# To Vaccinate or Not: Impact of Bovine Viral Diarrhoea in French Cow-Calf Herds

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## Abstract

**:**

^{®}, Bovela

^{®}, Rispoval

^{®}, and Mucosiffa

^{®}. We tested various virus introduction frequency in a naïve herd. We calculated BVD economic impact and vaccination reward. In Charolaise, BVD economic impact was 113€ per cow over 5 years after virus introduction. Irrespective of the vaccine and for a high enough risk of introduction, the yearly expected reward was 0.80€ per invested euro per cow. Vaccination should not be stopped before herd exposure has been decreased. In contrast, the reward was almost nil in Blonde d’Aquitaine and Limousine. This highlights the importance of accounting for herd specificities to assess BVD impact and vaccination efficiency. To guide farmers’ vaccination decisions against BVD, we transformed this model into a French decision support tool.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Herd Dynamics

#### 2.2. Within-Herd Infection Dynamics and Vaccination

_{1}) or vaccinated with progressive loss of immunity (V

_{2}). The M to S, T to R, and V

_{2}to S transitions depend on transition rates Φ

_{MS}, Φ

_{TR}, and Φ

_{VS}(Table 2). Since the duration of the maternal protection lasts generally 4–6 months [20], we assumed that the M to S transition occurs only in calves.

_{2}go to state V

_{1}if vaccinated (ρ

_{H/C}= 1). Other health states are not impacted by vaccination. The start of a progressive loss of immunity, i.e., the V

_{1}to V

_{2}transition, is defined by the duration in V

_{1}(Δ

_{V1}), which is considered as constant and depends on the vaccine. Parameter λ represents the ability of the vaccine to protect animals against infection (reduces the transition to state T), while parameter ω defines the level of protection against vertical transmission if infected (Figure 2). When the vaccine is no longer effective, the animal becomes susceptible again (transition from V

_{2}to S, which depends on the mean duration in V

_{2}(Δ

_{V2}), assuming an exponential distribution of the state duration). To account for the diversity of vaccines, parameter values are based on 4 commercial vaccines (Table 3): Bovilis

^{®}BVD-MD (Msd Animal Health, Madison, NJ, USA), Bovela

^{®}(Boehringer Ingelheim, Ingelheim, Germany), Rispoval

^{®}D-BVD (Pfizer, New York, NY, USA), and Mucosiffa

^{®}(Merial, Lyon, France). For all vaccines, a protection of at least one year is guaranteed by vaccine producers, thus the duration in V

_{1}is assumed to be 52 weeks. The mean duration in V

_{2}is unknown, thus we keep it short not to assume a too long vaccine immunity. The level of protection against infection (horizontal transmission) is also unknown. Hence, we assume that infection can occur with the same probability as for susceptible animals, but with a reduced risk of vertical transmission. Infected animals all have a lifelong post-infection immunity. We assess also the opposite case (in a single scenario using Bovilis

^{®}), i.e., vaccination protecting against infection. In that case, vaccinated animals are infected with a reduced probability compared to susceptible ones, but if infected, the risk of vertical transmission is similar. Most will not be infected, also meaning they will not develop post-infection immunity. All vaccines target BVD virus of type 1, which is the main one circulating in Europe [21]. We assume an average level of protection conferred by the vaccines, without explicitly accounting for the diversity of circulating virus sub-types and its impact on vaccine protection [22].

^{P}and N

^{T}the total number of P and T animals in the herd, respectively, N the herd size, and β

^{P}and β

^{T}the transmission rates per day associated with P and T animals, respectively (Table 2).

_{ext}. The force of infection for susceptible animals in pasture k is:

_{k}the number of animals in pasture k.

_{1}or V

_{2}to infected state T or recovered state R state are calculated as:

_{V}is the number of vaccinated females (either in V

_{1}or in V

_{2}), and ∆t the time step (7 days).

