Suzanne Touzeau

Modelling the spread of scrapie in a sheep flock: evidence for increased transmission during lambing seasons

Summary.Presence of scrapie infectivity in the placenta suggests the possibility of increased transmission of scrapie during the lambing season. This hypothesis was explored here using a mathematical model of scrapie transmission dynamics which has previously been successfully used to study several scrapie outbreaks in Scottish sheep flocks. It was applied here to the Langlade experimental sheep flock (INRA Toulouse, France), in which a natural scrapie epidemic started in 1993. Extensive data were available, including pedigree, scrapie histopathological diagnoses and PrP genotypes. Detailed simulations of the scrapie outbreak reveal that the observed patterns of seasonality in incidence can not be accounted for by seasonality in demography alone and provide strong support for the hypothesis of increased transmission during lambing. Observations from several other scrapie outbreaks also showing seasonal incidence patterns support these conclusions.

Sensitivity analysis to identify key parameters influencing Salmonella infection dynamics in a pig batch.

In the context of managed herds, epidemiological models usually take into account relatively complex interactions involving a high number of parameters. Some parameters may be uncertain and/or highly variable, especially epidemiological parameters. Their impact on the model outputs must then be assessed by a sensitivity analysis, allowing to identify key parameters. The prevalence over time is an output of particular interest in epidemiological models, so sensitivity analysis methods adapted to such dynamic output are needed. In this paper, such a sensitivity analysis method, based on a principal component analysis and on analysis of variance, is presented. It allows to compute a generalised sensitivity index for each parameter of a model representing Salmonella spread within a pig batch. The model is a stochastic discrete-time model describing the batch dynamics and movements between rearing rooms, from birth to slaughterhouse delivery. Four health states were introduced: Salmonella-free, seronegative shedder, seropositive shedder and seropositive carrier. The indirect transmission was modelled via an infection probability function depending on the quantity of Salmonella in the rearing room. Simulations were run according to a fractional factorial design enabling the estimation of main effects and two-factor interactions. For each of the 18 epidemiological parameters, four values were chosen, leading to 4096 scenarios. For each scenario, 15 replications were performed, leading to 61440 simulations. The sensitivity analysis was then conducted on the seroprevalence output. The parameters governing the infection probability function and residual room contaminations were identified as key parameters. To control the Salmonella seroprevalence, efficient measures should therefore aim at these parameters. Moreover, the shedding rate and maternal protective factor also had a major impact. Therefore, further investigation on the protective effect of maternal or post-infection antibodies would be needed.

Pathogen population dynamics in agricultural landscapes: the Ddal modelling framework.

Modelling processes that occur at the landscape scale is gaining more and more attention from theoretical ecologists to agricultural managers. Most of the approaches found in the literature lack applicability for managers or, on the opposite, lack a sound theoretical basis. Based on the metapopulation concept, we propose here a modelling approach for landscape epidemiology that takes advantage of theoretical results developed in the metapopulation context while considering realistic landscapes structures. A landscape simulator makes it possible to represent both the field pattern and the spatial distribution of crops. The pathogen population dynamics are then described through a matrix population model both stage- and space-structured. In addition to a classical invasion analysis we present a stochastic simulation experiment and provide a complete framework for performing a sensitivity analysis integrating the landscape as an input factor. We illustrate our approach using an example to evaluate whether the agricultural landscape composition and structure may prevent and mitigate the development of an epidemic. Although designed for a fungal foliar disease, our modelling approach is easily adaptable to other organisms.

The role of mathematical modelling in understanding the epidemiology and control of sheep transmissible spongiform encephalopathies: a review

To deal with the incompleteness of observations and disentangle the complexities of transmission much use has been made of mathematical modelling when investigating the epidemiology of sheep transmissible spongiform encephalopathies (TSE) and, in particular, scrapie. Importantly, these modelling approaches allow the incidence of clinical disease to be related to the underlying prevalence of infection, thereby overcoming one of the major difficulties when studying these diseases. Models have been used to investigate the epidemiology of scrapie within individual flocks and at a regional level; to assess the efficacy of different control strategies, especially selective breeding programmes based on prion protein (PrP) genotype; to interpret the results of scrapie surveillance; and to inform the design of surveillance programmes. Furthermore, mathematical modelling has played an important role when assessing the risk to human health posed by the possible presence of bovine spongiform encephalopathy in sheep. Here, we review the various approaches that have been taken when developing and analysing mathematical models for the epidemiology and control of sheep TSE and assess their impact on our understanding of these diseases. We also identify areas that require further work, discuss future challenges and identify data gaps.

