1 Department of Zoology, University of Oxford, South Parks Rd. Oxford, Oxfordshire OX1 3PS, UK
2 Compton Laboratory, Institute for Animal Health, Compton, Berkshire RG20 7NN, UK
3 Neuropathogenesis Unit, Institute for Animal Health, West Mains Rd, Edinburgh EH9 3JF, UK
Correspondence
Rowland Kao
rowland.kao{at}zoo.ox.ac.uk
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ABSTRACT |
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INTRODUCTION |
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In this report, we consider the available evidence on ARR/ARR susceptibility to BSE and construct a model that examines the question of how much impact this would have on the NSP.
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METHODS |
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Data on oral exposure of RR sheep to BSE are limited; of 15 exposed RR sheep thus far examined for PrPsc, the last group were at 28 months post-exposure, implying only that any RR sheep infected via oral exposure would have a long incubation period. If none of the five sheep currently under observation are infected, this only indicates an upper bound of 45 % probability of infection at the 5 g dose (Jeffrey et al., 2001). Here an incubation period equal to that for QR sheep is assumed, as is consistent with the experiment. If resistance of RR sheep to TSE infection is not absolute, will increasing the proportion of RR sheep create a TSE-resistant national flock? It is difficult to assess the impact of RR susceptibility on a potential epidemic of BSE in sheep without taking into account the lengthy incubation period and genotype dependence of the disease. Therefore, using scrapie epidemiology as a basis, we constructed an age-structured mathematical model of BSE in sheep to investigate the impact of different levels of RR susceptibility on the NSP.
In order to evaluate RR sheep susceptibility to BSE, we consider the relative dose-response of these sheep in comparison to available data for sheep of more susceptible genotype. The experiment showing RR susceptibility to i.c. exposure is ongoing; due to the staggered start dates for the experiment and the long incubation period expected, many of the infected sheep are in the very early stages of the experiment, and it will be some time before the final experimental results are available. Therefore we project the final number of infected animals using a maximum-likelihood estimation (MLE) analysis of right censored data. The distribution of incubation periods for fixed genotype and TSE strain is typically very narrow, especially at high dose (Houston et al., 2003; McLean & Bostock, 2000
). Given the lack of informative data, we assume that the distribution of incubation periods in RR sheep is the same width as the distribution for the QQ sheep in the same experiment (for QQ sheep, incubation period is 554 days, SD±45 days). A standard approach to account for right censoring of the data is used, with likelihood function (LF)
where
i is the value of the normal distribution evaluated at the incubation periods of the sheep i that developed clinical signs (total three sheep developing clinical signs), and
j is the cumulative normal distribution function, evaluated at the time the sheep j were last observed (total of seventeen with no clinical signs at time of report, including one sheep removed from the experiment due to poor health). The MLE parameters fit are the incubation period and the number of sheep infected. This calculation gives an upper estimate of the number infected, as sheep very early on in the experiment have very little effect on the incubation period distribution. Then the experimental results thus far are consistent with at most 7 of 20 infected (incubation period 1208 days, 95 % CI 11641292 days, and 95 % CI of 6 to 9 of 20 infected, including one intercurrent death), compared to 17 of 19 QQ sheep i.c. challenged at the same dosage (Fig. 1
) (Houston et al., 2003
).
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In this model, incubation periods are based on experimental data, and are the median values of the distribution used in a previous model, i.e. 2 years for QQ sheep, and 5 years for QR sheep (Foster et al., 2001; Kao et al., 2002
). For RR sheep, the limited data show only that incubation periods shorter than 5 years are inconsistent with the available data (Jeffrey et al., 2001
), and so this lower limit is assumed. Vertical transmission is also considered. Epidemiological observations provide strong evidence for perinatal transmission of scrapie (Elsen et al., 1999
); however, true vertical or in utero transmission is difficult to prove, and thus far no conclusive evidence has been found for transmission via germinal cells (Foster et al., 1992
, 1996b
, 1999
; Wang et al., 2001
) or for foetal infection (Andreoletti et al., 2002b
; Hadlow et al., 1982
). However, infectivity and PrPSc deposits have been found in the placentas of scrapie-infected ewes (Race et al., 1998
; Tuo et al., 2001
). Recent results indicate that placental infection is restricted mainly to foetal cells and is controlled by the PrP genotype of the foetus (Andreoletti et al., 2002b
; Tuo et al., 2002
). Together with the evidence for an association of scrapie with group lambing in pens (McLean et al., 1999
), this supports a hypothesis of post-natal infection by contact with infectious material derived from placental contamination of the environment. While this suggests that perinatal transmission may be genotype dependent and that control measures such as changes in lambing practices might effectively reduce it, we allow for 30 % vertical transmission to lambs throughout the incubation period for all genotypes. This transmission level is as examined in a previous report (Kao et al., 2002
), and roughly consistent with the results of other analyses for scrapie (Woolhouse et al., 1998
).
