# Better targeting treatments against Bovine Respiratory Disease by combining dynamic generalized linear models and mechanistic modelling

Carolina Merca, Baptiste Sorin-Dupont, Anders Ringgaard Kristensen, Sébastien Picault, Sébastien Assié, Pauline Ezanno

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Carolina Merca, Baptiste Sorin-Dupont, Anders Ringgaard Kristensen, Sébastien Picault, Sébastien Assié, et al.. Better targeting treatments against Bovine Respiratory Disease by combining dynamic generalized linear models and mechanistic modelling. 2025. hal-04876610

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Distributed under a Creative Commons Attribution 4.0 International License
# Better targeting treatments against Bovine
Respiratory Disease by combining dynamic
generalized linear models and mechanistic
modelling

**Carolina Merca**

cmgm@sund.ku.dk

University of Copenhagen Faculty of Health and Medical Sciences: Kobenhavns Universitet Det Sundhedsvidenskabelige Fakultet https://orcid.org/0000-0001-8598-9564

**Baptiste Sorin-Dupont**

INRAE Pays de la Loire: Institut National de Recherche pour l'Agriculture l'Alimentation et l'Environnement Centre Pays de la Loire

**Anders Ringgaard Kristensen**

University of Copenhagen Faculty of Health and Medical Sciences: Kobenhavns Universitet Det Sundhedsvidenskabelige Fakultet

**Sébastien Picault**

INRAE Pays de la Loire: Institut National de Recherche pour l'Agriculture l'Alimentation et l'Environnement Centre Pays de la Loire

**Sébastien Assié**

INRAE Pays de la Loire: Institut National de Recherche pour l'Agriculture l'Alimentation et l'Environnement Centre Pays de la Loire

**Pauline Ezanno**

INRAE Pays de la Loire: Institut National de Recherche pour l'Agriculture l'Alimentation et l'Environnement Centre Pays de la Loire

## Research Article

**Keywords:** decision support tool, early warnings, state-space models, livestock health, epidemiology

**Posted Date:** October 21st, 2024

**DOI:** https://doi.org/10.21203/rs.3.rs-5188273/v1

**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License.
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1 Better targeting treatments against Bovine Respiratory Disease by combining

2 dynamic generalized linear models and mechanistic modelling

3 Carolina Merca¹\*,²\*, Baptiste Sorin-Dupont²\*,³\*, Anders Ringgaard Kristensen¹, Sébastien

4 Picault², Sébastien Assié², Pauline Ezanno²

5 ¹Department of Veterinary and Animal Sciences, Faculty of Health and Medical Sciences, University

6 of Copenhagen, Grønnegårdsvej 2, Frederiksberg C 1870, Denmark.

7 ²Oniris, INRAE, BIOEPAR, 44300, Nantes, France.

8

9 * Corresponding authors

10 E-mail: cmgm@sund.ku.dk (CM)

11 E-mail: baptiste.sorin@inrae.fr (BS)

12 ¶ These authors contributed equally to this work and share first authorship.

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14 Keywords: decision support tool, early warnings, state-space models, livestock health, epidemiology
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# 1 Abstract

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Bovine Respiratory Disease (BRD) is a major health challenge for young bulls. To minimize economic losses, collective treatments have been widely adopted. Nevertheless, performing collective treatments involve a trade-off between BRD cumulative incidence and severity, and antimicrobial usage (AMU).

Therefore, we propose a proof of concept of a decision support tool aimed at helping farmers and veterinarians make informed decisions about the appropriate timing for performing collective treatment for BRD. The proposed framework integrates a mechanistic stochastic simulation engine for modelling the spread of a BRD pathogen (Mannheimia haemolytica), and a hierarchical multivariate binomial dynamic generalized linear model (DGLM) which provides early warnings based on infection risk estimates. Using synthetic data, we studied 48 scenarios, involving two batch sizes (small and large), four farm risk levels of developing BRD (low, medium, balanced, and high), two batch allocation systems (sorted by risk level or randomly allocated), and three treatment interventions (individual, conventional collective, and DGLM-based collective). In most scenarios, collective treatments triggered by the DGLM were associated with a reduction of BRD cumulative incidence and disease severity. DGLM-based collective treatments typically exhibited either lower or equivalent AMU compared to conventional ones, being particularly advantageous in medium, balanced, and high-risk scenarios. Additionally, DGLM estimates of infection risk aligned well with empirical risks during the first time steps of the simulation. These findings highlight the potential of the proposed decision support tool in providing valuable guidance for improving animal welfare and AMU. Further validation through real-world data collected from on-farm situations is necessary.

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# 2 Introduction

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Bovine Respiratory Disease (BRD) is a prevalent and complex respiratory condition that affects cattle, particularly calves and feedlot cattle. The disease is characterized by inflammation of the upper and lower respiratory tracts, leading to coughing, nasal discharge, rapid breathing, fever, depression, and reduced appetite. It is caused by a combination of viral (e.g. the Bovine Respiratory Syncytial Virus)
and bacterial pathogens (e.g. *Mannheimia haemolytica*). BRD can be triggered by various stressors that the animals are commonly exposed to, such as transportation, commingling, adverse weather conditions, or poor ventilation [1]. BRD leads to reduced feed efficiency, growth rates, and overall productivity, resulting in substantial financial losses for producers [2, 3]. Additionally, the clinical signs linked to the disease cause significant suffering in affected animals. The prevention and management of BRD are crucial for maintaining animal health, welfare, and sustainable livestock production.

The use of antimicrobials (AMU) is the main strategy employed worldwide to control BRD in the cattle industry [4]. Animals can be treated individually upon appraisal of clinical signs, but collective treatments are also a common practice. The latter is a metaphylactic approach that consists in administering a dose of antimicrobial to an entire group of animals, while only part of the group is diagnosed with the disease, to prevent additional cases [5]. The relevant threshold for such a collective intervention is however still largely questioned [6].