_{a}, R

_{b}or R

_{c}, respectively, until calving (Figure 2). Embryonic or foetal deaths are assumed to be highly probable after infection in early or mid-pregnancy (Table 2), after which females join state R. On the contrary, infection occurring in late pregnancy leads to the birth of R calves. When infection occurs in mid-pregnancy, vertical transmission leading to the birth of a P calf is assumed to be highly probable. Vaccinated females are assumed to give birth to calves protected by maternal antibodies (state M).

_{Ca}between birth and weaning, while P animals have a disease-related mortality μ

_{P}all their life. P and non-P calves also have a probability of dying at birth, μ

_{P,bi}and μ

_{Ca,bi}respectively (Table 2).

#### 2.3. Model Outputs

_{prod}the production cost per kg specific to each farming system (Table 4), N

_{i}the number of animals in group i, c

_{i}the price (in €) of an animal of group i, and k

_{i}the weight (in kg) of an animal of group i.

_{BVDV}and E

_{øBVDV}the earnings with and without BVD virus spread respectively. Impact thus is negative. However, due to stochastic events, pairs of repetitions with and without BVD spreading cannot be directly compared. We sorted repetitions in order to associate E

_{BVDV}and E

_{øBVDV}of similar ranking. Nevertheless, impacts still can be positive. In such a case, we considered them as nil. The expected vaccination reward is:

_{vacc}and I

_{øvacc}the BVD impacts with and without vaccination, respectively. The vaccination cost depends on the vaccine characteristics (price and number of doses required; Table 3), as well as on the number of females vaccinated, i.e., the number of breeding heifers and cows which is constant. An average cost is estimated based on the number of doses administered, knowing that for a first vaccination (for heifers) the doses can be higher:

_{H}and N

_{C}the number of breeding heifers and cows, respectively, ρ

_{H/C}the boolean indicating if there is vaccination (Table 3), n

_{1}and n

_{2}the number of vaccine doses for the first shot and for the following ones respectively, c

_{D}the cost of a vaccine dose, and y the number of years of vaccination. The first year, all breeding females are assumed to be at their first shot. Finally, the euros per euro invested per cow per year is:

_{cumul}the cumulated reward over the simulated years, N

_{y}the number of simulated years, and C the average vaccination cost per year. This output has the advantage of combining the information associated with disease losses, vaccination cost, and reward.

#### 2.4. Simulation Settings

_{ext}is:

_{ext}is the external risk, W the number of weeks on pasture, αRb the abortion rate due to infection mid-pregnancy, η

_{P}the probability of giving birth to a calf in state P after infection in mid-pregnancy and if no abortion, N

_{F}the number of breeding females, and Δt the time interval. (1−K

_{ext})^(W/2) is the probability not to be infected in mid-gestation on pasture. Using Equation (11), 0.4, 1.9, and 7.7 P calf births are expected if the BVD virus is introduced in a naïve Charolaise herd (W = 33 weeks, N

_{F}= 90) exposed to K

_{ext}= 0.00005, 0.00025, and 0.001, respectively.

_{ext}of 0.00025 over an 8-year period. We compared results without and with vaccination of all breeding heifers and cows with the vaccine Bovilis

^{®}.

_{ext}values (from 0 to 0.001). Second, we compared the three farming systems (Charolaise, Limousine and Blonde d’Aquitaine) under two K

_{ext}values (one moderate 0.00025 and one high 0.001). To reduce computational costs and because the largest losses due to BVD in beef cow-calf herds are known to occur in the first few years after virus introduction, we simulated 5 years for all these scenarios.

^{®}, and for a large range of K

_{ext}values (from 0 to 0.001). The scenario was explored over 20 years: vaccination was implemented the first 6 years, and then stopped. We considered two contrasted protections conferred to vaccinated animals: no infection (λ = 1 and ω = 0) versus no vertical transmission if infected (λ = 0 and ω = 1). For each scenario, we ran 1000 repetitions to ensure model output stability.

