# Combining dynamic epidemiological and genetic models to assess the impact of genetic selection strategies on the spread of classical scrapie within a sheep flock

Suzanne Touzeau, Anne Devalle Costard, Sébastien Gaucel, Thierry Bay, Carole C. Moreno, Jean Michel J. M. Elsen

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Suzanne Touzeau, Anne Devalle Costard, Sébastien Gaucel, Thierry Bay, Carole C. Moreno, et al. Combining dynamic epidemiological and genetic models to assess the impact of genetic selection strategies on the spread of classical scrapie within a sheep flock. 2. International Conference on Infectious Disease Dynamics - Epidemics 2, Dec 2009, Athens, Greece. 2009. hal-02811909

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# Combining dynamic epidemiological and genetic models to assess the impact of genetic selection strategies on the spread of classical scrapie within a sheep flock

S. Touzeau¹, A. Costard-Devalle², S. Gaucel¹, T. Bay¹, C. Moreno-Romieux², J.-M. Elsen²

¹UR341 Mathématiques et Informatique Appliquées, INRA Jouy-en-Josas, France

²UR631 Station d'Amélioration Génétique des Animaux, INRA Toulouse, France

## Introduction

Classical scrapie is a transmissible spongiform encephalopathy that affects small ruminants. Due to potential health risks, it is submitted to eradication measures. It is characterised in sheep by a **genetic factor** based on the PrP major susceptibility gene. Therefore, control strategies partly rely on selective breeding. Scrapie transmission mechanisms are still incompletely understood. The **long infectious and undetectable incubation period** makes direct data analyses difficult, hence the interest of a modelling approach.

**Aim:** study the **impact of selective breeding strategies** on the disease spread within a flock, using a dynamic epidemiological model coupled to the optimal outputs of a genetic model through the breeding function.

<figure><img src="image_2.png" /><figcaption>**FIG 1.** **a- Genetic model.** Population description with 7 categories (rectangles), 7 matings paths (thick lines), selection steps (dotted lines) and selection proportion *Wsac* (sex s=1: males, 2 :females; age a=1,...,as; category c=1: not elite, 2: elite).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**b- Epidemiological model.** Flock of susceptible (S) and infected (I) renewal ewes, structured by genotype (g), age class (a), and infection stage (i); demographic (purple) and epidemiological (green) processes.</figcaption></figure>

## Modelling

The **genetic deterministic dynamic model** (FIG 1.a) [1] represents breeding programs including:

* overlapping generations,

* different selection steps,

* different strategies for males and females,

* non-random mating.

It maximises scrapie resistance, with a constraint on loss of genetic progress in milk production.

The **realistic SI-based epidemiological model** (FIG 1.b) [2] takes into account demographic and epidemiological processes, including:

* seasonality in breeding and transmission,

* stochastic mating,

* genetic and age-dependent susceptibilities,

* long and variable incubation periods, etc.

It was calibrated using French outbreak data.

## Results

The model was applied to 3 French dairy flocks corresponding to breeds exhibiting contrasting PrP genotype frequencies: Lacaune (FIG 2.A), MTN (FIG 2.B), MTR (FIG 2.C). It was simulated for 9 scenarios combining:

* 3 scrapie introduction scenarios,

* 3 breeding strategies.

The robustness of the results was tested by a **sensitivity analysis**.

→ Parameters with the greatest impact on the incidence levels and patterns:

(i) the transmission scaling factor;

(ii) the flock;

(iii) the age and genetic susceptibilities.

<figure><img src="image_4.png" /><figcaption>A- Lacaune (66% R)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>B- Manech Tête Noire (44% R)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>C- Manech Tête Rousse (22% R)</figcaption></figure>

<caption>**FIG 2. Simulations.** Total cumulated incidence computed for the 3 flocks (Lacaune, MTN, MTR) according to 9 scenarios:</caption>

* **breeding strategies:**

- no selective breeding (black),

- selection for scrapie resistance with a maximum of 1% genetic loss (green),

- selection for scrapie without constraint, i.e. with maximum genetic loss (purple);

* **scrapie introduction:**

- 1 initial infected ewe (dotted line),

- 5 initial infected ewes (dashed line),

- 1 infected ewe per year (plain line).

## Conclusion

Breeding strategies have a strong impact on the disease outbreak and are therefore an **efficient tool to control scrapie**. However, their efficacy in terms of disease eradication strongly depends on the scrapie introduction scenarios.

These results hence emphasise the contribution of our **original approach**, which **combines genetic and epidemiological models in a realistic framework**.

<footnote>[1] A. D. Costard, Z. G. Vitezica, C. R. Moreno, and J.-M. Elsen. A dynamic deterministic model to optimize a multiple-trait selection scheme. *J. Anim. Sci.* 87(3): 885-894, 2009.</footnote>

<footnote>[2] S. Touzeau *et al*. Modelling the spread of scrapie in a sheep flock: evidence for increased transmission during lambing seasons. *Arch. Virol.*151(4):735-751, 2006.</footnote>