Stochasticity from Management Practices in Scrapie Outbreaks ... Most previous analyses of scrapie outbreaks have focused on a small number of epidemics in ...
Understanding Sources of Epidemic Variability: Disentangling Stochasticity from Management Practices in Scrapie Outbreaks Gryspeirt, A. (1) , Webb, C.R. (2), McIntyre, K.M. (1,3), Gubbins, S. (1) (1) Institute for Animal Health, Pirbright Laboratory, U.K. (2) Cambridge Infectious Diseases Consortium, Department of Veterinary Medicine, University of Cambridge, U.K. (3) Faculty of Veterinary Clinical Science, University of Liverpool, UK
ABSTRACT Most previous analyses of scrapie outbreaks have focused on a small number of epidemics in flocks managed by research institutes. This has the advantage of facilitating the study of disease, but may not reflect the field situation. Recently, detailed data have been published on 30 outbreaks in sheep flocks naturally-infected with scrapie. These show marked variability in their epidemiological characteristics (ranging in size from one to 131 cases), raising the question of how much of this variability is due to the stochastic nature of disease dynamics and how much is due to other factors, such as flock demography or management practices. In this study, we used an age- and prion protein (PrP) genotype-structured model for the transmission of scrapie to address this question. More specifically, the basic reproduction number (R0) was estimated for each of the outbreaks by fitting the model to case data using maximum-likelihood methods. The estimates for each flock will then compared to examine whether or not flocks with similar management practices have similar R0s and, moreover, whether outbreaks can be classified into distinct types.
INTRODUCTION Scrapie is a fatal neurodegenerative disease of sheep and goats, which has been present in sheep for at least two centuries. Despite this, there are still considerable uncertainties about the epidemiology of what is now called classical scrapie (Detwiler and Baylis 2003). Furthermore, with few exceptions, previous analyses of scrapie epidemics have focused on a small number of outbreaks in flocks managed by research institutes, which facilitates detailed study, but does not necessarily reflect the field situation. A recently published study sought to rectify this apparent deficit and presented data on the epidemiological characteristics of scrapie outbreaks in 30 sheep flocks in the United Kingdom (UK), which ranged in size from one to 131 cases (McIntyre et al. 2008). In this study we used the data presented by McIntyre et al. (2008) to investigate the dynamics of scrapie in each of the outbreaks and, in particular, disentangle the various sources of epidemic variability: stochasticity, prion protein (PrP) genotype frequencies, age structure and management practices. To do this we develop a simple age-genotype-cohort model and use it to estimate the basic reproduction number (R0) for each outbreak and, hence, take into account the first three sources of variability. Comparing R0s amongst flocks will then allow the impact of management practices on epidemic variability to be assessed.
METHODS Flock Data A full description of the field study is presented elsewhere (McIntyre et al. 2008). In brief, flocks were eligible to join the study if they had had at least one confirmed case of (classical) scrapie in the previous two years. On recruitment, flock-level data were collected using a questionnaire and the entire breeding flock was blood-sampled for PrP genotyping. In total 30 case flocks were recruited, though only 21 were included in the present study. Seven flocks were excluded because the PrP genotypes were not known for any of the cases, while a further two flocks were excluded because they each had only a single case.
Modelling Approach A simple age-genotype-cohort model was used to describe the dynamics of scrapie within a farm. Because of evidence for a decrease in the risk of infection with age (St Rose et al. 2006), all animals were assumed to become infected at or close to birth. In this case, the probability of animal of PrP genotype j born in cohort t develops clinical disease in age class a (comprising animals between a-1 and a years of age) is given by:
q jat = φ jt sa ∫
a
a −1
f j (v) dv,
where φjt is the risk of infection for genotype j in cohort t, sa is the probability of survival to age class a and fj is the log-normal incubation period distribution (with genotype specific parameters μj and σj). The risk of infection is given by, ⎛ ⎞ φ jt = 1 − exp ⎜ −β j ∑∑ ∑ ωia Ciaτ ⎟ , i τ< t a > t −τ ⎝ ⎠ where βj is the transmission parameter and ωja is the relative infectiousness of an infected animal of PrP genotype j in age class a and Cjat is the number of cases of PrP genotype j in age class a from cohort t. The basic reproduction number (R0) is given by the largest eigenvalue of the next generation matrix (K) (Diekmann & Heesterbeek 2000), the elements of which,
(
K ij = Bi ∑ (1 − exp(−βi ω ja ) ) sa ∫ a
a
a −1
∞
)
f j (v) dv + ( sa − sa +1 ) ∫ f j (v) dv , a
are the expected number of infected animals of genotype i arising from a single infected animal of genotype j.
