A mathematical model of the dynamics of scrapie in a sheep flock

Relationships between genetic change and infectious disease in domestic livestock

The relations between genetic change in domestic livestock and infectious disease (including both its epidemiology and the animal's reaction to it) are examined. The overall picture is confusing because there are different, and seemingly unrelated, ways of considering the issue. An attempt is made to put these together into a more general framework. Four processes of particular interest are distinguished and discussed in more detail: (i) the way a population's genetic potential for immunocompetence can be changed by breeding, (ii) the way an animal's immunocompetence is influenced by that animal's production potential, in combination with the environmental resources that are available to it at a given time, (iii) the way the disease status of an animal (and a population of animals) is influenced by its immunocompetence, and (iv) the way the production level of an animal is influenced by activation of its immune system. Ultimately, all four processes influence the realised level of production.

This comes down to four questions that need to be addressed: (i) can we use genetic variation in immunocompetence in animal breeding? (ii) does a higher production potential (today's direction of breeding) have a negative impact on immunocompetence? (iii) does improved immunocompetence result in improved health? and (iv) how large is the negative impact of disease on production?

A discrete-time epidemiological model to quantify selection for disease resistance

A genetic epidemiological model (GEM) for investigating the effect of selection for disease resistance on the epidemiology of infectious diseases is presented and applied to a pig breeding scenario. Fundamental to the model is R0, the basic reproductive ratio. R0 is the expected number of secondary infections caused by a single infection. If R0 is greater than 1, there will be an epidemic. The aim of the model is to quantify the effect of selection on R0 and the consequences this has on disease epidemiology. Two implementations are presented: selection for reduced susceptibility/infectivity to a disease and introgression of a major resistance gene. The results suggest that the effects of selection for reduced susceptibility I infectivity are critically dependent on the infectiousness of the disease. Under the assumptions made in the model, for a disease with a low infection level, it takes approximately 15 years of selection until R0 is less than 1 and the population is safe from epidemics should the infectious agent be present. For a highly infectious disease, this time may be as long as 100 years. For gene introgression, the population is expected to be free from epidemics within 5 years and the time to reduce R0 to less than 1 is largely independent of the disease being considered. With gene introgression, the proportion of the population which needs to be resistant to ensure that R0 is less than one is shown to be a function of the initial R0 for the disease. Although selection, as modelled, results in a linear decline in R0, the reduction in the proportion of animals infected during an epidemic is non-linear. The selection process reduces the amount of infectious material that is in the environment when an infection occurs and this decreases the force of infection on unselected animals. This phenomenon results in a marked interaction between host genotype and disease epidemiology. Thus, the results of the model show that altering the genetics of individual animals affects the epidemiology of the disease at the population level. The model can be applied to any farm structure and any microparasitic infectious disease.

Genetic resistance to infections in sheep

This paper considers genetic resistance to infectious disease in sheep, with appropriate comparison with goats, and explores how such variation may be used to assist in disease control. Many studies have attempted to quantify the extent to which host animals differ genetically in their resistance to infection or in the disease side-effects of infection, using either recorded animal pedigrees or information from genetic markers to quantify the genetic variation. Across all livestock species, whenever studies are sufficiently well powered, then genetic variation in disease resistance is usually seen and such evidence is presented here for three infections or diseases of importance to sheep, namely mastitis, foot rot and scrapie. A further class of diseases of importance in most small ruminant production systems, gastrointestinal nematode infections, is outside the scope of this review. Existence of genetic variation implies the opportunity, at least in principle, to select animals for increased resistance, with such selection ideally used as part of an integrated control strategy. For each of the diseases under consideration, evidence for genetic variation is presented, the role of selection as an aid to disease control is outlined and possible side effects of selection in terms of effects in performance, effects on resistance to other diseases and potential parasite/pathogen coevolution risks are considered. In all cases, the conclusion is drawn that selection should work and it should be beneficial, with the main challenge being to define cost effective selection protocols that are attractive to sheep farmers.

