In Model 1, the overall abortion rate (number of abortions per cow and year) for abortions of female fetuses, arTOT, was set to 1%, in consistence with the total abortion rate of 2% reported for dairy herds in Switzerland (Hassig, 2000). Animals seropositive for N. caninum were set to have a four-fold increased risk for abortion compared with seronegative animals (Sager et al., 2001). Therefore, the absolute abortion rates for susceptible, arS, and infected animals, arI, were calculated as arS ¼

arTOT  ðI mature þ Smature Þ ; 4I mature þ Smature

arI ¼

arTOT  4ðI mature þ Smature Þ 4I mature þ Smature

where Imature and Smature are the sums of the compartments I3–I12 and S3–S12, respectively. Each age class X was set to have a defined pregnancy rate, prX (number of pregnancies per number of animals in age class per year), which was used to calculate the number of births for susceptible, BSX, and infected, BIX, animals by age class and time step by subtracting the abortion rate from the pregnancy rate and multiplying this by the number of susceptible or infected animals of the respective age class: BSX ¼ ðprX  arS ÞSX ;

BIX ¼ ðprX  arI ÞI X

All births from each age class flowed either into the first compartment of susceptible animals, S1, or into the first compartment of infected animals, I1 (Fig. 1). Vertical

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Fig. 1. Baseline model for the simulation of Neospora caninum infection dynamics in the Swiss dairy cattle population (females only). AC: age class, I: infected, S: susceptible, BS: number of calves from susceptible animals, BI: number of calves from infected animals, cr: culling rate, htf: horizontal transmission factor, and vtf: vertical transmission factor.

transmission from an infected cow to its calf was accommodated by multiplying the total number of births among infected animals, BI, by a vertical transmission factor vtf. According to the results of previous studies that found a high probability of vertical transmission (Pare et al., 1996; Schares et al., 1998; Davison et al., 1999; Hietala and Thurmond, 1999), vtf was set to 0.9. Flows into the S1 compartment were the calves of all susceptible cows, BS, plus the non-infected calves of infected mothers, BI(1  vtf). Flows into the I1 compartment were the infected calves of infected cows, BIvtf, plus the horizontally infected animals from S1 (Fig. 1). The age class-specific culling rates, crX, were the rates per time step at which animals were removed from the population. These culling rates were used to calculate the number of animals that were leaving the compartments, culled animals SX (CASX) and culled animals IX (CAIX), respectively CASX ¼ crSX  SX ;

CAIX ¼ crIX  I X

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The culling rates of the infected compartments, crI1 to crI12 were set a vector of constants (Table 1). To prevent accumulation of susceptible animals in the last compartment, the culling rate of the compartment S12, crS12, was also set to constant (Table 1). Assuming that the population size was stable, the culling rates of the susceptible compartments were allowed to vary depending on the constant inflows and outflows of the model, i.e. the total number of births, BTOT and the number of culled animals of all infected compartments and the last susceptible compartment, CAI and CAS12. The culling factor for susceptible animals was calculated as follows: cf ¼ BTOT  CAI  CAS12 The culling rate of the susceptible animals, crSX, was then calculated by dividing cf by the total number of susceptible animals S1–S11: cf crSX ¼ P11

x¼1

SX

The horizontal transmission process, HT, from susceptible to infected cattle was modeled using two independent parameters that determined the rate at which susceptible individuals became infected. The first one was a prevalence dependent factor, pf, which was multiplied by the prevalence in the adult population. The second one, uf, accounted for the per capita force of infection from unknown transmission factors such as putative N. caninum cycles in the wild life population. Due to lack of reliable information concerning the horizontal transmission process, these two parameters could not be arithmetically quantified. Therefore, iterative sensitivity testing was performed to determine the values of uf and pf that allowed to reach a steady state seroprevalence of 12%. In Model 1, the values pf = 0.028 and uf = 0.001181 were obtained (Table 1). The horizontal transmission factor, htf, which was assumed to be age-independent, was then obtained as follows: htf ¼ pf 

I mature þ uf I mature þ Smature

The number of susceptible animals per age class that got infected per time step, HTX, was subsequently calculated by multiplying htf by the number of susceptible animals per age class: HTX ¼ htf  SX To account for the aging process in the population, in each time step susceptible or infected animals that were not horizontally infected or culled moved over to the next age class (AS = aging susceptible, AI = aging infected) according to the formulae: ASX ¼ ð1  htf  crSX ÞSX ;

AIX ¼ ð1  crIX ÞI X

The demographic data from the TVD were used as initial values for each compartment, assuming a prevalence of 12% per age class (Table 2).

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Table 2 Number of female Swiss dairy cattle per age class (recorded by the Swiss Animal Movement Database, TVD) and initial number of susceptible (S) and infected (I) individuals assuming a seroprevalence of 12% Age class 1 2 3 4 5 6 7 8 9 10 11 12 Total

Total number of animals

%

Initial values S

Initial values I

224414 174111 153061 126147 99663 88003 80018 72036 48777 34729 22912 40091

19.28 14.96 13.15 10.84 8.56 7.56 6.87 6.19 4.19 2.98 1.97 3.44

197484 153218 134694 111009 87704 77442 70416 63391 42924 30561 20162 35280

26930 20893 18367 15138 11960 10560 9602 8644 5853 4167 2749 4811

1163962

100.00

1024285

139675

The differential equations of the compartments S2–S12 and I2–I12 all followed the same principle of inflows and outflows (Table 3): dSX dI X ¼ ASX1  HTX  ASX  CASX ; ¼ AIX1 þ HTX  AIX  CAIX dt dt The flows of compartments I1 and S1 could be described by the same system of differential equations, but they comprised additionally the births of infected and susceptible calves (Table 3): dS1 ¼ BS þ BI  ð1  vtfÞ  HT1  AS1  CAS1 ; dt dI 1 ¼ BI  vtf þ HT1  AI1  CAI1 dt Monte Carlo sensitivity testing was performed to examine the impact of different constants on the model (see sensitivity analysis below). 2.3.3. Simulation of control strategies: Models 2–5 The steady state of the baseline model was chosen as starting point for all intervention strategies. Differential equations and intervention-related parameters used in Models 2 (test-and-cull model), 3 (discontinued breeding with offspring model), 4 (chemotherapy model) and 5 (vaccination model) can be found in Tables 3 and 4, respectively. 2.3.4. Model 2: the test-and-cull model One possible strategy of controlling N. caninum infection in a population is to cull seropositive animals. An important requirement for control programs of this type is the availability of a reliable test that identifies infected animals. In our model, the baseline value of the sensitivity of the test (Se) was set to 0.96, in accordance to the sensitivity of the ELISA

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Table 3 Differential equations used in susceptible (S)–infected (I)—Models 1–5 Compartment(s)