The concerns raised by antimicrobial resistance motivate the need for responsible treatment strategies. Indeed, a trade-off exists between BRD occurrence and the use of antimicrobials. On one hand, curative and metaphylactic treatments can participate in reducing the occurrence of respiratory diseases [4, 7]. On the other hand, an overuse of antimicrobials promotes the positive selection of resistant bacterial strands, which can lead to their proliferation and the loss of efficacy of treatments [8], in animals but also in humans. This trade-off highlights the need for targeted collective treatments and/or better usage of vaccination. Veterinarians and animal scientists also highlight the need to implement early warning systems and preventive measures [9].

State-space models have emerged as a promising approach for obtaining early warnings in the context of animal production health [10, 11]. These models utilize a Bayesian framework to generate their estimates, incorporating both observed data and any prior knowledge that may be available prior to a given observation [12]. One key advantage of these models is their capacity to estimate the true state of an unobservable variable at each point in time [13]. These specifications make state-space models a valuable tool for monitoring animal production, allowing the detection of potential issues early on.
Coupling state-space models with mechanistic modelling could allow to assess the impact of the early warnings on the system. Mechanistic modelling is often used to simulate complex infection dynamics, to comprehend and anticipate them. Such models can thus produce synthetic data as well as compare scenarios and rank interventions [14].

In the case of BRD, only two mechanistic models ranking treatment practices at batch level have been published [15, 16]. The first one simulates the circulation of an average pathogen in conditions mimicking contrasted farming contexts such as small versus large batches (considered as isolated from other batches). The authors concluded on a bigger BRD circulation in large batches composed of high-risk individuals, which could benefit the most from collective treatments. The second model compares the impact of farm management practices on the spread of three causal pathogens of BRD in multi-batch farms featuring several individual risk levels of contracting BRD. This study highlighted the need for prior knowledge on the individual risk of the animals to contract BRD, as grouping animals together in batches in accordance with their individual risk level of developing BRD participates in limiting the spread of the most contagious pathogens. While mechanistic approaches are relevant for assessing early warning tools added-value to make early and informed on-farm interventions, to the best of our knowledge, no coupling between such mechanistic models and automated early warning system has been studied in animal health so far.

Our objective was to make the proof of concept that a decision support tool combining automated early warnings and a mechanistic epidemiological model enables identifying when triggering collective treatments are relevant for BRD and when individual treatments should be preferred to limit both AMU and BRD cases. Comparing contrasted situations, we evaluated the tool effectiveness in reducing the number of BRD cases, the duration in severe clinical signs and AMU. To that end, we used a pipeline that combines a mechanistic stochastic simulation engine modelling the spread of a BRD pathogen (M. haemolytica) and a hierarchical multivariate binomial dynamic generalized linear model, a type of state-space model, applied to synthetic data. This tool enables proactive decision-making, by initiating timely collective treatment interventions, to minimize the spread and severity of the disease. By leveraging
collective treatment strategies based on these early warnings, this system may have the potential to enhance the efficiency and effectiveness of BRD control programs.

## 3 Materials and methods

### 3.1 Processes and assumptions of the mechanistic model

We proposed to build our proof of concept on a pipeline modelling the spread of *M. haemolytica*. This pathogen is commonly reported in BRD outbreaks. Furthermore, the dynamics of a *M. haemolytica* outbreak have already been modelled and bear the advantage of displaying a limited stochasticity and a repeatable behaviour [15].

The mechanistic part of the modelling pipeline was developed using the EMULSION framework [17]. This framework uses a Python simulation engine on models written as structured text files. The model was structured into processes described as finite state machines to describe states and transitions. This framework also allows the user to implement code add-ons written in Python to pilot events with outputs coming from outside of the model (e.g. data input).

We extended a previously existing model [15]. The model was written in discrete time with time steps of half a day. It simulated the first 40 days of fattening, i.e., the most at-risk period of BRD occurrence on fattening farms. As an individual-based model, it featured the individual risk status defining the individual risk level of being infected and of shedding respiratory pathogens. This qualitative information (low, medium, or high) summarized the level of stressors encountered by the individual prior to its arrival at the farm [18, 19]. The higher the risk, the higher the infection rate and the more likely the animals were to shed pathogens if infected. The model monitored five processes: hyperthermia (either unspecific or due to BRD), health status (susceptible, infected, resistant), clinical signs (asymptomatic, or with mild or severe clinical signs), detection (detected or not), and treatment (treated or not). Hereafter, we detail how treatments were triggered in this new version of the model. Details on other (unchanged) processes and transitions can be found in the first section of the Supporting Information.
As in the previous model, any detected animal could be individually treated with antibiotics. A treatment dose had a success probability $pT$. In case of treatment failure, the treatment could be repeated up to a maximum number of doses per animal ($maxT$). After the treatment period, the animals could transition back from treated to not treated, even if still exhibiting clinical signs after $maxT$ treatments.

In addition to individual treatment upon detection, collective treatments were included in new the model. Two criteria for collective treatments were implemented. First, a conventional collective treatment could be performed once the cumulative number of detected animals reached a fixed threshold. In European fattening operations, a threshold around 10% of the batch size is commonly used, although this value is not backed up by dedicated field or experimental observations [20]. Second, a collective treatment could also be triggered by automated alarms generated by the dynamic generalized linear model connected to the mechanistic model, as described in section 3.4.

## 3.2 Scenarios

The analysis was conducted on 48 simulated scenarios. These scenarios were based on a combination of two batch sizes, two types of batch allocation systems, four farm risk levels of BRD, and three treatment interventions.