An economic evaluation of preclinical testing strategies compared to the compulsory scrapie flock scheme in the control of classical scrapie

Cost-benefit is rarely combined with nonlinear dynamic models when evaluating control options for infectious diseases. The current strategy for scrapie in Great Britain requires that all genetically susceptible livestock in affected flocks be culled (Compulsory Scrapie Flock Scheme or CSFS). However, this results in the removal of many healthy sheep, and a recently developed pre-clinical test for scrapie now offers a strategy based on disease detection. We explore the flock level cost-effectiveness of scrapie control using a deterministic transmission model and industry estimates of costs associated with genotype testing, pre-clinical tests and the value of a sheep culled. Benefit was measured in terms of the reduction in the number of infected sheep sold on, compared to a baseline strategy of doing nothing, using Incremental Cost Effectiveness analysis to compare across strategies. As market data was not available for pre-clinical testing, a threshold analysis was used to set a unit-cost giving equal costs for CSFS and multiple pre-clinical testing (MT, one test each year for three consecutive years). Assuming a 40% within-flock proportion of susceptible genotypes and a test sensitivity of 90%, a single test (ST) was cheaper but less effective than either the CSFS or MT strategies (30 infected-sales-averted over the lifetime of the average epidemic). The MT strategy was slightly less effective than the CSFS and would be a dominated strategy unless preclinical testing was cheaper than the threshold price of £6.28, but may be appropriate for flocks with particularly valuable livestock. Though the ST is not currently recommended, the proportion of susceptible genotypes in the national flock is likely to continue to decrease; this may eventually make it a cost-effective alternative to the MT or CSFS.

Use of a preclinical test in the control of classical scrapie

Scrapie control in Great Britain (GB) was originally based on the National Scrapie Plan's Ram Genotyping scheme aimed at reducing the susceptibility of the national flock. The current official strategy to control scrapie in the national flock involves culling susceptible genotypes in individual, known affected flocks (compulsory scrapie flock scheme or CSFS). However, the recent development of preclinical test candidates means that a strategy based on disease detection may now be feasible. Here, a deterministic within-flock model was used to demonstrate that only large flocks with many home-bred ewes are likely to be a significant risk for flock-to-flock transmission of scrapie. For most other flocks, it was found that the CSFS could be replaced by a strategy using a currently available live test without excessive risk to other farmers, even if the proportion of susceptible genotypes in the flock is unusually large. Even for flocks that represent a high risk of harbouring a high prevalence of infection, there would be limited probability of onward transmission if scrapie is detected soon after disease introduction (typically less than 5 years). However, if detection of disease is delayed, the existing CSFS strategy may be the most appropriate control measure in these cases.

Surveillance and simulation of bovine spongiform encephalopathy and scrapie in small ruminants in Switzerland

BACKGROUND

After bovine spongiform encephalopathy (BSE) emerged in European cattle livestock in 1986 a fundamental question was whether the agent established also in the small ruminants' population. In Switzerland transmissible spongiform encephalopathies (TSEs) in small ruminants have been monitored since 1990. While in the most recent TSE cases a BSE infection could be excluded, for historical cases techniques to discriminate scrapie from BSE had not been available at the time of diagnosis and thus their status remained unclear. We herein applied state-of-the-art techniques to retrospectively classify these animals and to re-analyze the affected flocks for secondary cases. These results were the basis for models, simulating the course of TSEs over a period of 70 years. The aim was to come to a statistically based overall assessment of the TSE situation in the domestic small ruminant population in Switzerland.

RESULTS

In sum 16 TSE cases were identified in small ruminants in Switzerland since 1981, of which eight were atypical and six were classical scrapie. In two animals retrospective analysis did not allow any further classification due to the lack of appropriate tissue samples. We found no evidence for an infection with the BSE agent in the cases under investigation. In none of the affected flocks, secondary cases were identified. A Bayesian prevalence calculation resulted in most likely estimates of one case of BSE, five cases of classical scrapie and 21 cases of atypical scrapie per 100'000 small ruminants. According to our models none of the TSEs is considered to cause a broader epidemic in Switzerland. In a closed population, they are rather expected to fade out in the next decades or, in case of a sporadic origin, may remain at a very low level.