Model(s)

Inflows and outflows

S1

dS1 =dt ¼ BS þ BI  ð1  vtfÞ  HT1  AS1  CAS1

I2–I12 S1 I1 S1

1, 2, 3ai, 3b, 3c 1–4 1, 2, 3ai, 3b, 3c 1–4 4ai 4ai 4aii

I1

4aii

S1 I1 S1

4b 4b 5

I1 W1 V1 S2–S12 W2–W12 I2–I12 V2–V12

5 5 5 5 5 5 5

S2–S12 I1

dSX =dt ¼ ASX1  HTX  ASX  CASX dI 1 =dt ¼ BI  vtf þ HTX  AIX  CAIX dI X =dt ¼ AIX1 þ HTX  AIX  CAIX dS1 =dt ¼ BI  ð1  vtfÞ þ BI  vtf  eff M  Se þ BS  HT1  CAS1 dI 1 =dt ¼ BI  vtf  ð1  SeÞ þ BI  vtf  ð1  eff M Þ  Se þ HT1  CAI1 dS1 =dt ¼ ðBINT þ BITP þ BI3 Þð1  vtfÞ þ BI3  vtf  eff M  Seþ BITP  vtf  eff M þ BS  HT1  CAS1 dI 1 =dt ¼ BINT  vtf þ BI3  vtf  ð1  SeÞ þ BI3  vtf  ð1  eff M Þ  Seþ BITP  vtf  ð1  eff M Þ þ HT1  CAI1 dS1 =dt ¼ BI  ð1  vtfÞ þ BI  vtf  eff M þ BS  HT1  CAS1 dI 1 =dt ¼ BI  vtf  ð1  eff M Þ þ HT1  CAI1 dS1 =dt ¼ BW þ BS þ BI  ð1  vtfÞ þ BV  ð1  vtf 2 Þ  AS1  CAS1  HT1  VS1 þ LIW1 dI 1 =dt ¼ BI  vtf þ BV  vtf 2  AI1  CAI1 þ HT1  VI1 þ LIV1 dW 1 =dt ¼ VS1  AW1  CAW1  LIW1 dV 1 =dt ¼ VI1  AV1  CAV1  LIV1 dSX =dt ¼ ASX1  CASX  ASX  HTX  VSX þ LIWX dW X =dt ¼ AWX1  CAWX  AWX þ VSX  LIWX dI X =dt ¼ AIX1  CAIX  AIX þ HTX  VIX þ LIVX dV X =dt ¼ AVX1  CAVX  AVX þ VIX  LIVX

AI: aging process of infected animals, AS: aging process of susceptible animals, AV: aging process of vaccinated infected animals, AW: aging process of vaccinated susceptible animals, BI: calves from infected cows, BINT: calves from horizontally infected, serologically not tested cows, BITP: calves from infected cows tested seropositive in year 1, BS: calves from susceptible cows, BV: calves from vaccinated infected cows, BW: calves from vaccinated susceptible cows, CAI: culled infected animals, CAS: culled susceptible animals, CAV: culled vaccinated infected animals, CAW: culled vaccinated susceptible animals, effM: efficacy of medication, HT: horizontal transmission, LIV: loss of vaccination immunity of vaccinated infected animals, LIW: loss of vaccination immunity of vaccinated susceptible animals, Se: sensitivity, VI: vaccination of infected animals, VS: vaccination of susceptible animals, vtf: vertical transmission factor, and vtf2: vertical transmission factor of vaccinated infected animals.

assay used in the Swiss Neospora reference laboratory (H. Sager, Institute of Parasitology, University Bern, pers. commun.). To simulate the test-and-cull strategy, various sub-scenarios were considered. (2a) Culling of all seropositive animals. i. Yearly testing of all animals in the population and subsequent culling of seropositive animals. ii. Testing of all animals in the population and subsequent culling of seropositive animals in the first year. Only testing and subsequent culling of all seropositive calves (S1 plus I1) in years 2–25. For sub-scenario (2ai), the culling rates of all infected compartments (crI1–crI12) were set to 1. To account for the sensitivity of the test, the number of culled animals

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Table 4 Intervention-related parameters used in Models 2–5 Model(s)

Intervention parameter(s)

Notation

Value or equation

2–4 2, 3 2, 3

Sensitivity of serological test Neospora-abortion fraction Accessible fetuses

Se na accf

0.96a 0.25b 0.8 c

2ai, 2aii 2bi 2bii

crI1–crI12 crI3–crI12 crI2–crI12

1 1 1

CAIA CAINA

=2arIIXSe =2arIaccfnaIXSe

2dii

Culling rates of seropositive animals I1–I12 (1/year) Culling rates of seropositive mature animals (1/year) Culling rates of seropositive mature animals and heifers (1/year) Culled seropositive cows with abortion (animals/year) Culled seropositive cows with Neospora-abortion (animals/year) Culled animals with Neospora-abortion (animals/year)

CANA

=2arIaccfnaIX

3ai, 3aii 3b 3c

Births of calves from infected cows (animals/year) Births of calves from infected cows (animals/year) Births of calves from infected cows (animals/year)

BIX BIX BIX

=(prX  arI)IX(1  Se) =prXIX(1  2arI) =prXIX(1  2arI)

4ai, 4aii, 4b

Efficacy of medication

effM

0.6 c

5

Efficacy of vaccine to prevent Neospora-abortion Efficacy of vaccine to prevent horizontal transmission Vaccination immunity loss (1/year) Vertical transmission factor of vaccinated infected animals Vaccination coverage (1/year)

eff1 eff2 vil vtf2

0.6 c 0.7 c 0.1 c 0.4 c

cge

0.95c

2c 2di

arI: abortion rate of infected animals, IX: infected animals per age class, prX: pregnancy rate per age class. a Sensitivity of the ELISA test used in the Swiss Neospora reference laboratory (H. Sager, Institute of Parasitology, University Bern, pers. commun.). b Gottstein et al. (1998) and Sager et al. (2001). c Assumption.

correctly identified as infected, CAIX, was then CAIX ¼ crIX  I X  Se For sub-scenario (2aii), the culling rates of all infected compartments were set to 1 in year 1 of the simulation. In years 2–25, only the culling rate of the I1 compartment was set to 1 and the culling rates of the other infected compartments were re-set to their baseline values of Model 1. (2b) Culling of all seropositive mature animals. i. Yearly testing of all mature animals (3 years old) in the population and subsequent culling of seropositive animals. ii. Testing of all animals of the age classes 2–12 and subsequent culling of seropositive animals in the first year. Only testing (and subsequent culling) of heifers (S2 plus I2) in years 2–25. For sub-scenario (2bi), the culling rates of only the infected mature animals (crI3–crI12) were set to 1. For sub-scenario (2bii), the culling rates of the I2–I12 compartments were set to 1 in year 1. In years 2–25, only the culling rate of the