Maximum-likelihood Methods Parameters in the model were estimated using maximum likelihood methods. The case data are drawn from a multinomial distribution, so that the likelihood is given by, ⎛ ⎞ S jt B jt ! ⎞ C ⎜ ⎟⎛ L = ∏∏ ⎜ 1 − ∑ q jat ⎟ ∏ q jatjat , ⎜ ⎟ a ⎠ a t j ⎜ S jt !∏ C jat ! ⎟ ⎝ a ⎝ ⎠ where S jt = B jt − ∑ C jat , a
is the number of animals of PrP genotype j from cohort t that do not develop clinical disease and Bjt is the number of animals of genotype j born in cohort t. For each flock, the genotype-specific transmission parameters and, if there were sufficient cases in a genotype in the flock, incubation period parameters were estimated from the case data; otherwise, estimates based on surveillance data were used (Gubbins 2008). Demographic parameters (survival data, genotype frequencies in birth cohorts) were estimated using data collected at the farm visits. All outbreaks were assumed to be initiated by a single purchased ewe of the highest risk PrP genotype found in the flock.
RESULTS Here we present only preliminary results; a more complete analysis will be presented at the conference. Estimates for the basic reproduction number (R0) were obtained for each flock, though the confidence limits were very wide in most cases (Figure 1).
CONCLUSIONS Our results indicate that there is substantial variation amongst flocks in the basic reproduction number (R0), which will reflect differences in the frequencies of PrP genotypes and age structure of the flock, as well as in management practices. The next stage of the analysis is to identify whether high or low values of R0 are associated with particular management practices, though the uncertainty in the estimates may make this difficult. The estimates for the basic reproduction number are consistent with those previously reported for two scrapie outbreaks: 3.9 for an outbreak in a Cheviot flock (Matthews et al. 1999); and 2.5-14 for an outbreak in a Romanov flock (Hagenaars et al. 2003). Moreover, we found similar (or higher) levels of uncertainty in the estimates for R0 as were identified by Hagenaars et al. (2003). The three flocks with very high estimates for R0 (15, 16, 21 in Figure 1) are those for which there are large numbers of cases in early cohorts during their outbreak. This could indeed be a result of high levels of transmission or, alternatively, may reflect that these cases were infected before they were brought into the flock. Indeed, this is the case for several of the outbreaks (McIntyre et al. 2008; see their Figure 1a), though unfortunately the dates at which the animals were brought into the flock are not available in most instances. The large 95% confidence intervals and, especially, the upper 95% confidence limits for R0 are a consequence of the model formulation, which means that it can be problematic to identify an upper limit for a transmission parameter if a large proportion of animals of a genotype become infected (i.e. such that φjt is close to one).
Figure 1. Estimates (bars and circles) and 95% confidence intervals (error bars) of the basic reproduction number (R0) for scrapie outbreaks in 21 sheep flocks in the United Kingdom. For ease of comparison the flock IDs correspond with those used by McIntyre et al. (2008).
REFERENCES Detwiler, L.A. and Baylis, M. (2003) The epidemiology of scrapie. Revue Scientifique et Technique de l’O.I.E. 22, 121-143. Gubbins, S. (2008) Prevalence of sheep infected with classical scrapie in Great Britain: integrating multiple sources of surveillance data for 2002. Journal of the Royal Society Interface 5, 1343-1351. Hagenaars, T.J., Donnelly, C.A., Ferguson, N.M. and Anderson, R.M. (2003) Dynamics of scrapie in a flock of Romanov sheep - estimation of transmission parameters. Epidemiology and Infection 131, 1015-1022. Diekmann, O. and Heesterbeek, J.A.P. (2000) Mathematical Epidemiology of Infectious Diseases. 303pp. Chichester, England: John Wiley & Sons. Matthews, L., Woolhouse, M.E.J. and Hunter, N. (1999) The basic reproduction number for scrapie. Proceedings of the Royal Society Series B 266, 1085-1090. McIntyre, K.M., Gubbins, S., Goldmann, W., Hunter, N. and Baylis, M. (2008) Epidemiological characteristics of classical scrapie outbreaks in 30 sheep flocks in the United Kingdom. PLoS ONE 3, e3994. St Rose, S.G., Hunter, N., Matthews, L., Foster, J.D., Chase-Topping, M.E., Kruuk, L.E.B., Shaw, D.J., Rhind, S.M., Will, R.G. and Woolhouse, M.E.J. (2006) Comparative evidence for a link between Peyer’s patch development and susceptibility to transmissible spongiform encephalopathies. BMC Infectious Diseases 6, 5.
ACKNOWLEDGEMENTS This work was funded by the Department for Environment, Food and Rural Affairs (Defra) [grant code: SE0249]. The scrapie field study was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) [grant codes: BS309857, IAH1055, IAH1320]. The authors are grateful to all the farmers who participated in the study for their assistance and generosity.