CONCLUSIONS

In summary, these data indicate that despite a significant epidemic of BSE in cattle, there is no evidence that BSE established in the small ruminant population in Switzerland. Classical and atypical scrapie both occur at a very low level and are not expected to escalate into an epidemic. In this situation the extent of TSE surveillance in small ruminants requires reevaluation based on cost-benefit analysis.

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.

Evidence for maternal transmission of scrapie in naturally affected flocks

It has been known for many years that the offspring of scrapie affected ewes are at increased risk of developing scrapie but whether this is simply the result of an increased genetic susceptibility or transmission of infection has always been unclear. To contribute to clarify this we analysed the data collected in a detailed study of scrapie occurrence in a number of naturally affected commercial sheep flocks in Great Britain (GB) to investigate the association between PrP genotype and parental scrapie status and the incidence of scrapie. Our analyses confirmed the strong association between PrP genotype and the incidence of scrapie found in previous studies and a low incidence of scrapie in animals carrying the ARR allele and a high risk in homozygous VRQ animals. However, we also demonstrate an increased incidence of scrapie in the offspring of scrapie affected ewes controlling for the confounding effect of PrP genotype, but no increased scrapie incidence in the offspring of scrapie affected sires. Our results suggest that some of the increased incidence of scrapie in the offspring of scrapie affected ewes is the result of transmission of infection from mother to offspring. Our results confirm that a breeding policy aimed at decreasing the genetic susceptibility of the population should decrease the incidence of scrapie and that removing the offspring of scrapie affected animals from affected flocks could contribute to the control of this disease.

Implications of conflicting associations of the prion protein (PrP) gene with scrapie susceptibility and fitness on the persistence of scrapie

BACKGROUND

Existing mathematical models for scrapie dynamics in sheep populations assume that the PrP gene is only associated with scrapie susceptibility and with no other fitness related traits. This assumption contrasts recent findings of PrP gene associations with post-natal lamb survival in scrapie free Scottish Blackface populations. Lambs with scrapie resistant genotypes were found to have significantly lower survival rates than those with susceptible genotypes. The present study aimed to investigate how these conflicting PrP gene associations may affect the dynamic patterns of PrP haplotype frequencies and disease prevalence.

METHODOLOGY/PRINCIPAL FINDINGS

A deterministic mathematical model was developed to explore how the associations between PrP genotype and both scrapie susceptibility and postnatal lamb mortality affect the prevalence of scrapie and the associated change in PrP gene frequencies in a closed flock of sheep. The model incorporates empirical evidence on epidemiological and biological characteristics of scrapie and on mortality rates induced by causes other than scrapie. The model results indicate that unfavorable associations of the scrapie resistant PrP haplotypes with post-natal lamb mortality, if sufficiently strong, can increase scrapie prevalence during an epidemic, and result in scrapie persisting in the population. The range of model parameters, for which such effects were observed, is realistic but relatively narrow.

CONCLUSIONS/SIGNIFICANCE

The results of the present model suggest that for most parameter combinations an unfavourable association between PrP genotype and post-natal lamb mortality does not greatly alter the dynamics of scrapie and, hence, would not have an adverse impact on a breeding programme. There were, however, a range of scenarios, narrow, but realistic, in which such an unfavourable association resulted in an increased prevalence and in the persistence of infection. Consequently, associations between PrP genotypes and fitness traits should be taken into account when designing future models and breeding programmes.

Comparison of strategies for substantiating freedom from scrapie in a sheep flock

Background

The public health threat represented by a potential circulation of bovine spongiform encephalopathy agent in sheep population has led European animal health authorities to launch large screening and genetic selection programmes. If demonstrated, such a circulation would have dramatic economic consequences for sheep breeding sector. In this context, it is important to evaluate the feasibility of qualification procedures that would allow sheep breeders demonstrating their flock is free from scrapie. Classical approaches, based on surveys designed to detect disease presence, do not account for scrapie specificities: the genetic variations of susceptibility and the absence of live diagnostic test routinely available. Adapting these approaches leads to a paradoxical situation in which a greater amount of testing is needed to substantiate disease freedom in genetically resistant flocks than in susceptible flocks, whereas probability of disease freedom is a priori higher in the former than in the latter. The goal of this study was to propose, evaluate and compare several qualification strategies for demonstrating a flock is free from scrapie.