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infected compartment I2 was set to 1 and the culling rates of the other infected compartments were re-set to their baseline values. (2c) Culling of all seropositive animals that experience an abortion by any reason. In this sub-scenario, all seropositive aborting cows were removed from the population—in addition to the regular elimination process from Model 1. This was simulated by adding the abortion rate of infected animals to the baseline culling rate. The abortion rate was multiplied by 2 to account for abortions of male calves: CAIX ¼ crIX  I X þ 2arI  I X  Se (2d) Culling of all infected animals that experience an N. caninum-induced abortion. i. Serological testing of all animals that have an abortion and subsequent polymerase chain reaction (PCR) testing of only the aborted fetuses from seropositive cows. Subsequent culling of cows that have a confirmed N. caninum abortion. ii. PCR testing of all aborted fetuses in the population and subsequent culling of cows that have a confirmed N. caninum abortion. In sub-scenario (2d), only the cows that experienced a N. caninum abortion were eliminated. Previous studies conducted in Switzerland reported a proportion of N. caninum abortions of 21% and 29%, respectively (Gottstein et al., 1998; Sager et al., 2001). Therefore, the baseline value for the Neospora-abortion fraction (na) in the model was set to 0.25. Because all aborted fetuses in a population are rarely accessible for examination, a parameter ‘‘accessible fetuses’’ (accf; baseline value = 0.8) was used to define the proportion of abortions that would be submitted to PCR examination. Assuming that the PCR sensitivity is a 100%, the culled animals of the compartments I3–I12 in sub-scenario (2di) were calculated using the following formula: CAIX ¼ crIX  I X þ 2arI  na  accf  I X  Se In sub-scenario (2dii), the aborted fetuses were directly submitted for PCR examination and the cows were not serologically tested. Therefore, the culled animals of the compartments I3–I12 were calculated as follows: CAIX ¼ crIX  I X þ 2arI  na  accf  I X 2.3.5. Model 3: the discontinued breeding with offspring from seropositive animals model Another option for the control of infection with N. caninum is to discontinue breeding with offspring from seropositive animals and to use them for fattening. In analogy to Model 2, three different sub-scenarios were considered. (3a) No breeding with offspring from all seropositive animals. i. Yearly testing of all mature animals in the population and discontinued breeding with offspring from seropositive cows. ii. Testing of all mature animals in the population in the first year and discontinued breeding with offspring from seropositive cows. Only testing (and exclusion from

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breeding with offspring) of the cows of the compartments S3 and I3 in years 2–25 of simulation. Sub-scenario (3ai) was simulated by reducing the number of infected animals that gave birth to breeding calves to the lowest possible value, i.e. the animals that were not correctly identified by the serological test: BIX ¼ ðprX  arI ÞI X ð1  SeÞ In sub-scenario (3aii), the animals of the age classes 4–12 that would get infected horizontally, were not serologically tested and their calves flowed into the S1 and I1 compartments as described in Model 1. The animals that were tested and detected were excluded from breeding and their births were calculated the same way as in subscenario (3ai). The infected animals that were tested and found to be negative (false negatives) were not excluded from breeding and their calves flowed into the S1 and I1 compartments as described in Model 1. (3b) No breeding with offspring from seropositive animals that experience an abortion by any reason. This was simulated by reducing the number of infected animals per age class, IX, by the proportion of animals that would have an abortion and that would test seropositive (=IX2arISe). These animals would definitely be excluded from breeding and not add to births in the subsequent years, but still remain in the population. The infected animals that did not suffer an abortion gave birth to breeding calves, which flowed into the S1 and I1 compartments as described in Model 1. The number of births from these animals was calculated as follows: BIX ¼ prX  I X ð1  2arI Þ (3c) No breeding with offspring from seropositive animals that experience a PCRconfirmed N. caninum abortion. This was simulated by reducing the number of infected animals per age class, IX, by the number of animals that had a confirmed N. caninum abortion. In analogy to subscenario (2di) of the culling model, the parameters ‘‘sensitivity’’, ‘‘accessible fetuses’’ and ‘‘Neospora-abortion fraction’’ were included to determine the number of seropositive animals that had a confirmed Neospora-abortion (=IX2arIaccfnaSe). These animals would definitely be excluded from breeding and not add to births in the subsequent years, but still remain in the population. The infected animals that did not suffer an abortion gave birth to breeding calves, which was calculated as in sub-scenario (3b). 2.3.6. Model 4: the chemotherapy model A promising but still hypothetical strategy for controlling N. caninum infection in a population would be the treatment of newborn calves with an agent that leads to the elimination of the parasite. Although there is no such N. caninum chemotherapy available to date, a metaphylactic medication control strategy was modeled in preparation for expected forthcoming developments. Similar to the other models, there were two possible options for a putative control policy:

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(4a) Chemotherapeutic treatment of newborn calves from seropositive cows. i. Yearly serological testing of all mature cattle in the population and subsequent chemotherapeutic treatment of all offspring from seropositive cows. ii. Serological testing of all mature cattle in the population in the first year and subsequent chemotherapeutic treatment of all offspring from seropositive cows. Only testing of the cows of the compartments S3 and I3 in years 2–25. For sub-scenario (4ai), all equations remained the same as in Model 1 apart from the flow of calves into the compartments S1 and I1. These flows were modified to account for the efficacy of medication, effM (baseline value = 0.6) and for the sensitivity (Se) of the test that would be used to identify N. caninum seropositive cattle: newborn I ¼ BI  vtf  ð1  SeÞ þ BI  vtf  ð1  eff M Þ  Se; newborn S ¼ BI  ð1  vtfÞ þ BI  vtf  eff M  Se þ BS In sub-scenario (4aii) all cows were tested in the first year and their calves added to the S1 and I1 compartments as described in sub-scenario (4ai). In years 2–25 – as in Model 3 – the cows of the age classes 4–12 that would get horizontally infected were not tested (=infected, not tested animals, INT) and their calves flowed into the S1 and I1 compartments as described in Model 1. The calves of the serologically tested cows of the compartments I3 and S3 were treated and flowed into the S1 and I1 compartments as in sub-scenario (4ai). The calves of the cows that were tested positive in year 1 (BITP), would all be treated. In summary, the flow of newborn animals in sub-scenario (4aii) was calculated as follows: newborn I ¼ BINT  vtf þ BI3  vtf  ð1  SeÞ þ BI3  vtf  ð1  eff M Þ  Se þ BITP  vtf  ð1  eff M Þ; newborn S ¼ ðBINT þ BI3 þ BITP Þ  ð1  vtfÞ þ BI3  vtf  eff M  Se þ BITP  vtf  eff M þ BS (4b) Chemotherapeutic treatment of all newborn calves in the population without any serological testing of the mothers. In sub-scenario (4b), all calves in the population were treated yearly without previously testing the cows. This means that only the efficacy of medication was taken into account: newborn I ¼ BI  vtf  ð1  eff M Þ; newborn S ¼ BI  ð1  vtfÞ þ BI  vtf  eff M þ BS