The British sheep industry can be stratified into the hill, upland and lowland industries, roughly in accordance with the geography to which the breed of sheep is best suited. As lowland flocks received a greater relative proportion of protein supplement compared to hill and upland flocks and thus are more likely to have been exposed to BSE-infected MBM (DNV, 1998), the model is stratified into two groups: hill/upland and lowland. Hill and upland ewes near the end of their lifespans are incorporated in large numbers into lowland flocks (draft ewes), and are a potential contributor to BSE in lowland flocks. However, as lambs raised for slaughter leave the flock too soon to contribute much to TSE transmission, for purposes of exploring TSE transmission we are only interested in the breeding flock, and draft ewes mainly produce lambs for slaughter. In 1997, only 0·88 million of 10·73 million breeding ewes in the lowland sector were the progeny of draft ewes (Pollott, 1998
). Thus draft ewes are unlikely to have added significantly to a feed-borne BSE epidemic in lowland breeding sheep, and the equations contain no direct interaction between the stratified industries.
The series of feed bans over the late 1980s and 1990s eliminated the majority of BSE cases in cattle (Stevenson et al., 2000), and would have also ended BSE transmission to sheep in the absence of horizontal transmission. Thus the current stability of any epidemic of BSE in sheep is analysed using a within-flock transmission model that does not consider feedborne transmission. We construct a model incorporating 14 age and 14 infection stages, to allow for consideration of realistic incubation periods (Foster et al., 2001
; Kao et al., 2002
) and mortality rates (McLean et al., 1999
). We assume that infection load increases exponentially, with maximum load achieved when the clinical stage is reached, at which point the animal dies or is removed (Matthews et al., 2001
; Stringer et al., 1998
). The duration of the clinical stage is taken to be on average 1 month. Incubation periods are as in the feedborne transmission model, with the same assumptions about vertical transmission. The age structure is as previously described for the breeding flock only (McLean et al., 1999
); given the incubation periods involved, non-breeding lambs (i.e. those going directly to slaughter) do not remain in the flock for a sufficient time to contribute to infection. The full mathematical details are presented in the Appendix.
Evaluation of the efficacy of control is based on the calculation of the basic reproduction ratio. The standard definition of the basic reproduction ratio (R0) for this system is the average number of BSE-infected sheep that would result following the introduction of a single infected sheep into a flock harbouring no existing infection (MacDonald, 1952). It is well known that if R0 is less than one, a disease cannot persist, and therefore this is used as the benchmark for disease eradication policies, and provides our definition of a resistant flock (Anderson & May, 1990
). Here, we calculated R0 based on the related next generation matrix approach (Diekmann et al., 1990
). For simple systems in which there is only a single infected class, the definition is identical to the one given above, and for all systems R0=1 remains the threshold for disease eradication. The next generation matrix for a reduced form of the model with only two age and two infection classes is presented in the Appendix.
Based on our estimates of genotype differences in susceptibility at low dose, we consider ranges of relative susceptibility of RR sheep to QQ sheep of 1·5 to 138, and transmission rates up to =0·1 infections per infectious sheep per sheep per year (R0 ranging up 3·6). At the upper value, for a within-flock epidemic beginning in 1995, i.e. the year by which 90 % of the feedborne infections would have occurred (Kao et al., 2002
), a typical flock of 450 sheep (16 % RR, 36 % QQ and 48 % QR sheep) would have a case incidence of 30 in 2002 with 100 cases from 1995 to 2002, and therefore flock-level incidence would now be well above detectable limits (see Fig. 2
). While only one in eight flocks was reporting scrapie in the late 1990s (Hoinville et al., 1999
), such an epidemic would be difficult to miss with current awareness of scrapie and BSE, and thus transmission rates above this level are unlikely in the context of this model.
