# Studying the seasonality of scrapie transmission in an experimental flock

Suzanne Touzeau, Margo E. Chase-Topping, Louise Matthews, Daniel Lajous,
Jean Michel J. M. Elsen, Mark E. J. Woolhouse

► To cite this version:

Suzanne Touzeau, Margo E. Chase-Topping, Louise Matthews, Daniel Lajous, Jean Michel J. M. Elsen, et al.. Studying the seasonality of scrapie transmission in an experimental flock. International conference on transmissible spongiform encephalopathies, Sep 2002, Edinburgh, United Kingdom. 1 p., 2002. [hal-02832968](https://hal.inrae.fr/hal-02832968)

HAL Id: hal-02832968

https://hal.inrae.fr/hal-02832968

Submitted on 7 Aug 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# Studying the seasonality of scrapie transmission in an experimental flock

S. Touzeau¹, M.E. Chase-Topping², L. Matthews², D. Lajous³, J.-M. Elsen³, M.E.J Woolhouse²

Institut National de la Recherche Agronomique: ¹Jouy-en-Josas, ³Toulouse, France – ²Centre for Tropical Veterinary Medicine, Edinburgh, Scotland

## I. INTRODUCTION/OBJECTIVES

Presence of scrapie prions in the placenta suggests the possibility of increased transmission during lambings, an hypothesis we explore with a mathematical model focused on the disease transmission. The initial model was developed by Woolhouse's group [1] for several outbreaks in British sheep (e.g. [2]). We apply it here to the Langlade experimental flock in which a natural scrapie outbreak started in 1993 [3].

<figure><img src="image_2.png" /></figure>

Natural scrapie outbreak
at Langlade

**Data available:** birth & death/removal, pedigree, scrapie histopathological diagnosis, PrP genotypes (10 from 4 alleles: VRQ, ARQ, AHQ, ARR).

### II.2. MODEL

**Dynamic system:** time $t \ge 0$, age $0 \le a \le A$, infection load $0 \le \theta \le 1$.

**Seasonal birth:** rate $b(t, a') = b(t)$ if dam $a'$ mature, 
= control / flock size $\approx$ constant; 
+ genetics: random mating $G_{gg'}(t)$.

**Natural mortality:** truncated Weibull $\mu(a)$, $a < A$ (survival).

**Horizontal transmission $g' \to g$:** rate $\beta_{gg'}(t, \theta') = k_h \sigma_g \theta' s(t)$, 
genetic susceptibility $\sigma_g$, infectiousness $\propto \theta'$, season $s(t)$; 
+ variable initial load $\theta_0$: gamma distribution $\Theta$.

**Vertical transmission $g' \to g$:** rate $\gamma_{gg'}(t, \theta') = k_v \sigma_g \theta'$.

**Scrapie:** during incubation $\frac{d\theta}{dt} = c_g \theta \to \theta = 1$: clinical signs & death.

### II.1. DATA

* Experimental flock, INRA Toulouse; 
created 1971, closed 1979-96.

* Mostly Romanov breed (prolificity: 
1-6, mean 3.1), size ca. 900.

→ **Study flock:** Romanov, > 8 months, 
cohorts 83-95.

## II. METHODS

<figure><img src="image_3.png" /></figure>

(g: genotype)

$$ \left(\frac{\partial}{\partial t} + \frac{\partial}{\partial a}\right) S_g(t, a) = -S_g \sum_{g'} \int_0^A \int_0^1 \beta_{gg'} [H_{g'} + V_{g'}] d\theta' d\alpha' - \mu S_g $$

$$ S_g(t, \theta) = \sum_{g'} G_{gg'} \int b \left( S_{g'} + \int (1 - \gamma_{gg'}) [H_{g'} + V_{g'}] d\theta' \right) d\alpha' $$

$$ \left(\frac{\partial}{\partial t} + \frac{\partial}{\partial a} + \frac{\partial c_g \theta}{\partial \theta}\right) H_g = \Theta S_g \sum_{g'} \iint \beta_{gg'} [H_{g'} + V_{g'}] d\theta' d\alpha' - \mu H_g $$

$$ H_g(t, 0, \theta) = 0 \qquad H_g(t, a, 0) = 0 $$

$$ \left(\frac{\partial}{\partial t} + \frac{\partial}{\partial a} + \frac{\partial c_g \theta}{\partial \theta}\right) V_g(t, a, \theta) = -\mu V_g $$

$$ V_g(t, 0, \theta) = \Theta \sum_{g'} G_{gg'} \iint b \gamma_{gg'} [H_{g'} + V_{g'}] d\theta' d\alpha' \quad V_g(t, a, 0) = 0 $$

## III. RESULTS

### Outbreak simulation

#### 1. Parameters

**From data:** lambing/transmission season, random mating $G_{gg'}$, natural mortality $\mu$, genetic susceptibility $\sigma_g$ (VRQ-VRQ=0.78, VRQ-ARQ=0.57, ARQ-ARQ=0.48).

**Fitted:** transmission $k_h, k_v$ and incubation $\Theta, c_g$ (mean = 2 yrs).

**Outputs:** $\parallel$ incidence = scrapie case distribution with seasonal transmission (= during lambings) or without; 
$\parallel$ prevalence = proportion of infecteds with seasonal transmission.

Scrapie incidence (prevalence) vs time (years)

<figure><img src="image_4.png" /></figure>

Scrapie incidence vs age (years)

<figure><img src="image_5.png" /></figure>

Scrapie incidence vs genotype

<figure><img src="image_6.png" /></figure>

## IV. DISCUSSION

**A.** Oscillations appear with seasonal transmission, closer to data. 
1st peak from initial condition.

**B.** No age dependent susceptibility implemented, still peak 
around 2 years because of exposure.

**B&C.** Both case distributions quite in accordance with the data.

## V. CONCLUSIONS

The seasonal transmission hypothesis seems consistent with the patterns 
we observe with our model.

**Further work:** • better fit for transmission;

• vertical → perinatal transmission.

### REFERENCES

[1] Stringer et al. 1998, Math. Biosci. 153(2):79-98.

[2] Matthews et al. 2001, Arch. Virol. 146(6):1173-1186.

[3] Elsen et al. 1999, Arch. Virol. 155(3):431-445.