2.3.7. Model 5: the vaccination model Due to lack of reliable data concerning the efficacy of the presently available vaccine and its capacity to prevent horizontal or vertical infection, the effect of a N. caninumvaccination strategy in Switzerland was modeled under the assumption that a potential vaccine is able to prevent abortions caused by N. caninum in cattle and to reduce vertical

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and horizontal transmission in vaccinated animals to a certain degree. The protocol implied annual vaccination of all susceptible and infected cattle in the population without previous serological testing. Two new compartments per age class were added to Model 1 to simulate Model 5 (Figs. 2 and 3). Compartments V1–V12 were the vaccinated infected animals that were protected, i.e. the animals that were protected from having an abortion due to Neospora. The rate at which infected animals flowed into the compartments VX was influenced by the coverage of cattle-vaccination, cge (baseline value = 0.95), i.e. the proportion of cattle covered by a national vaccination program, and by the efficacy of the vaccine to prevent Neospora-abortion, eff1 (baseline value = 0.6): VIX ¼ I X  cge  eff 1 where VIX is the number of vaccinated, infected animals. All animals in the compartments VX were protected by the vaccine from suffering Neospora induced abortions. Flows out of the VX-compartments were the loss of vaccination immunity, LIV, culled animals of the vaccinated animals, CAV, and the aging process, AV. The loss of vaccination immunity in cattle was calculated by multiplying the number of vaccinated animals per compartment by vil (baseline value = 0.1), a vaccination immunity loss parameter that defined the proportion of animals losing their protection status before the booster vaccination in the following year: LIVX ¼ V X  vil

Fig. 2. Compartments and animal flows in Model 5 (vaccination model). CA: culled animals, I: infected, S: susceptible, V: vaccinated infected animals, and W: vaccinated susceptible animals.

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Fig. 3. Model representing the flows of animals of age class 1 in Model 5. I: infected, S: susceptible, V: vaccinated infected animals, W: vaccinated susceptible animals. BI: all births I, BS: all births S, BV: all births V, BW: all births W, cge: vaccination coverage, cr: culling rate, eff1: efficacy of vaccine to prevent N. caninum abortion, eff2: efficacy of vaccine to prevent horizontal transmission, htf: horizontal transmission factor, vil: vaccination immunity loss parameter, vtf: vertical transmission factor, and vtf2: vertical transmission factor of vaccinated infected animals.

In analogy, compartments W1–W12 contained the vaccinated susceptible animals that were protected from getting horizontally infected. The rate at which susceptible animals flowed into the compartments WX was influenced by the efficacy of the vaccine to prevent horizontal transmission, eff2 (baseline value = 0.7): VSX ¼ SX  cge  eff 2 where VSX is the number of vaccinated susceptible animals. The loss of vaccination immunity among seronegative animals was then LIWX ¼ W X  vil The calves of the vaccinated infected cows, BV, were either added to the compartments I1, BV  vtf2, or S1, BV  (1  vtf2), where vtf2 was the probability of vertical transmission in vaccinated infected adult cattle (baseline value = 0.4). The calves of the vaccinated, susceptible mother cows, BW, were all added to the compartment S1 (Fig. 3). The culling rates for the vaccinated, susceptible and the vaccinated, infected animals were the same as for the non-vaccinated animals. The birth rates for the susceptible animals that were protected remained the same, assuming that the vaccine applied in seronegative animals only prevented horizontal transmission. The births in vaccinated, infected animals increased, accounting for the reduction in Neospora-abortions in vaccinated, infected cattle. This was achieved by reducing the abortion rate by the percentage of Neosporaabortion in the population: BVX ¼ ½prX  arI  ð1  naÞV X

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In summary, the differential equations for the compartments S2–S12, W2–W12, I2–I12 and V2–V12 in the vaccination model were as follows (Table 3): dSX ¼ ASX1  CASX  ASX  HTX  VSX þ LIWX ; dt dI X ¼ AIX1  CAIX  AIX þ HTX  VIX þ LIVX ; dt dW X ¼ AWX1  CAWX  AWX þ VSX  LIWX ; dt dV X ¼ AVX1  CAVX  AVX þ VIX  LIVX dt whereas the flows of the compartments I1 and S1 also included the births from all mature animals in the population (Table 3): dS1 ¼ BW þ BS þ BI  ð1  vtfÞ þ BV  ð1  vtf 2 Þ  AS1 dt  CAS1  HT1  VS1 þ LIW1 ; dI 1 ¼ BI  vtf þ BV  vtf 2  AI1  CAI1 þ HT1  VI1 þ LIV1 dt 2.4. Model check All the units in the model were checked for consistency and possible errors by using the units check feature in the modeling software which allowed finding mistyped unit names or errors of more substantive nature, such as multiplying instead of dividing. Moreover, the model was checked for syntax errors or systematic errors such as non-defined variables or missing values, with the ‘‘check model’’ option of the software. 2.5. Sensitivity analysis The impact of uncertainty due to the incomplete knowledge about the life cycle of N. caninum and the variable nature of infectious processes was assessed using sensitivity analysis for selected parameters. The multivariable Monte Carlo sensitivity simulation (MVSS) tool of the modeling software (Vensim# Professional32 Version 5.4a, Ventana Systems, Inc., Harvard, USA) was used to obtain a range of prevalence outputs by varying the parameters specified in Table 5. This was performed with repeated simulations in which defined parameters were changed in a randomized process for each simulation. In each model, a different combination of parameters was included in the sensitivity analysis, except for the parameters ‘‘unknown factor’’ (uf), ‘‘prevalence dependent factor’’ (pf) and ‘‘vertical transmission factor’’ (vtf), which were the least confident in the model and were therefore included in the sensitivity analysis of each model. Each scenario was run with 1000 iterations. The data of all iterations per scenario were processed in Microsoft1 Excel 2000 (Microsoft Corporation, Redmond, USA) and transferred to the statistical software package (NCSS 2001, Kaysville, UT, USA), where multivariable regression analyses were

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Table 5 Parameters and their ranges and distributions used in the sensitivity analyses conducted for Models 1–5 Model(s) Parameter no.