### 3.2.1 Batch sizes

We considered two possible batch sizes: small batches of 20 animals and large batches of 100 animals (both cases entailed 10 batches in total). We intended to assess whether the proposed tool is effective for varying batch sizes, as there is considerable heterogeneity in batch sizes across the globe [21, 22].

### 3.2.2 Batch allocation systems

We investigated two types of batch allocation systems (sorted by individual risk level and randomly allocated). In Random scenarios, the animals were randomly distributed among batches, thus all batches
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differed in composition. In the Sorted scenarios, we considered that the farmer has access to prior risk
level information and allocates animals into batches accordingly, grouping those of similar risk.

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### 3.2.3 Risk levels of BRD

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Four scenarios on farm risk level proportions were assessed: Low, Medium, Balanced, and High. This categorization allowed testing contrasted scenarios reflective of real situations.

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The scenarios were defined at farm scale by the proportions of animals in the farm belonging to one of the three possible individual BRD risk levels (low, medium and high). Table 1 shows the proportions used in each of the four risk level scenarios.

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For the Sorted scenarios, the animals were grouped into batches according to their individual risk level.

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Therefore, the same proportions were used but at batch scale. For instance, in the Low-risk level scenario, 90% of the 10 batches were composed exclusively by low-risk animals and 10% of the batches were exclusively composed of medium-risk animals.

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### 3.2.4 Treatment interventions

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We tested three treatment interventions: individual treatment of the detected animals, conventional collective treatment, and collective treatment triggered by early warnings (proposed tool). The conventional collective treatment consists of using a threshold of 10% of the batch size. For the collective treatments triggered by early warnings, several thresholds were tested (further explained in the Supporting Information) and the best one was shown to be 0.05. This means that when the estimated risk of infection was higher than 0.05, an alarm was triggered and a collective treatment initiated.

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## 3.3 Hierarchical multivariate binomial dynamic generalized linear model

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Dynamic generalized linear models (DGLMs) represent a specific type of state-space models employed when monitoring non-normally distributed observations. The primary objective of a DGLM is to

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estimate an underlying parameter vector (θ) from observed data, while considering the prior knowledge available before any observations are made [12].

It is not possible for farmers and veterinarians to accurately determine the true number of infected animals due to the existence of subclinical cases and the not perfectly reliable diagnostic tests. Therefore, we used a DGLM to estimate the true risk of infected animals with BRD and alert the farmer/veterinarian when the estimated risk of infection exceeds a predefined threshold, acting as an early warning system.

Risk is here defined as the probability of an arbitrary animal at risk being infected with BRD. To estimate the true underlying risk of BRD infection, we used four variables which can be observable by the farmers/veterinarians per batch (j) and at each time step (t). Those variables were the number of animals considered by the farmer as infected, here called detected (D); the number of hyperthermic animals (H); the number of animals with mild clinical signs (M); and the number of animals with severe clinical signs (C). As multiple variables were considered simultaneously in the model, it is called a multivariate DGLM. Those variables were monitored as risks, such as:

$$R_{Xjt} = \frac{y_{Xjt}}{N_{Xjt}},$$

being $R_{Xjt}$ a naive estimate for the risk of state $X \in \{D, H, M, C\}$ in batch $j$ at time step $t$, $y_{Xjt}$ the number of new cases, and $N_{Xjt}$ the population at risk.

The observations $y_{Xjt}$ of each state and batch at time $t$ were binomially distributed with probability $p_{Xjt}$ and number of trials $N_{Xjt}$ since they had two possible outcomes, such as being detected or not detected, hyperthermic or not hyperthermic, etc., making it a binomial DGLM. It is natural to model the risk on a logistic scale:

$$\eta_{Xjt} = \log\left(\frac{p_{Xjt}}{1-p_{Xjt}}\right),$$
where $\eta_{Xjt}$ corresponds to the logistic transformation of the risk for each state, batch and time step. In turn, the risk was equal to $(\exp(-\eta_{Xjt}) + 1)^{-1}$.

A DGLM consists of an observation equation and a system equation. These equations work synergistically to capture the underlying dynamics and relate them to observable measurements.

### 3.3.1 Observation equation

The risks of being detected, hyperthermic, having mild and severe clinical signs in each batch on logistic scale ($\eta_{Xjt}$) were defined as:

$$ \eta_{Xjt} = \mu_{1t} + \delta_{jt} + \beta_{X}, $$

where $\mu_{1t}$ is the true risk of infection for batch 1 at time t, $\delta_{jt}$ is the deviation between the true risk for batch j and batch 1 (accordingly, $\delta_{1t} = 0$ by definition), and $\beta_X$ is an observation bias for state X reflecting that the observations of detections, hyperthermia and clinical signs (mild and severe) were indirect observations of the true infection state. Thus, they were assumed to be biased.

At each time step, four observation pairs $(y_{Djt}, N_{Djt})$, $(y_{Hjt}, N_{Hjt})$, $(y_{Mjt}, N_{Mjt})$, $(y_{Cjt}, N_{Cjt})$ were done for each of $J = 10$ batches. Then, we defined

$$ \eta_t = (\eta_{D1t}, \eta_{H1t}, \eta_{M1t}, \eta_{C1t}, \eta_{D2t}, \eta_{H2t}, \eta_{M2t}, \eta_{C2t}, \dots, \eta_{Djt}, \eta_{Hjt}, \eta_{Mjt}, \eta_{Cjt})' $$

as a vector of logistically transformed binomial probability parameters that depend on an underlying parameter vector ($\theta_t$) as described by the following observation equation:

$$ \eta_t = F'_t \theta_t $$

where $\theta_t = (\mu_{1t}, \delta_{2t}, \delta_{3t}, \delta_{4t}, \delta_{5t}, \delta_{6t}, \delta_{7t}, \delta_{8t}, \delta_{9t}, \delta_{jt}, \beta_D, \beta_H, \beta_M, \beta_C)'$ and $F'_t$ is a design matrix linking the parameter vector to the transformed binomial probabilities. This matrix represents how the risks of infection in each batch were related to the risk of each of the four states and their respective
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biases, at each time step. The number of rows in $F_t'$ corresponds to the four states in each batch (4 × 10)