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RESULTS |
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DISCUSSION |
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The impact of vertical transmission in this model is dependent on the assumption that RR sheep would have the same level of susceptibility to vertical transmission as QQ sheep. Should the relative susceptibility of RR lambs to both horizontal and vertical transmission scale in the same fashion (i.e. RR lambs half as susceptible as QQ lambs via horizontal transmission, implying that they are half as susceptible via vertical transmission as well) then high levels of vertical transmission would make no difference to the success of the NSP.
BSE has never been recognized in sheep except under experimental conditions, and RR sheep have never been orally infected with BSE or scrapie. Thus one may question whether the risk to RR sheep is all sound and fury. We point out that the scrapie case notification data in Britain have only resulted in 276 ARQ/ARQ TSE cases being reported. Since ARQ/ARQ and ARR/ARR sheep exist in similar proportions, this implies that ARR/ARR are no more than 1 % as susceptible to scrapie as ARQ/ARQ sheep but does not preclude it, and of course no equivalent data on BSE exists. Increased surveillance and genotyping across Europe (http://europa.eu.int/comm/food/fs/sc/ssc/out238_en.pdf) may result in the discovery of scrapie in putatively resistant sheep; however, at 1 % susceptibility compared to ARQ/ARQ sheep, this is unlikely to result in a national flock of ARR/ARR sheep being able to maintain endemic scrapie, though danger remains from either an as yet undiscovered strain of scrapie to which ARR/ARR sheep are more susceptible, or carrier sheep (i.e. sheep that can transmit infection but never exhibit clinical signs). However, should BSE be discovered in the UK national sheep flock, we illustrate scenarios for RR susceptibility consistent with all the available data on BSE in sheep, and show that we cannot rule out levels of RR susceptibility that would cause the failure of the NSP.
This study highlights the need for additional data on relative infectivity of BSE in different genotypes and breeds of sheep, titration of infectivity in sheep, and the possible infectivity of tissues from sheep with very long incubation periods, or sheep that may never develop clinical infection. Experiments to study these factors are either in progress or imminent; however, the long incubation period of the disease and the expense of conducting large-scale experiments preclude definitive answers for at least several years. While an exercise of this type is by nature speculative, we have used the best current estimates to establish that ARR/ARR susceptibility to BSE is unlikely to preclude the development of a BSE-resistant national flock, typically requiring that one out of two flocks take 6 years instead of 5 to achieve TSE resistance.
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APPENDIX: MATHEMATICAL DETAILS |
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The sheep-to-sheep transmission model
Investigation of the effect of the impact of RR susceptibility on sheep-to-sheep transmission is based on a system of age and infection stage-structured differential equations. Here SRR,i are susceptible RR sheep of age class i, and IRR,i,j are infected RR sheep of age class i and infection stage j (ij), with similar definitions for QQ and QR sheep. Equation (A2.f) describes the rise in infectivity over time (to a maximum of one at the end of the incubation period,
inc). Equation (A2.g) is the total mortality at time t, which must be balanced by births and/or the buying-in of sheep in (A2.a). The genotype of offspring is described by proportionate mixing of all genotypes in the flock ([AA] is the proportion of AA).
Vertical transmission is incorporated as in the feed-borne transmission equations. The parameter vi,j represents the proportion of infected lambs of genotype i born to infected ewes at infection stage j (i.e. infection is lamb genotype dependent; Andreoletti et al., 2002a; Tuo et al., 2002
). The age structure of the breeding population is as previously described (McLean et al., 1999
).
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The next generation matrix
Defining the next generation matrix as M, element mijM is the average number of individuals of infectious class i created when a single individual of class j is introduced into a wholly susceptible, equilibrium population. For a simplified model with only two age classes, the infectious classes are IRR,1,1, IRR,2,1, IRR,2,2, IQR,1,1, IQR,2,1, IQR,2,2, IQQ,1,1, IQQ,2,1 and IQQ,2,2, and M is a 9x9 matrix of the form
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In all cases, the equations were analysed numerically using standard algorithms in Mathematica v4.0 (Wolfram, 1999) for the solution of systems of ODEs (NDSolve) and the lead eigenvalue of the next generation matrix (Eigenvalue).
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Received 7 February 2003;
accepted 16 August 2003.
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