Notation Minimum Model value value

1–5 1–5

uf pf

0.00095 0.0224

0.001181 0.00142 0.028 0.0336

Uniform Uniform

1/year 1/year

vtf

0.85

0.9

0.95

Uniform

Dimensionless

Se effM cge eff1

0.93 0.4 0.9 0.45

0.96 0.6 0.95 0.6

0.99 0.8 1 0.75

Uniform Uniform Uniform Uniform

Dimensionless Dimensionless 1/year Dimensionless

eff2

0.55

0.7

0.85

Uniform

Dimensionless

vil

0.05

0.1

0.15

Uniform

1/year

vtf2

0.2

0.4

0.6

Uniform

Dimensionless

1–5 2–4 4 5 5

5

5 5

Unknown factor Prevalence dependent factor Vertical transmission factor Sensitivity Efficacy of medication Vaccination coverage Efficacy of vaccine to prevent Neosporaabortion Efficacy of vaccine to prevent horizontal transmission Vaccination immunity loss Vertical transmission factor of vaccinated infected animals

Maximum Distribution Unit value

performed to obtain standardized coefficients (Kleinbaum et al., 1998). The response variable in the multivariable regression analysis was the prevalence in years 5, 10, 15, 20 and 25 of simulation, and the explanatory variables were the scenario-specific parameters that had been sampled in a random process in the 1000 iterations in the multivariable sensitivity runs (Table 5). Additional analyses had shown that there was no substantial difference in the output when using uniform or triangular distributions. Therefore, uniform distributions were used to define the scenario-specific parameters (Table 5).

3. Results and discussion 3.1. Simulation of the baseline model and of control measures The impact of the control strategies on the prevalence of N. caninum infection in the Swiss dairy cow population is presented in Figs. 4–6. Each figure shows the trend of the prevalence of infection over time. The simulations were run for 25 years. 3.1.1. The baseline model (Model 1) The values for the parameters ‘‘prevalence dependent factor’’ (pf) and ‘‘unknown factor’’ (uf) that allowed to reach a steady state prevalence of 12%, were 0.028 and 0.001181, respectively. The value for the horizontal transmission factor (htf) at equilibrium was 0.0045.

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Fig. 4. Development of the prevalence of N. caninum infection in the Swiss dairy cow population as a result of the control strategy testing and culling of infected, seropositive animals (Model 2). (^) Sub-scenario (2ai): yearly testing of all animals in the population and subsequent culling of all seropositive cattle. (&) Sub-scenario (2aii): first year testing of all cattle and culling of seropositive animals. Years 2–25: testing of the animals of age class 1, i.e. S1 plus I1 and subsequent culling of seropositive animals. (*) Sub-scenario (2bi): yearly testing of all mature animals (I3–I12) in the population and subsequent culling of all seropositive animals. (~) Sub-scenario (2bii): first year testing of animals of the age classes I2–I12 and subsequent culling of seropositive animals. Years 2–25: testing of all animals of age class 2, e.g. S2 and I2 and subsequent culling of seropositive animals. (5) Sub-scenario (2c): culling of all seropositive animals that have an abortion irrespective of its cause. (^) Sub-scenario (2d): culling of all seropositive animals that have a N. caninum-induced abortion.

3.1.2. The test-and-cull model (Model 2) A policy of culling all seropositive animals in the population was effective because it rapidly reduced the prevalence from 12% (Model 1) to <1% in the first year of simulation (Fig. 4). There was a difference in the curve progression between scenarios (2ai) (yearly testing of all animals) and (2aii) (testing of all animals in the first year and only testing of calves in years 2–25). In sub-scenario (2ai), the prevalence declined rapidly (prevalence in year 1 of simulation = 0.97%) and reached an equilibrium prevalence of 0.13% in year 4 of control. In sub-scenario (2aii), the prevalence was rapidly reduced in year 1, increased slightly in years 2 and 3 and finally steadily declined until it reached a stable value of 0.67% in year 18. The policy of culling all seropositive mature animals was also a very effective method to reduce prevalence rapidly (Fig. 4). In both sub-scenarios (2bi) and (2bii), the prevalence decreased to 3.3% and 1.0%, respectively, in the first time step of simulation, and subsequently steadily declined until it came to an equilibrium state of 0.23% (2bi) and 0.52% (2bii), respectively. Although all these sub-scenarios were effective, the prevalence did not decline to zero, but only to 0.13–0.7%, because the horizontal transmission factor (htf) was not only

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Fig. 5. Development of the prevalence of N. caninum infection in the Swiss dairy cow population as a result of the strategy discontinued breeding with offspring from seropositive cows (Model 3). (^) Sub-scenario (3ai): no breeding with offspring from seropositive cows, when all the cows in the population are yearly tested. (&) Subscenario (3aii): no breeding with offspring from seropositive cows, when all the cows are tested in the first year and only the cows of age class 3 in years 2–25. (5) Sub-scenario (3b): no breeding with offspring from seropositive cows that have an abortion, irrespective of its cause. (^) Sub-scenario (3c): no breeding with offspring from cows that have a N. caninum-induced abortion.

defined by a prevalence dependent factor (pf), but also by an unknown factor (uf), which was a constant, age class independent per capita force of infection. This is consistent with the findings of French et al. (1999) who demonstrated that Neospora-infection in a herd cannot be completely eliminated as long as the horizontal transmission rate is not reduced to zero. To eradicate the infection in the population, it would be necessary to know the complete life cycle of N. caninum and to control the horizontal transmission process as well. Particularly with regard to the economic assessment, we created two alternative testing options. A substantial reduction in prevalence was possible even when not all animals were annually tested. In contrast, scenarios considering the culling of seropositive animals only after having an abortion were not effective. A policy of culling all seropositive, aborting animals (subscenario (2c)) was clearly less effective than culling of all animals that tested positive; in the first 4 years of simulation, prevalence declined from 12% to 10% and afterwards it constantly declined about 0.1–0.3% per year and reached 5.8% at the end of the simulation period (Fig. 4). A policy of culling all animals that had experienced a N. caninum abortion (sub-scenario (2d)) was the least effective of the culling strategies; after a simulation period of 25 years the prevalence was still 10.4%, which is an absolute decrease of only 1.6% (Fig. 4).

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Fig. 6. Development of the prevalence of N. caninum infection in the Swiss dairy cow population as a result of the medication of calves from infected cows (Model 4) and vaccination of cattle of all ages (Model 5) on the prevalence of N. caninum infection in the Swiss dairy cow population. (^) Sub-scenario (4ai): chemotherapeutic treatment of calves from seropositive cows, when all the cows in the population are yearly tested. (&) Subscenario (4aii): chemotherapeutic treatment of calves from seropositive cows, when all the cows are tested in the first year only, and only the cows of age class 3 in years 2–25. (*) Sub-scenario (4b): chemotherapeutic treatment of all newborn calves without previously testing the dams. (~) Sub-scenario (5): vaccination of all susceptible and infected cattle in the population.