#### 2.5. Sensitivity Analysis

_{P,bi}, μ

_{P}, β

^{P}, β

^{T}, Φ

_{MS}, Φ

_{TR}, α

_{Ra}, α

_{Rb}and η

_{P}. To limit the number of simulations, closely related parameters were grouped (β

^{P}and β

^{T}, Φ

_{MS}and Φ

_{TR}, α

_{Rb}and η

_{P}) and thus varied in the same direction at the same time. A total of 729 scenarios were run, with 1000 repetitions per scenario.

## 3. Results

#### 3.1. BVD Impact and Vaccination Reward in Exposed Beef Cow-Calf Herds of Charolaise System

#### 3.2. Influence of the Vaccine Used and of the External Risk of Virus Introduction

^{−5}, which corresponds to one new P calf born on average every two years in a fully susceptible herd (Figure 4). Then, for an external risk of 0.00025, the reward over the first five years increased up to 0.85€ per invested euro per year and per vaccinated animal. An external risk of 0.00025 corresponds to two persistently infected calves born on average over a pasture period in an exposed naive herd. A plateau was reached: the reward did not increase further for higher values of the external risk. It has to be noted the extreme variability of the reward for a given external risk: it varied from −3€ to +4€ per invested euro if the external risk was at least moderate, the variations occurring among repetitions of a given scenario, thus related to the model stochasticity and the occurrence of quite rare events such as the birth of a P calf, or on the contrary its death quickly after birth.

#### 3.3. Comparison of Three French Farming Systems

#### 3.4. When to Stop Vaccinating?

#### 3.5. Sensitivity of BVD Impact and Vaccination Reward to Epidemiological Parameters

_{ext}= 0.00025) induced a variation of the median BVD impact, which ranged between −136 and −87€ per breeding female. Most of this variation (70%) was explained by the consequences of infection occurring during female pregnancy, especially during its early stage, the infection-related abortion rate in early pregnancy explaining half the variance of this model output (Figure 7). More surprisingly, the mortality rate of P animals and the transmission rates barely contributed to the variation of the BVD impact. No interaction between parameters contributed to explain output variations.

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Calendar of the Charolaise farming system. The periods where each of the 7 animal groups are present in a cow-calf herd across a year are shown in blue. With a breeding period from end of March to end of July, the risk period is from start of May to mid-December, where cows can be in mid-pregnancy and vertical transmission is then highly probable if infection occurs. Animals can be in contact with infected neighbouring farms during the pasture period. Only male and female grassers are kept indoor.

**Figure 2.**Transitions between health states. M: protected by maternal antibodies; S: susceptible; T: transiently infected; P: persistently infected; R: immune; R

_{a}, R

_{b}, R

_{c}: immune and pregnant, infected respectively in early, mid-, and late pregnancy; V

_{1}: vaccinated without loss of immunity; V

_{2}: vaccinated with progressive loss of immunity. Symbols ρ

_{H/C}, ω and λ stand respectively for the vaccination of breeding heifers and cows (Boolean), the protection conferred by the vaccine against vertical transmission, and the protection conferred by the vaccine against infection. Health state M, mortality rate μ

_{Ca}, and transition rate Ф

_{MS}only concern calves. Health states R

_{a}, R

_{b}, R

_{c}, V

_{1}and V

_{2}only concern breeding heifers and cows. Transitions from S to V

_{1}and from V

_{2}to V

_{1}occur once a year at the beginning of the breeding period (ρ

_{H/C}= 1). Transition from V

_{1}to V

_{2}depends on the duration in state V

_{1}(Δ

_{V1}). The force of infection f is derived from Equations (1) and (2), other parameters are given in Table 2 and Table 3.

**Figure 3.**BVD impact and reward after vaccination (in € per breeding female). A beef cow-calf herd of Charolaise breeding system is exposed to a moderate external risk of virus introduction (K

_{ext}= 0.00025). The Bovilis

^{®}vaccine is provided yearly to all breeding females before the start of the breeding period. The envelop shows the percentiles 25 and 75 of the 1000 stochastic repetitions for both scenarios.