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and the number of columns corresponds to the size of $\theta_t$, thus it is a 40 × 14 matrix:

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$$F_t' = \begin{bmatrix} 1 & \cdots & 0 & \cdots & 0 & 1 & 0 & 0 & 0 \\ 1 & \cdots & 0 & \cdots & 0 & 0 & 1 & 0 & 0 \\ 1 & \cdots & 0 & \cdots & 0 & 0 & 0 & 1 & 0 \\ 1 & \cdots & 0 & \cdots & 0 & 0 & 0 & 0 & 1 \\ \vdots & \ddots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots \\ 1 & \cdots & 1 & \cdots & 0 & 1 & 0 & 0 & 0 \\ 1 & \cdots & 1 & \cdots & 0 & 0 & 1 & 0 & 0 \\ 1 & \cdots & 1 & \cdots & 0 & 0 & 0 & 1 & 0 \\ \vdots & \ddots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots \\ 1 & \cdots & 0 & \cdots & 1 & 1 & 0 & 0 & 0 \\ 1 & \cdots & 0 & \cdots & 1 & 0 & 1 & 0 & 0 \\ 1 & \cdots & 0 & \cdots & 1 & 0 & 0 & 1 & 0 \\ 1 & \cdots & 0 & \cdots & 1 & 0 & 0 & 0 & 1 \end{bmatrix}$$

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where the first column corresponds to the risk of infection of batch 1; the second column corresponds to the risk of infection of batch j; the third column corresponds to the risk of infection of batch 10; and columns 4 to 7 correspond to the biases of each of the four states D, H, M and C (in this order). The first four rows represent the risk of infection of D, H, M and C (in this order) for batch 1; rows 5 to 8 correspond to the risk of infection of D, H, M and C for batch j; and rows 9 to 12 correspond to the risk of infection of D, H, M and C for batch 10. Our approach consisted of using batch 1 as the reference, meaning that all the remaining batches had their risks presented as deviations from batch 1, thereby creating a hierarchical DGLM.

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### 3.3.2 System equation

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The system equation expresses the evolution of the parameter vector over time. The general form of the system equation is:

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$$\theta_t = G_t \theta_{t-1} + w_t, \quad w_t \sim [0, W_t],$$

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where $G_t$ stands for system matrix. Since no patterns or trends were expected, $G_t$ was assumed to be equal to the identity matrix. The notation $w_t \sim [0, W_t]$ means that $w_t$ (random error) has zero mean (0
is a vector of zeros) and a known variance-covariance matrix $W_t$, which describes how much the risks of infection of each batch and the biases of each state were likely to randomly change over time. The systematic variance-covariance matrix was assumed constant, so that $W_t = W$, and its dimensions correspond to the size of $\theta_t$, being a 14 × 14 matrix.

We created two structured $W$ matrices. For the scenarios where the animals were randomly allocated into batches (Random scheme), we created a specific variance-covariance matrix ($W_R$), where we used one parameter considering the herd level variance ($\sigma_h^2$) and another parameter for the batch level variance ($\sigma_b^2$):

$$ W_R = \begin{bmatrix} \sigma_h^2 + \sigma_b^2 & \cdots & \sigma_h^2 & \cdots & \sigma_h^2 & 0 & 0 & 0 & 0 \\ \vdots & \ddots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \sigma_h^2 & \cdots & \sigma_h^2 + \sigma_b^2 & \cdots & \sigma_h^2 & 0 & 0 & 0 & 0 \\ \vdots & \ddots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \sigma_h^2 & \cdots & \sigma_h^2 & \cdots & \sigma_h^2 + \sigma_b^2 & 0 & 0 & 0 & 0 \\ 0 & \cdots & 0 & \cdots & 0 & 0 & 0 & 0 & 0 \\ 0 & \cdots & 0 & \cdots & 0 & 0 & 0 & 0 & 0 \\ 0 & \cdots & 0 & \cdots & 0 & 0 & 0 & 0 & 0 \\ 0 & \cdots & 0 & \cdots & 0 & 0 & 0 & 0 & 0 \end{bmatrix} $$

so that the variances and covariances of the risks of infection of all batches changed according to $\sigma_h^2$, since they all belonged to the same herd. For the variances, we added the batch effect $\sigma_b^2$. The values for the biases were set as 0 because the biases were not expected to change over time.

For the scenarios where the animals were sorted into batches by risk level (Sorted scheme), we used a different variance-covariance matrix ($W_S$). It consisted of the same structure as $W_R$ with one extra parameter considering the risk level ($\sigma_r^2$). We added $\sigma_r^2$ to the variances of the risks of infection of all batches and to the covariances of the batches with the same risk level. If we consider that the batches represented in columns 1 and 2 have the same risk level (and different from the batch represented by column 3), their covariances also changed according to $\sigma_r^2$:
$$239 \quad W_S = \begin{bmatrix} \sigma_h^2 + \sigma_b^2 + \sigma_r^2 & \dots & \sigma_h^2 + \sigma_r^2 & \dots & \sigma_h^2 & 0 & 0 & 0 & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \sigma_h^2 + \sigma_r^2 & \dots & \sigma_h^2 + \sigma_b^2 + \sigma_r^2 & \dots & \sigma_h^2 & 0 & 0 & 0 & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \sigma_h^2 & \dots & \sigma_h^2 & \dots & \sigma_h^2 + \sigma_b^2 + \sigma_r^2 & 0 & 0 & 0 & 0 \\ 0 & \dots & 0 & \dots & 0 & 0 & 0 & 0 & 0 \\ 0 & \dots & 0 & \dots & 0 & 0 & 0 & 0 & 0 \\ 0 & \dots & 0 & \dots & 0 & 0 & 0 & 0 & 0 \\ 0 & \dots & 0 & \dots & 0 & 0 & 0 & 0 & 0 \end{bmatrix}$$