3.1.3. The discontinued breeding with offspring from seropositive animals model (Model 3) A policy of discontinued breeding with offspring from seropositive cows ((3ai) and (3aii)) was shown to have a slower impact on the prevalence when compared with the most effective culling scenarios, but it also reduced the prevalence of infection in the population to a comparable level (Fig. 5). There was no major difference in effect between the subscenarios (3ai) and (3aii); with both strategies the curves rapidly decreased and reached a stable level of 0.8% and 1.3%, respectively, after 20 years of simulation. The effect of the strategies not breeding with offspring from seropositive aborting animals (3b) and seropositive Neospora aborting animals (3c) were much less substantial and only led to a minor reduction in the prevalence within 25 years of control (Fig. 5). The end prevalence values for these two sub-scenarios were 8.7% (3b) and 11.7% (3c), respectively. A policy of keeping seropositive cattle in a herd and to discontinue breeding with offspring from such animals would be a less drastic control strategy and would probably be better accepted among farmers and the public, as animals do not have to be culled. However, this policy would not be as effective as culling because it would only block vertical transmission and infected, mature animals could still form part of the horizontal transmission cycle.

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3.1.4. The chemotherapy model (Model 4) A policy of chemotherapeutic treatment of calves from seropositive mothers ((4ai) and (4aii)) or of all calves without previously testing the dams (4b) using a medication with an estimated efficacy of 60% generally reduced the prevalence of N. caninum infection more slowly than culling and discontinued breeding with offspring, but still showed a remarkable decline over time (Fig. 6). As in the other models, there was no relevant difference between the two options for testing the animals in the population. In all three simulations (4ai), (4aii) and (4b), prevalence dropped below 4% after 12–14 years of control. With an efficacy of medication of at least 80%, the prevalence would drop below 2% after 13 years of control. Similarly to the discontinued breeding with offspring model, only the vertical transmission could be blocked and cows could still contribute to the horizontal transmission cycle. It is suggested that a policy of chemotherapeutic treatment of calves could only be successful if the drug was efficacious. 3.1.5. The vaccination model (Model 5) A policy of vaccinating all animals in the population with a hypothetical vaccine exhibiting an estimated efficacy of 60% to prevent Neospora-abortion, an efficacy of 70% to prevent horizontal transmission, a vertical transmission factor for vaccinated, infected animals of 40% and a ‘‘loss of vaccination immunity’’ parameter over a year of 10% was very effective (Fig. 6). Prevalence decreased rapidly from 12% to 2% in the first 3 years and then declined steadily to 0.2% by year 25 of the simulation. A N. caninum vaccine is currently available in several countries in the world, but its efficacy is controversially discussed within the scientific community (Heuer et al., 2004; Romero et al., 2004). Because transmission is a function of biological and environmental factors, a vaccination program with a certain type of vaccine might be effective in one country but not in another. A useful vaccine would preferably reduce abortion risk and both horizontal and vertical transmission risk. In conclusion, a policy of vaccinating all the animals in the population would only be justifiable if the efficacy and the duration of immunity were acceptable. 3.2. Sensitivity analysis The summarized results of the multivariable Monte Carlo sensitivity simulations are presented in Figs. 7–11 and Tables 6–9. Since the outcomes of the sensitivity simulation of similar sub-scenarios did not differ substantially, only a representative selection of the sensitivity graphs is presented in Figs. 7–11, namely the graphs of Model 1 and those of the most effective sub-scenarios per model, i.e. the control strategies (2ai), (2c), (3ai), (4b) and (5). Each graph presents the mean value of the sensitivity runs and the 95% upper and lower confidence bounds. These confidence bounds define the interval that includes 95% of the prevalence values obtained in the 1000 simulations. Tables 6–9 show the standardized coefficients obtained from the multivariable regression analyses on the parameters defined in Table 5. In Model 1, the 95% confidence bounds were narrow in the beginning and wide at the end of the simulation period, where the interval reached from 9% to 15% (Fig. 7). The range of prevalence of the sensitivity simulation of sub-scenario (2ai) was very narrow

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Fig. 7. Sensitivity graph of the multivariable sensitivity analysis of Model 1 on the parameters ‘‘unknown factor’’, ‘‘prevalence dependent factor’’ and ‘‘vertical transmission factor’’ as specified in Table 5. (- - -) Mean value and (—) upper and lower 95% confidence bounds.

Fig. 8. Sensitivity graph of the multivariable sensitivity analysis of the test-and-cull model (Model 2) on the parameters ‘‘unknown factor’’, ‘‘prevalence dependent factor’’, ‘‘vertical transmission factor’’ and ‘‘sensitivity’’ as specified in Table 5. Sub-scenario (2ai): (- - -) mean value, (—) upper and lower 95% confidence bounds. Subscenario (2c): (-   -) mean value, (  ) upper and lower 95% confidence bounds.

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Fig. 9. Sensitivity graph of the multivariable sensitivity analysis of sub-scenario (3ai) of the discontinued offspring model (Model 3) on the parameters ‘‘unknown factor’’, ‘‘prevalence dependent factor’’, ‘‘vertical transmission factor’’ and ‘‘sensitivity’’ as specified in Table 5. (- - -) Mean value and (—) upper and lower 95% confidence bounds.

Fig. 10. Sensitivity graph of the multivariable sensitivity analysis of sub-scenario (4b) of the therapy model (Model 4) on the parameters ‘‘unknown factor’’, ‘‘prevalence dependent factor’’, ‘‘vertical transmission factor’’, ‘‘sensitivity’’ and ‘‘efficacy of medication’’ as specified in Table 5. (- - -) Mean value and (—) upper and lower 95% confidence bounds.

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Fig. 11. Sensitivity graph of the multivariable sensitivity analysis of the vaccination model (Model 5) on the parameters ‘‘unknown factor’’, ‘‘prevalence dependent factor’’, ‘‘vertical transmission factor’’, ‘‘vaccination coverage’’, ‘‘efficacy of vaccine to prevent Neospora-abortion’’, ‘‘efficacy of vaccine to prevent horizontal transmission’’, ‘‘vaccination immunity loss’’ and ‘‘vertical transmission factor of vaccinated infected animals’’ as specified in Table 5. (- - -) Mean value and (—) upper and lower 95% confidence bounds.