**Figure 4.**Reward after vaccination against BVD according to the vaccine used and the external risk of virus introduction. A beef cow-calf herd of Charolaise breeding system is considered. All breeding females are vaccinated yearly before the start of the breeding period using one of four commercial vaccines (see Table 1 for details on vaccines). The curves show the median over 1000 stochastic repetitions of the euros obtained per euro invested per year per vaccinated animal over 5 years according to the external risk. The violin plots show the values for the 1000 stochastic repetitions for three K

_{ext}: 0, 0.00025, 0.001. Each side of the violin plots shows two overlapping scenarios: Bovilis

^{®}and Bovela

^{®}on the left; Rispoval

^{®}and Mucosiffa

^{®}on the right.

**Figure 5.**Return on investment after vaccination against BVD according to the farming system and the external risk of virus introduction. All breeding females are vaccinated yearly before the start of the breeding period using Bovilis

^{®}. Three farming systems are compared: Charolaise, Limousine and Blonde d’Aquitaine. The percentiles 10, 50 and 90 of the euros per euro invested per year per vaccinated animal over 5 years are shown from 1000 stochastic repetitions.

**Figure 6.**BVD impact and vaccination reward according to the type of protection conferred by the vaccine. A beef cow-calf herd of the Charolaise breeding system is considered. In scenarios with vaccination, all breeding females are vaccinated yearly with Bovilis

^{®}before the start of the breeding period. Vaccination is stopped after 6 years and 2 types of protection are tested: against vertical transmission and against infection. (

**A**): BVD impact per breeding female and reward per euro invested per vaccinated animal when assuming a moderate external risk (K

_{ext}= 0.00025); (

**B**): Cumulative BVD impact per breeding female over three years (years 9, 10 and 11) according to the external risk. In all cases, the median over 1000 stochastic repetitions is shown.

**Figure 7.**Sensitivity of BVD impact to variations in epidemiological parameters (±25%), using a complete factorial design. A beef cow-calf herd of the Charolaise breeding system is considered. Parameters are from left to right: mortality of P calves at birth, mortality of all P animals, transmission rates, transition rates between health states other than infection, abortion rate in early pregnancy, other consequences of infection during pregnancy.

Parameters | Charolaise | Limousine | Blonde d’Aquitaine |
---|---|---|---|

Number of cows kept for breeding | 68 | 56 | 53 |

Number of heifers kept for breeding | 22 | 12 | 13 |

Probability of infertility of cows | 0.061 | 0.048 | 0.080 |

Probability of infertility of heifers | 0.039 | 0.026 | 0.058 |

Probability of having twins | 0.023 | 0.004 | 0.022 |

Probability of calf mortality before weaning | 0.08 | 0.05 | 0.07 |

Weaning date | 14 October | 1 October | 29 August |

Breeding period | 22 March–19 July | 4 February–4 June | 19 February–19 July |

Pasture period | 1 April–22 November | 1 April–14 November | 10 April–9 November |

Pasture length | 237 days | 229 days | 215 days |

Sale period of male grassers | 15 November (+/−3 weeks) | 15 November (+/−3 weeks) | |

Sale period of female grassers | 15 June (+/−3 weeks) | ||

Number of heifers sold at breeding | 2 | 0 | 0 |

Scheme | Definition | Value | Reference |
---|---|---|---|

μ_{P,bi} | Probability of mortality at birth of P calves | 0.0667 | [7,23] |

μ_{Ca,bi} | Probability of mortality at birth of non-P calves | 0.02 | |

μ_{P} | Mortality of P animals per day | 0.0019 | [7,23] |

μ_{Ca} | Mortality of non-P calves per day | 0.000326 | |

Ф_{MS} | Transition rate from state M to state S per day | 0.00667 | [24] |

Ф_{TR} | Transition rate from state T to state R per day | 0.2 | [25] |

Ф_{VS} | Transition rate from state V_{2} to state S per day | 1/ Δ_{V2} | |

β^{T} | Transmission rate for T animals | 0.03 | [26,27] |

β^{P} | Transmission rate for P animals | 0.5 | [26,28] |

α_{Ra} | Abortion rate due to infection early pregnancy | 0.8 | [6,25,29] |

α_{Rb} | Abortion rate due to infection mid-pregnancy | 0.2 | [6,30,31] |

η_{P}η _{M} = η_{R} | Probability of giving birth to a calf in state P, M, or R if infection in mid-pregnancy and no abortion | 0.9375 0.03125 | [6,28,30,31,32] |