Parameter identification for a PDE model representing scrapie transmission in a sheep flock

In this paper a strategy for the identification of the parameters in a mathematical model which describes the dynamics of a scrapie outbreak in a sheep flock is proposed. Scrapie is a transmissible spongiform encephalopathy that affects sheep, characterised by a genetic susceptibility factor and a long incubation period. To represent the outbreak, demographic and epidemiological processes need to be taken into account in the model, as well as seasonality in breeding and scrapie transmission. The eflock is hence structured according to scrapie status (susceptible or infected), genotype, time, age, and infection load (related to the incubation period), resulting into a PDE model. We built a hierarchy of two aggregated models and take advantage of the hyperbolic structure of the PDEs to part the parameters of the model into three groups, which can theoretically be separately identified. The problem of identifiability and identification is addressed and tests with data from a natural scrapie outbreak are performed.

Within-herd biosecurity and Salmonella seroprevalence in slaughter pigs: A simulation study

In Europe, on-farm biosecurity measures, involving a strict all-in/all-out batch-management system and decontamination of the rearing rooms between consecutive batches, are recommended to control Salmonella infection in growing pigs. However, implementation of these measures is often relaxed under common farming conditions. Therefore, this study was conducted to assess the relative contributions of batch-management system and room decontamination efficacy on Salmonella seroprevalence for different growing rates and subsequent slaughter ages of pigs. Because the impact of these factors cannot be easily evaluated by an observational approach in commercial farms, a stochastic simulation model representing the population dynamics, herd management, and Salmonella infection within a farrow-to-finish pig herd was used. Realistic levels were set for each factor under study (3 for batch-management system and slaughter age; 4 for room decontamination) to generate 54 simulation scenarios. Salmonella shedding prevalence in groups of slaughter pigs was then compared. A sensitivity analysis was performed to rank the impacts of the 3 factors on output. Batch-management system had little effect. In contrast, room decontamination efficacy had the greatest impact on Salmonella prevalence in pigs at slaughter. A drop in decontamination efficacy from 100 to 50%, with a strict all-in/all-out batch-management system and for all slaughter ages tested, noticeably increased (P<0.001) the prevalence and almost doubled it for the reference slaughter age. Our results suggest that the control of Salmonella in pig herds should primarily focus on room decontamination efficacy. Provided that a good level of room decontamination is ensured, some flexibility in batch management, in terms of pig mixing, would be acceptable to limit the number of underweight pigs delivered to the slaughterhouse.

Using singular perturbations to reduce an epidemiological model: Application to bovine viral diarrhoea virus within-herd spread

Studying the spread of a pathogen in a managed metapopulation such as cattle herds in a geographical region often requires to take into account both the within- and between-herd transmission dynamics. This can lead to high-dimensional metapopulation systems resulting from the coupling of several within-herd transmission models. To tackle this problem, we aim in this paper at reducing the dimension of a tractable but realistic dynamical system reproducing the within-herd spread. The context chosen to illustrate our purpose is bovine viral diarrhoea virus (BVDV) transmission in a cattle herd structured in two age classes and several epidemiological states, including two infectious states (transiently and persistently infected). Different time scales, corresponding to the epidemiological and demographic processes, are identified which allow to build a reduced model. Singular perturbation technique is used to prove that, under some non-restrictive conditions on parameter values, the behaviour of the original system is quite accurately approximated by that of the reduced system. Simulations are also performed to corroborate the approximation quality. Our study illustrates the methodological interest of using singular perturbations to reduce model complexity. It also rigorously proves the biologically intuitive assumption that transiently infected individuals can be neglected in a homogeneous population, when capturing the global dynamics of BVDV spread.