(Fig. 8), indicating that this scenario was not very sensitive towards uncertainty in the parameters that were assessed. The confidence bounds of sub-scenario (2c) (Fig. 8) and (4b) (Fig. 10) showed a similar behavior as Model 1: they were narrow at the beginning and wider towards the end of the simulation period (4.6–7.4% and 1–3.2%, respectively), indicating that the parameters included in the sensitivity analysis had a considerable effect on the range of prevalence. The interval in sub-scenario (3ai) (Fig. 9) followed closely the mean value, indicating that this scenario was not very sensitive towards uncertainty in the parameters that were assessed. In the vaccination model, the range of prevalence was widest in years 2–10 of control and got smaller with declining prevalence (Fig. 11). Table 6 Standardized coefficients from the multivariable regression analysis of the sensitivity analysis data of Model 1 in years 5, 10, 15, 20 and 25 of simulation Parameter

Year 5

Year 10

Year 15

Year 20

Year 25

ufa pfb vtf c

0.2306 0.6681 0.6937

0.1964 0.5679 0.7875

0.1856 0.5351 0.8126

0.1807 0.5195 0.8233

0.1779 0.5100 0.8290

All values were significant ( p < 0.05). a Unknown factor. b Prevalence dependent factor. c Vertical transmission factor.

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Table 7 Standardized coefficients from the multivariable regression analysis of the sensitivity analysis data of Model 2 in years 5, 10, 15, 20 and 25 of simulation Sub-scenario

Parameter

Year 5

Year 10

Year 15

Year 20

Year 25

2aia

ufb pfc vtfd See

0.9732 0.0318 0.0019 0.2133

0.9774 0.0295 0.0002 n.s. 0.1946

0.9776 0.0295 0.0004 n.s. 0.1936

0.9776 0.0294 0.0004 n.s. 0.1938

0.9776 0.0294 0.0004 n.s. 0.1938

2aiia

ufb pfc vtfd See

0.7222 0.1817 0.0080 0.6509

0.8921 0.1918 0.0148 0.3835

0.9440 0.1708 0.0139 0.2509

0.9573 0.1580 0.0126 0.2091

0.9608 0.1538 0.0123 0.1972

2bif

ufb pfc vtfd See

0.4697 0.2404 0.3755 0.7226

0.8376 0.1221 0.2034 0.4545

0.9583 0.0648 0.1035 0.2229

0.9686 0.0556 0.0736 0.1993

0.9697 0.0546 0.0710 0.1961

2biif

ufb pfc vtfd See

0.5243 0.1193 0.0063 0.8332

0.8393 0.1493 0.0131 0.5036

0.9415 0.1328 0.0120 0.2845

0.9594 0.1217 0.0104 0.2274

0.9631 0.1183 0.0100 0.2142

2cg

ufb pfc vtfd See

0.2467 0.6290 0.6747 0.1531

0.2314 0.5381 0.7629 0.1186

0.2385 0.5096 0.7818 0.1084

0.2521 0.4965 0.7859 0.1038

0.2684 0.4885 0.7845 0.1012

2dh

ufb pfc vtfd See

0.2347 0.6565 0.7052 0.0334

0.2019 0.5544 0.7959 0.0250

0.1933 0.5219 0.8193 0.0221

0.1908 0.5071 0.8287 0.0207

0.1904 0.4986 0.8332 0.0198

All values were significant ( p < 0.05), except those labeled as non-significant (n.s.). a Testing and culling of all seropositive cattle with and without yearly serological testing. b Unknown factor. c Prevalence dependent factor. d Vertical transmission factor. e Sensitivity. f Testing and culling of seropositive, mature cattle with and without yearly serological testing. g Testing and culling of seropositive cows with abortion. h Testing and culling of seropositive cows with N. caninum abortion.

In Model 1, the standardized coefficients of the parameters ‘‘prevalence dependent factor’’ (pf) and ‘‘vertical transmission factor’’ (vtf) indicated that these parameters were the most influential on the simulation outcome over the whole simulation period (Table 6). For sub-scenarios (2ai), (2aii), (2bi) and (2bii), it was shown that the parameter ‘‘unknown factor’’ (uf) was most influential if prevalence was very low (Table 7). Unlike ‘‘uf’’, the impact of ‘‘pf’’, ‘‘vtf’’ and ‘‘test sensitivity’’ (Se) decreased with declining prevalence. In sub-scenarios (2c), (2d), (3b) and (3c), where the prevalence was not markedly reduced, the parameters ‘‘pf’’ and ‘‘vtf’’ were, similar to Model 1, the most influential ones (Tables 7 and 8). In sub-scenarios (3ai) and (3aii), the effect of ‘‘uf’’ increased with declining prevalence, whereas the effect of the other factors decreased with declining prevalence (Table 8). In the

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Table 8 Standardized coefficients from the multivariable regression analysis of the sensitivity analysis data of Model 3 in years 5, 10, 15, 20 and 25 of simulation Sub-scenario

Parameter

Year 5

Year 10

Year 15

Year 20

Year 25

3ai a

ufb pfc vtf d Se e

0.3143 0.7590 0.0376 0.5341

0.4719 0.6435 0.0422 0.5645

0.7398 0.4816 0.0336 0.4256

0.9037 0.3088 0.0207 0.2502

0.9507 0.2251 0.0140 0.1669

3aiia

ufb pfc vtf d Se e

0.3751 0.8873 0.0500 0.1959

0.5122 0.7730 0.1089 0.2878

0.6897 0.6275 0.1240 0.2606

0.8239 0.4737 0.1162 0.2063

0.8907 0.3673 0.1053 0.1642

3bf

ufb pfc vtf d Se e

0.2438 0.6806 0.6501 0.0003 n.s.

0.2185 0.5945 0.7386 0.0010 n.s.

0.2169 0.5685 0.7593 0.0018 n.s.

0.2218 0.5574 0.7652 0.0025 n.s.

0.2290 0.5512 0.7664 0.0033 n.s.

3cg

ufb pfc vtf d Se e

0.2378 0.6628 0.6702 0.0052

0.2043 0.5676 0.7641 0.0062

0.1941 0.5369 0.7891 0.0069

0.1898 0.5229 0.7993 0.0076

0.1876 0.5149 0.8045 0.0083

All values were significant ( p < 0.05), except those labeled as non-significant (n.s.). a Discontinued breeding with offspring from seropositive cows with and without yearly serological testing. b Unknown factor. c Prevalence dependent factor. d Vertical transmission factor. e Sensitivity. f Discontinued breeding with offspring from seropositive aborting cows. g Discontinued breeding with offspring from N. caninum aborting cows.

therapy model (Model 4), the efficacy of medication was clearly the most influential parameter (Table 9). In the vaccination model (Model 5), the factors ‘‘efficacy of the vaccine to prevent Neospora-abortion’’ and the ‘‘vaccination immunity loss’’ were the most influential (Table 9), whereas ‘‘uf’’, ‘‘pf’’ and ‘‘vtf’’ did not have much influence. It was also interesting to see that the factor ‘‘efficacy of the vaccine to prevent horizontal transmission’’ was of secondary importance. 3.3. Model limitations The deterministic simulation model was based on available demographic and seroprevalence data referring to Switzerland. One major limitation of the model was the lack of reliable data concerning the horizontal transmission process. A more specific model geared towards long-term simulations would include the life cycle of N. caninum in a definitive host population. Dogs are known to be definitive hosts for N. caninum and have been shown to become experimentally infected by eating infectious material from cattle, such as placenta or raw meat, and to be able to shed infectious oocysts (McAllister et al., 1998; Dijkstra et al., 2001; Gondim et al., 2002). To our knowledge, however, there are only three studies that reported to have found N. caninum oocysts in naturally infected dogs