Results

A probabilistic framework was defined that accounts for scrapie specificities and allows solving the preceding paradox. Six qualification strategies were defined that combine genotyping data, diagnostic tests results and flock pedigree. These were compared in two types of simulated flocks: resistant and susceptible flocks. Two strategies allowed demonstrating disease freedom in several years, for the majority of simulated flocks: a strategy in which all the flock animals are genotyped, and a strategy in which only founders animals are genotyped, the flock pedigree being known. In both cases, diagnostic tests are performed on culled animals. The less costly strategy varied according to the genetic context (resistant or susceptible) and to the relative costs of a genotyping exam and of a diagnostic test.

Conclusion

This work demonstrates that combining data sources allows substantiating a flock is free from scrapie within a reasonable time frame. Qualification schemes could thus be a useful tool for voluntary or mandatory scrapie control programmes. However, there is no general strategy that would always minimize the costs and choice of the strategy should be adapted to local genetic conditions.

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

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.

A modelling framework to describe the spread of scrapie between sheep flocks in Great Britain

My aim was to develop a stochastic, spatial model describing the spread of scrapie between sheep flocks in Great Britain; I wanted a model, which could subsequently be used to assess the efficacy of different control strategies. The structure of the model reflects the demography of the British sheep flock, including a description of the contact structure between flocks. The dynamics of scrapie were incorporated through two probabilities associated with each flock: of acquiring infection and of experiencing a within-flock outbreak following exposure. The acquisition of infection depends on whether or not a flock buys-in sheep and, if it does, whether or not it trades with an affected flock. Once a flock is exposed, the probability of a within-flock outbreak occurring and its duration depend on the basic reproductive number, the prion-protein (PrP) genotype profile and the flock size. The model was validated using regional data from two postal surveys conducted in 1998 and 2002, which demonstrated that the model captures the spatial dynamics of scrapie (at least at a regional level). Moreover, the predicted distribution for the duration of a within-flock outbreak reflects the duration of outbreaks reported in the literature. Using the model to predict long-term trends in the proportion of affected flocks suggested that, even without control measures beyond the removal of animals with clinical signs, scrapie ultimately will disappear from the national flock, though it is likely to be decades before the disease is eliminated. However, there were scenarios consistent with the available data which suggested that scrapie could remain endemic within the British sheep flock. Consequently, it is essential to take this uncertainty in the long-term dynamics of scrapie into account when considering the efficacy of control strategies. Although control strategies were not explicitly examined, the model suggests two aspects important for control: larger flocks remain affected for longer and provide infection for other, smaller flocks and animal movements must be traceable.

Polygenic variation and transmission factors involved in the resistance/susceptibility to scrapie in a Romanov flock

Data from 4049 Romanov sheep belonging to a flock affected by natural scrapie were analysed by using survival-analysis techniques. Failure time was defined as the period of time between first exposure to infection and the date that animals left the flock with scrapie signs. Four hundred and forty-seven sheep were identified as ‘scrapie animals’. Several models, including level of exposure as a time-dependent effect, PrP genotype, sex, age at first exposure, litter size and factors related to vertical transmission, were tested. The best model was extended to a sire–dam frailty model, in order to estimate the polygenic variation in addition to that in the Prnp gene. A combined effect of rearing type and the dam's disease status was detected. Thus, only sheep with a low degree of exposure to infection as lambs (lambs reared artificially and born out of a healthy dam) showed less risk than others. Animals first exposed to infection at older ages seemed to be less susceptible to scrapie. In this Romanov population, new genotypes (AHQ/AHQ, AHQ/VRQ, ARR/VRQ and ARR/ARQ) were associated with risk, suggesting the effect of genotypes on the incubation period of animals. Polygenic variance was responsible for 21 % of the total genetic variability that was related to susceptibility to scrapie. Therefore, the genetic susceptibility to scrapie may be explained by the joint effect of point mutations at the Prnp major gene and a number of genes that modulate its effect.