240 The values for the biases were also set as 0.

241 The parameters used for $W_R$ ($\sigma_h^2$ and $\sigma_b^2$) and for $W_S$ ($\sigma_h^2$, $\sigma_b^2$ and $\sigma_r^2$) were estimated by numerical optimization as the values that minimized the Root Mean Square Error (RMSE) of the forecast errors.
242 Two learning sets with a Balanced risk level were used for this purpose, one with a Random scheme and the other with a Sorted scheme. The built-in function *optim* in R [23] was used for the estimation with the optimization algorithm specified as Nelder-Mead. The estimated parameters used in this study can be found in the Supporting Information.
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### 247 3.3.3 Initialization

248 In order to fully specify the DGLM, we need to provide the matrices $F_t$, $G_t$, $W_R$ and $W_S$ along with the initial distribution of $(\theta_0|D_0) \sim N(m_0, C_0)$. The initial belief at time 0 is represented by $D_0$, which consists of an initial mean ($m_0$) with the same dimension as $\theta_t$, and a variance-covariance matrix ($C_0$) which had a 14 x 14 structure.
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252 Both initial $m_0$ and $C_0$ were first arbitrarily defined. For the initial $m_0$, the risks of infection of all batches were defined as the logistic transformation of 0.01 (the risks of infection of batches 2 to 10 were given as deviations from batch 1) and as 0 for the biases, thus $m_0 = (-4.56, 0, ..., 0)$. For the initial $C_0$, we set the variances for the risks of infection of all batches as 4 and for the biases equal to 8.
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Some adjustments were made to the smoothed $m_0$ and $C_0$ for the Medium, Balanced, and High-risk scenarios since they were created with a low-risk level dataset. In the Random scheme, the herd risk level was known, but the allocation of animals into batches was randomly done. Therefore, for the initialization process, we considered that all the batches had the same risk level (equal to the herd risk level). On the other hand, for the Sorted scheme, the risk level of each batch was known. Therefore, each batch was addressed according to its risk of infection. In both cases, the risks of infection in $m_0$ and the variances and covariances for the risks of infection in $C_0$ were increased for the batches that were defined as having Medium or Balanced-risk, and even further on the High-risk batches. The magnitude of those increases and the methodology employed can be found in the Supporting Information.

The biases in $m_0$ and $C_0$ were kept the same as those given by the smoothed $m_0$ and $C_0$ as we did not expect them to change between scenarios, since they were farmer dependent. However, the covariances in $C_0$ between the biases and the risks of infection of the Medium, Balanced, and High-risk batches had to be adjusted. Refer to Supporting Information for further explanation.

### 3.3.4 Sequential update

The theoretical foundation of a univariate binomial DGLM is well-established in the literature [12]. However, for our specific study, it became necessary to extend this framework to a multivariate binomial DGLM. Therefore, to update the model at each time step, a Taylor expansion of the probability density function of $y_t$ given $\eta_t$ was employed as described in Appendix A of Bono et al. [13].

In some cases, the rank of $F_t'$ was less than the number of rows. This led to the formation of a singular variance-covariance matrix, which cannot be inverted, and thus the sequential update was not possible. In such cases, a stepwise updating technique was employed also as described in Appendix A of Bono et al. [13].
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## 3.4 Global Pipeline workflow

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The next step consisted of connecting the mechanistic model with the DGLM. The global pipeline
workflow is presented in Figure 1. The interface between the mechanistic model and the DGLM was
established in Python. At each time step, the EMULSION state-machines (1) created synthetic data for
the specific time step and saved it in a CSV file (2). The data was sent to a Python script (3) which
called the execution of the DGLM (4). In the R script, the DGLM analyzed the data and estimated the
risk of infection for each batch. If the estimated risk of infection exceeded the chosen threshold (0.05;
see Supporting Information for the explanation about the selection of the best threshold), the DGLM
triggered an alarm. Subsequently, the R script wrote a CSV file containing booleans determining if an
alarm was triggered by the DGLM in any batch (5). The Python add-on retrieved these booleans (6) and
sent that information back to EMULSION state-machines (7). If the decision was yes in one or several
batches, EMULSION triggered a collective treatment for these specific batches. The pipeline continued
to work as explained above for all the time steps. A collective treatment was carried out at most once
in each batch.

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## 3.5 Outputs

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For each scenario, 200 stochastic replicates were performed. Each stochastic replicate simulated the first 40 days after entering a fattening farm featuring 10 batches. The following outputs were compared across scenarios:

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* **Cumulative incidence:** For each stochastic replicate of each scenario, we summed the number of new cases over the course of the simulation. We then computed the median of this quantity.

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* **Average time in severe clinical signs:** For each stochastic replicate of each scenario, we summed the time spent by each animal in the state of severe clinical signs. We divided this by the cumulative incidence to get the average time spent with severe clinical signs per affected animal. We then computed the median of this quantity.
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*   **Antimicrobial usage (AMU):** The number of doses used in each stochastic replicate of each scenario was counted and divided by the population size. The median of this quantity was computed.