K_{ext} | External risk of virus introduction during pasture | 0–0.001 |

Scheme | Definition | Bovilis^{®} | Bovela^{®} | Rispoval^{®} | Mucosiffa^{®} |
---|---|---|---|---|---|

ρ_{H/C} | Boolean | 1 if vaccination, 0 otherwise | |||

λ | Probability of protection against infection ^{£} | 0/1 * | 0 | 0 | 0 |

ω | Probability of protection against vertical transmission ^{§} | 1/0 * | 0.985 | 0.9 | 0.9 |

Δ_{V1} | Duration in V_{1} state (weeks) ^{§} | 52 | 52 | 52 | 52 |

Δ_{V2} | Duration in V_{2} state (weeks) ^{£} | 8 | 8 | 8 | 8 |

c_{D} | Dose cost (euro) ^{§} | 4.59 | 5.80 | 4.33 | 5.72 |

n_{1} | Number of vaccine doses for the first shot ^{§} | 2 | 1 | 2 | 1 |

n_{2} | Number of vaccine doses for the second shot ^{§} | 1 | 1 | 1 | 1 |

*****According to the type of protection considered.

^{§}Commercial information (vaccine producers, vet costs, etc.).

^{£}Assumed.

**Table 4.**Weight and price of sold and purchased animals. Parameter values depend on the farming systems, based on data from Inosys Réseaux d’élevage (2014, https://idele.fr/detail-dossier/cas-types-bovins-allaitants (accessed on 4 October 2020)).

Parameters | Charolaise | Limousine | Blonde d’Aquitaine | ||||
---|---|---|---|---|---|---|---|

€ | Kg | € | Kg | € | Kg | ||

Price and weight per animal type | Replacement calf | 352 | 47 | 352 | 42 | 352 | 46 |

Gestating cow | 1689 | 747 | 1621 | 682 | 1828 | 814 | |

Male grasser | 1051 | 420 | 966 | 315 | 915 | 260 | |

Female grasser (sold in fall) | - | - | 793 | 300 | 724 | 240 | |

Female grasser (sold in spring) | 985 | 400 | - | - | - | - | |

Fattened heifer | 1330 | 630 | - | - | - | - | |

Culled cow | 1337 | 700 | 1570 | 691 | 1710 | 798 | |

C_{prod} | Production cost per kg | 0.754 | - | 0.652 | - | 0.775 | - |

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## Share and Cite

**MDPI and ACS Style**

Arnoux, S.; Bidan, F.; Damman, A.; Petit, E.; Assié, S.; Ezanno, P. To Vaccinate or Not: Impact of Bovine Viral Diarrhoea in French Cow-Calf Herds. *Vaccines* **2021**, *9*, 1137.
https://doi.org/10.3390/vaccines9101137

**AMA Style**

Arnoux S, Bidan F, Damman A, Petit E, Assié S, Ezanno P. To Vaccinate or Not: Impact of Bovine Viral Diarrhoea in French Cow-Calf Herds. *Vaccines*. 2021; 9(10):1137.
https://doi.org/10.3390/vaccines9101137

**Chicago/Turabian Style**

Arnoux, Sandie, Fabrice Bidan, Alix Damman, Etienne Petit, Sébastien Assié, and Pauline Ezanno. 2021. "To Vaccinate or Not: Impact of Bovine Viral Diarrhoea in French Cow-Calf Herds" *Vaccines* 9, no. 10: 1137.
https://doi.org/10.3390/vaccines9101137