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Table 9 Standardized coefficients from the multivariable regression analysis of the sensitivity analysis data of Models 4 and 5 in years 5, 10, 15, 20 and 25 of simulation Sub-scenario

Parameter

Year 5

Year 10

Year 15

Year 20

Year 25

4aia

ufb pfc vtf d Se e effM f

0.0894 0.2397 0.1156 0.0876 0.9440

0.0914 0.1869 0.1207 0.0903 0.9532

0.1166 0.1741 0.1249 0.0922 0.9451

0.1546 0.1702 0.1284 0.0936 0.9288

0.2021 0.1693 0.1307 0.0943 0.9077

4aiia

ufb pfc vtf d Se e effM f

0.1062 0.2817 0.1183 0.0322 0.9334

0.1135 0.2366 0.1369 0.0661 0.9384

0.1466 0.2361 0.1494 0.0859 0.9234

0.1901 0.2390 0.1585 0.0962 0.9024

0.2392 0.2407 0.1650 0.1012 0.8781

4ba

ufb pfc vtf d effM f

0.0881 0.2338 0.1044 0.9507

0.0902 0.1873 0.1099 0.9589

0.1171 0.1800 0.1148 0.9494

0.1594 0.1806 0.1191 0.9310

0.2132 0.1827 0.1221 0.9076

5g

ufb pfc vtf d vtf2 h eff1 i eff2 j vil k cgel

0.0106 0.0183 0.0251 0.0653 0.6778 0.0238 0.7004 0.1347

0.0194 0.0206 0.0407 0.3053 0.6324 0.0003 n.s. 0.6502 0.1313

0.0316 0.0206 0.0494 0.4546 0.5626 0.0205 0.6007 0.1223

0.0478 0.0199 0.0529 0.5254 0.5136 0.0452 0.5616 0.1177

0.0682 0.0189 0.0537 n.s. 0.5464 0.4855 0.0718 0.5414 0.1174

All values were significant ( p < 0.05), except those labeled as non-significant (n.s.). a Chemotherapy of offspring from seropositive cows with and without yearly serological testing. b Unknown factor. c Prevalence dependent factor. d Vertical transmission factor. e Sensitivity. f Efficacy of medication. g Vaccination of female susceptible and infected animals. h Vertical transmission factor of vaccinated infected animals. i Efficacy of vaccine to prevent Neospora-abortion. j Efficacy of vaccine to prevent horizontal transmission. k Vaccination immunity loss. l Coverage of vaccination.

(Basso et al., 2001; Slapeta et al., 2002; McGarry et al., 2003). In a study conducted in Switzerland, 3289 fecal samples from 249 monthly examined dogs were coprologically tested for the presence of N. caninum oocysts (Sager et al., 2006). Although Hammondia/ Neospora-like-oocysts were detected in 25 samples out of 24 dogs, the presence of N. caninum DNA could not be confirmed by PCR in any of the specimens. These results indicate that the importance of the horizontal infection by dogs in Switzerland is probably very low. Our model can be expanded to include more information on horizontal transmission as soon as more specific data about this process are available. Model results also showed that the influence of horizontal transmission becomes only significant once the

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vertical transmission cycle is interrupted and prevalence of infection due to this pathway decreases. Parameter optimization on the basis of goodness-of-fit (called ‘‘payoff’’ in Vensim) could not be carried out in our model due to the lack of longitudinal serological data. Generating a field study to gather such data would allow the fit of the described model. Another uncertainty we had to deal with was the lack of data concerning the efficacy and the protocol of medication and vaccination. At the moment, there is no Neospora-vaccine or drug available on the European market that has been appropriately evaluated and assessed for efficacy. One could argue that including such control strategies in the model is too speculative. However, keeping in mind that a vaccine is already on the market in various countries (New Zealand, South, Central and North America, http://www.intervet.com), it is only a question of time until the vaccine gets approved for the European market. Therefore, we included the control strategies medication and vaccination, although assumptions had to be made concerning the drug and vaccine efficacy. One could also argue that the immune status of infected cows should be included. So far, there is only one study that demonstrated protective immunity in chronically infected cows (Williams et al., 2003). It revealed that chronically infected cows had significantly less abortions than naı¨ve pregnant cows when challenged with N. caninum tachyzoites at 10 weeks of gestation. Further evidence about this kind of immunity is required in order to justify inclusion in our model. Several studies have examined the presence of the parasite in bulls. N. caninum DNA was sporadically found in the blood and the semen of infected bulls (Ortega-Mora et al., 2003; Caetano-da-Silva et al., 2004; Ferre et al., 2005), but evidence of venereal transmission is still missing, the respective probability very low. Therefore, the present model only included female cattle. Although we did not model the combination of different control strategies, it cannot be ruled out that such combinations could also be a useful tool for the control of N. caninum in Switzerland. With regard to the implementation of a control program on national level, one has to bear in mind that the intervention strategies involving the culling of seropositive cattle and not breeding with offspring from seropositive cows – apart from the economic risk – may have a considerable influence on the structure and genetic diversity of the population, whereas the strategies medication and vaccination would not cause such changes. However, a medication or vaccination program would only be accepted among farmers and the public if the efficacy and safety of the drugs or the vaccine were guaranteed.

4. Conclusions Various strategies were shown to reduce prevalence quickly and efficiently. The most effective strategy was the policy of testing and culling all seropositive animals in the population. However, only taking into account the cost and benefit of each control strategy will allow policy makers to assess the viability and justification of a control program. The availability of reliable data concerning the efficacy of medication and vaccination would increase the accuracy of the estimations of the model. None of the modeled intervention strategies was able to reduce the prevalence to zero because the horizontal transmission was not controlled. Once there is a better

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understanding of the horizontal transmission process, it will be possible to build a more specific model that also includes the cycle of infection in the definitive host populations.

Acknowledgements The authors are very grateful to M.C.M. de Jong and K. Frankena from the group of Quantitative Veterinary Epidemiology in Wageningen, The Netherlands, and J. Zinsstag from the Swiss Tropical Institute in Basel, Switzerland, for their valuable modeling advice and software assistance. The study was financially supported by the Swiss Federal Veterinary Office and the Swiss Federal Office of Science and Education (grants nos. BBW 00.0498 and BBW C01.0122 in the frame of COST 854).

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