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*   **Risks of infection:** The estimated risk of infection by the DGLM was recorded for each stochastic replicate of each scenario where the collective treatments were based on early warnings. The empirical risk of infection at time $t$ was also computed, as the ratio between the true number of newly infected individuals at time $t$ ($I_t - I_{t-1}$) over the number of individuals at risk of being infected at $t-1$. The individuals at risk consisted of susceptible animals ($S$) and asymptomatic carriers ($E$). This translated to $Q_t = \frac{I_t - I_{t-1}}{S_{t-1} + E_{t-1}}$. For the Random scenarios, the 95% confidence interval (CI) and the median of these two quantities were computed according to the scenarios. For the Sorted scenarios, the 95% CI and the median of these two quantities were computed by batch category (i.e., batches composed only of low, medium, and high-risks).

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# 4 Results

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## 4.1 Cumulative incidence

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Collective treatments triggered by the early warnings yielded lower median cumulative incidence when compared to the conventional collective treatment in all cases, except for the Balanced-risk scenarios with small batches (Figure 2). This treatment strategy performed especially well in the High-risk scenarios and with larger batches. Moreover, sorting batches seemed to further reduce the incidence

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## 4.2 Average time in severe clinical signs

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DGLM-based collective treatments yielded lower median average time in severe clinical signs than their conventional counterparts in the Medium and High-risk scenarios (Figure 3: 2^nd^ and 4^th^ columns). Moreover, sorting batches seemed to further reduce the severity in Medium-risk scenarios. In the Balanced-risk scenarios, conventional collective treatments strategies displayed slightly lower durations in severe clinical signs, except for larger sorted batches. In the Low-risk scenario, there was no clear difference in severe clinical signs durations between the three treatment strategies, except in
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the small sorted batches, where the scenario with collective treatment based on DGLM yielded the lowest severe clinical signs duration.

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## 4.3 AMU

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The collective treatment strategy based on early warnings was associated with lower AMU than the other two strategies in High-risk scenarios, especially in large batches (Figure 4). In Balanced and Medium-risk scenarios, DGLM-based collective treatments yielded lower or equal AMU than the conventional collective treatment, except for the large sorted Balanced-risk scenario where the collective treatments based on early warnings had a slightly higher AMU. Moreover, in Low-risk scenarios with larger batches, AMU was the highest for collective treatment triggered by early warnings. In the Low, Medium and Balanced-risk scenarios, both collective treatment strategies were associated with higher AMU than individual treatments.

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We observed that the density of the AMU distributions could display local maxima (Figure 4). In the Medium-risk scenarios, we could observe up to 3 local maxima at regular intervals on the x-axis on the density plots. For the Low-risk scenarios, the density appeared to be spread wider, with peaks less clear.

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## 4.4 Risks of infection

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Among scenarios where animals were randomly allocated to batches, scenarios with larger batches had a better overlap between the estimated and the empirical risks of infection (Figure 5). The scenarios with a majority of low-risk animals had the poorest overlap. On the other hand, the best overlap was found in the Medium and High-risk scenarios. The overlaps between the distributions were generally the best during the first time steps of the simulation. Overall, there was a consistent overestimation of the estimated risk of infection.

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In the sorted scenarios, the estimated risk of infection had the best overlap with the empirical one in batches featuring high-risk animals, especially in larger batches (Figure 6). Conversely, batches featuring only low-risk individuals had the poorest overlap. Similarly to the Random scenarios, the

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overlaps were the best along the first time steps of simulation. An overestimation of the risks of infection
was also observed.

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# 5 Discussion

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As a proof of concept, we showed here that a decision support tool combining automated early warnings
and a mechanistic epidemiological BRD model in a multi-batch cattle fattening farm helps better
triggering collective treatments to both limit AMU and BRD cases, as well as identifying situations
where individual treatments should be preferred over collective ones. We compared 48 scenarios in
terms of cumulative incidence, average time spent with severe clinical signs, and AMU. The risk of
infection estimated by the DGLM was also compared with its empirical value. Our findings suggested
that collective treatments triggered by early warnings were associated with a reduction in the cumulative
incidence of BRD cases in most cases, particularly in High-risk scenarios. In Medium and High-risk
scenarios, this treatment strategy was also associated with reduced severity of the disease for infected
animals. Additionally, collective treatments triggered by early warnings had overall lower or equal
AMU than conventional collective treatments. A clear exception were the Low-risk scenarios in larger
batches, where individual treatments should be preferred. The use of DGLM-based collective treatments
was found to be an advantage in Medium, Balanced, and High-risk scenarios. Moreover, the DGLM
correctly estimated the risk of infection in the first time steps of the simulation, emphasizing its
capability to adequately predict the risks of infection in batches using data on clinical signs.
Nevertheless, the DGLM consistently overestimated the risk afterwards, without necessarily affecting
the outputs. Our findings illustrated the potential of this tool in enabling the timely implementation of
collective treatment interventions, providing valuable guidance in improving animal welfare and AMU.

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We showed that DGLM-based collective treatment could efficiently reduce the incidence of a bacterial
respiratory disease in population with high individual risk of BRD. This reduction is especially
important in larger batches. This finding is consistent with a previous simulation study that found that
larger High-risk batches tended to benefit more from collective treatments [16], but in which such
treatments were triggered using the conventional approach. The American system often implements

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prophylactic treatments of at-risk cattle at feedlot entry [24]. In our study, a metaphylactic treatment strategy based on early warnings was associated with a reduction in the cumulative incidence of BRD cases in large batches, which are similar to the Anglo-Saxon farming context. Such results were acquired without preventive treatment upon arrival. Future studies could compare the performances of collective treatment strategies based on early warnings and preventive treatment upon arrival.

Our study also demonstrated that the average time in severe clinical signs was reduced by the implementation of DGLM-based collective treatments in herds mainly composed of high and medium-risk individuals. This reduction could be due to a shorter delay between the onset of clinical signs and the treatment, which assessed the timely response of the collective treatment based on early warnings. Reducing the duration of severe clinical signs is crucial for animal welfare. Furthermore, clinical signs are associated with reduced daily weight gain, which causes economical losses to the farmers [25]. Thus, the timely response generated by early warnings could have beneficial welfare and economical impacts on the field.

Our simulations showcased the trade-off between antimicrobial consumption and the reduction of BRD incidence and severity. While the benefit of performing collective treatments for High-risk scenarios is clear in this study, in the remaining scenarios collective treatments successfully reduced the incidence and severity, but they were associated with a larger AMU than the baseline individual treatment. This compromise is advantageous in Medium and Balanced-risk scenarios, where the reduction in incidence is substantial. While this trade-off was already showcased in Picault et al. [16], our study showed that DGLM-based collective treatments bore the advantage of reducing the AMU, incidence and severity when compared to conventional collective treatments, leading to a more advantageous trade-off.

Our results showed that the individual risk level proportions strongly influence the performance of the treatment strategies. Indeed, collective treatment strategies were globally relevant for incidence and severity reduction in Medium, Balanced, and High-risk scenarios, but they did not present an advantage in Low-risk situations. This suggests that characterizing the overall stress and risk of respiratory diseases could be highly beneficial and help the decision-making regarding treatment strategies. The
preconditionning programs put in place in US farming systems, frequently characterize the animal risk levels, in order to process high-risk cattle separately or to perform prophylactic treatment upon arrival. These programs have been studied in Europe, but it is suggested that the sector should rather focus on beef sector reorganisation and on other husbandry practices, as the results of preconditionning programs were inconclusive [26].

Sorting the animals according to their risk level into batches further enhanced the benefits of DGLM-mediated response. As shown in Sorin-Dupont et al. [15], such batch allocations usually perform well in reducing the circulation of bovine respiratory pathogens. In our study, it further reduced the disease occurrence in all situations, and disease severity in Medium-risk scenarios when DGLM-based collective treatment were implemented. This suggests that combining DGLM with transparent information on stress and husbandry practices would allow better farm management and the implementation of suitable treatment strategies.

In some scenarios with collective treatment, we observed local maxima in the density function of the AMU across the replicates. This could be due to collective treatments being triggered on batch level. Therefore, each local maximum could correspond to a given number of batches having triggered collective treatment in a particular scenario. We noticed the absence of local maximum for the High-risk scenario, suggesting that collective treatments were probably triggered in every batch. The difference observed in terms of cumulative incidence and average time in severe clinical signs could thus have been due to the earliness of the response. Therefore, these results indicated that the DGLM-mediated response was more timely than the conventional.

We estimated the risk of infection of each batch at each time step based on information about the clinical signs and the number of animals that were detected as infected. Then, the estimated risks of infection were compared with the true risks of infection (empirical) used by EMULSION to generate the synthetic data. The differences between the estimated risks of being infected and the empirical ones were typically small during the first time steps of the simulation. However, the differences increase after the peaks of risks of infection. This suggests that the DGLM correctly anticipates the peak of the risk of being
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infected, but the estimated risk does not decay as fast as the empirical risk. This led to an overestimation.

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On an operational point of view, this did not affect the outputs in scenarios with higher risk as the alarms
were triggered in a timely manner. The subsequent overestimation by the DGLM had no impact
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afterwards as collective treatments could only be triggered once. This overestimation did however lead
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to higher AMU in Low-risk scenarios, as it sometimes triggered unnecessary collective treatments. Such
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a situation could be avoided by using a less sensitive threshold on low-risk batches, provided that the
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information on individual risk level is available.
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The novel tool combined mechanistic modelling with automated early warnings based on the DGLM
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estimated risk of infection. To the best of our knowledge, no other combinations of those two modelling
techniques exist in animal health. Using the mechanistic modelling allowed us to generate synthetic
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data for various scenarios, which we then used to test the relevance of the response by the early
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warnings. We also used it to trigger different treatment interventions and evaluate them in terms of
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cumulative incidence, disease severity and antimicrobial usage. An interesting perspective is to adapt
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this tool to run on observed on-farm data in real-time, so that farmers and veterinarians could make
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more informed treatment decisions, with customized guidance on how to manage BRD cases. Indeed,
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the DGLM part of the tool could trigger an alarm based on these real data and provide an estimate of
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the risk of infection of each batch of the farm at the time of the alarm. This information being provided
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to the EMULSION BRD model, the tool could eventually forecast what may happen if the veterinarian
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decides to perform a collective treatment in response to the alarm, and compare it to what may occur if
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the conventional threshold for collective treatment is used, or if only individual treatments are
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performed. Within the tool, farmers can input the number of animals per batch and the number of
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batches in their farm, since the proposed tool can work with different values than the ones used in this
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study.
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This study provides a basis for building a broad decision-making tool for ranking treatment strategies
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regarding BRD. Future work would also include other respiratory pathogens and co-circulation of
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different pathogens, as well as other livestock species.

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458 **6 Conclusion**

459 This study successfully demonstrated the potential of integrating mechanistic epidemiological
460 modelling with an automated early warning system to optimize decision-making regarding collective
461 treatments for BRD. By simulating various scenarios using synthetic data, we found that collective
462 treatments triggered by the early warnings provided the best overall outcome for Medium, Balanced,
463 and High-risk scenarios. In Low-risk scenarios, individual treatments performed better, suggesting the
464 need for tailored strategies based on BRD risk levels. The importance of this study lies in its innovative
465 approach, combining two modelling techniques to create a novel decision support tool. This tool has
466 the potential to improve animal welfare by reducing both BRD cases and duration of severe clinical
467 signs, while also addressing the critical issue of antimicrobial resistance through reducing antimicrobial
468 usage. Further validation with real-world, on-farm data is necessary. If implemented in real-time this
469 tool could offer veterinarians and farmers more informed and customized guidance on managing BRD
470 cases.

471 **7 Declarations**

472 **7.1 Ethics approval and consent to participate**

473 Not applicable.

474 **7.2 Consent for publication**

475 Not applicable.

476 **7.3 Availability of data and materials**

477 Access to the codes utilized in developing the models detailed in this study is publicly available at
478 https://doi.org/10.5281/zenodo.13842980.
479

**7.4 Competing interests**

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The authors declare that they have no competing interests.

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**7.5 Funding**

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This work has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 101000494 (DECIDE) and from the French region Pays de Loire.

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This document reflects only the author's view and the Research Executive Agency (REA) and the
European Commission cannot be held responsible for any use that may be made of the information it
contains.

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**7.6 Authors' contributions**

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CM and BS participated in the study conception, carried out the models programming, conducted the analysis of the tool, and drafted the manuscript. ARK, SP, and PE participated in the study conception, assisted with programming the models, and contributed to improving the manuscript. SA contributed to the study conception and improved the manuscript. All authors have read and approved the final manuscript.

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**7.7 Acknowledgements**

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We thank our colleagues from the BIOEPAR Dynamo for their comments and advice on this work. We are most grateful to the INRAE MIGALE bioinformatics facility [27] for the use of their computing resources.

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**8 Figures, titles and legends**

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**Figure 1: Global Pipeline workflow.** The EMULSION state machines (1) generate synthetic data at a given time step (2). This data goes through a python script (3) that runs the execution of the DGLM by the R script (4) with the data (2) given as input. The DGLM script outputs an alarm file (5) that contains a boolean per batch

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determining if an alarm was triggered in any given batch at the current time step. This alarm file is given back to the Python script (6) which completes the loop to the state-machines with a collective treatment decision at the current time step (7).

**Figure 2: Distribution of the cumulative incidence across the 48 scenarios.** The dashed lines represent the median of the distributions. L-large; S-small; CT-collective treatment.

**Figure 3: Average time in severe clinical signs (in hours) for an infectious animal across the 48 scenarios.** The dashed lines represent the median of the distributions. L-large; S-small; CT-collective treatment.

**Figure 4: Distributions of AMU across the 48 scenarios.** The dashed lines represent the median of the distributions. L-large; S-small; CT-collective treatment.

**Figure 5: Empirical and estimated risks of infection in the Random scenarios.** The shaded areas correspond to the 95% CI.

**Figure 6: Empirical and estimated risks of infection in the Sorted scenarios.** The shaded areas correspond to the 95% CI.

## 9 Tables

<table><caption>Table 1: Definition of the four scenarios on farm risk level proportions.</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Farm-wise proportion of individual risk level (%)</th></tr><tr><th>low-risk</th><th>medium-risk</th><th>high-risk</th></tr></thead><tbody><tr><th rowspan="4" scope="rowgroup">Scenarios</th><th scope="row">Low-risk level</th><td>90</td><td>10</td><td>0</td></tr><tr><th scope="row">Medium-risk level</th><td>10</td><td>90</td><td>0</td></tr><tr><th scope="row">High-risk level</th><td>0</td><td>10</td><td>90</td></tr><tr><th scope="row">Balanced-risk level</th><td>30</td><td>40</td><td>30</td></tr></tbody></table>

## 10 Supporting Information

File name: Supporting Information
Title of data: Graphic overview of the mechanistic model simulating the spread of *M. haemolytica*,
Explanation of the Processes of the mechanistic model, Parameters used for the systematic variance-
covariance matrices, DGLM Initialization methodology, and Threshold selection for the DGLM-based
collective treatments.

Description of data: not applicable

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Figures

<figure><img src="image_2.png" /><figcaption>Figure 1</figcaption></figure>

**Global Pipeline workflow.** The EMULSION state machines (1) generate synthetic data at a given time step (2). This data goes through a python script (3) that runs the execution of the DGLM by the R script (4) with the data (2) given as input. The DGLM script outputs an alarm file (5) that contains a boolean per batch determining if an alarm was triggered in any given batch at the current time step. This alarm file is given back to the Python script (6) which completes the loop to the state-machines with a collective treatment decision at the current time step (7).

<figure><img src="image_3.png" /></figure>
<caption>Figure 2</caption>

**Distribution of the cumulative incidence across the 48 scenarios.** The dashed lines represent the median of the distributions. L-large; S-small; CT-collective treatment.

<figure><img src="image_4.png" /><figcaption>Figure 3</figcaption></figure>

**Average time in severe clinical signs (in hours) for an infectious animal across the 48 scenarios.** The dashed lines represent the median of the distributions. L-large; S-small; CT-collective treatment.

<figure><img src="image_5.png" /></figure>
<caption>Figure 4</caption>

**Distributions of AMU across the 48 scenarios.** The dashed lines represent the median of the distributions. L-large; S-small; CT-collective treatment.

<figure><img src="image_6.png" /><figcaption>Figure 5</figcaption></figure>

**Empirical and estimated risks of infection in the Random scenarios.** The shaded areas correspond to the 95% CI.

<figure><img src="image_7.png" /></figure>
Figure 6

**Empirical and estimated risks of infection in the Sorted scenarios.** The shaded areas correspond to the 95% CI.

**Supplementary Files**

This is a list of supplementary files associated with this preprint. Click to download.

* SupportingInformation.pdf