Monte Carlo simulation of surveillance strategies for scrapie in Norwegian sheep

Our aim was to compare the efficiency of different surveillance strategies for detecting scrapie-infected sheep flocks in the Norwegian population using simulation modelling. The dynamic Monte Carlo simulation model has the flock as the unit. The input parameters include properties of the sheep population (number of flocks, flock size, age distribution, reasons for culling, breeds, prion protein-allele distribution); properties of scrapie (genotype-dependent infection rate and incubation periods, and age- and genotype-dependent prevalence of scrapie); properties of the surveillance strategy (selection of sheep for examination, period in which infected sheep are detectable, and properties of the diagnostic tests). For simplification, the prion protein-alleles were grouped into three allele groups: VRQ, ARR, and ARQ' (ARQ' represents ARQ, ARH and AHQ). Through either abattoir surveillance or surveillance of fallen stock, <or=9% of scrapie flocks were detected. The necessary sample size for detecting any particular number of scrapie flocks was considerably lower using surveillance of fallen stock than abattoir surveillance. After increasing the diagnostic method's sensitivity, only the efficiency of abattoir surveillance increased. The prion protein-genotypes ARQ'/ARQ', VRQ/ARQ' and VRQ/VRQ were overrepresented both in the sampled infected sheep and in the detected sheep. Sheep with ARQ'/ARQ' constituted >70% of the detected sheep (compared to 33% in the underlying population). The model output was sensitive to the susceptibility of infection for the genotype ARQ'/ARQ'. The effect was large for abattoir surveillance (increased susceptibility increased the efficiency of abattoir surveillance).

Epidemiological implications of the susceptibility to BSE of putatively resistant sheep

The experimental infection of sheep with bovine spongiform encephalopathy (BSE) by the oral route and the likelihood that sheep were fed BSE-infected meat and bone meal has led to extensive speculation as to whether or not sheep are naturally infected with BSE. In response, the UK government has initiated the National Scrapie Plan (NSP), an ambitious £120 million per year project to create a BSE- and scrapie-resistant national sheep flock, by selectively breeding for a genotype of sheep believed to be resistant to both diseases. This genotype has recently been shown to be susceptible to BSE by intracerebral (i.c.) inoculation. Should these sheep be sufficiently susceptible to BSE via natural transmission, the NSP might fail. Here we estimate the susceptibility of this genotype to horizontal (sheep-to-sheep) transmission of BSE by comparison with more extensive oral and i.c. exposure data for other sheep genotypes. We show that a previous estimate of the risk of BSE transmission to sheep via the feedborne route remains robust. However, using a mathematical model for the within-flock transmission of BSE, we show that, while the best estimate indicates that the NSP should be successful, current data cannot exclude the failure of the NSP.

Assessing the efficacy of a ram-genotyping programme to reduce susceptibility to scrapie in Great Britain

Susceptibility to clinical scrapie is associated with polymorphisms in the PrP gene. The 'ARR' allele of this gene reduces susceptibility to clinical disease caused by all known strains of the transmissible spongiform encephalopathy (TSE) agent. The British government proposes to use a ram-genotyping scheme to breed genetic resistance to clinical scrapie into the national sheep population. We considered how best to target limited genotyping resources to achieve the maximum rate of genotype evolution. We created a metapopulation model of the British sheep industry, which includes the major pure-breeds of sheep and the cross-breeds produced by crossing these pure-bred animals. The main criterion for assessing the efficacy of different strategies was the time taken to increase the prevalence of the ARR allele in the slaughter-lamb population. Our model predicted that the most-effective strategy would be to target genotyping to those rams used for pure-breeding (i.e. mated with the same breed of ewe). This strategy was compared to two further strategies, in which the proportion of rams genotyped in each breed depended on the prevalence of the ARR/ARR genotype in that breed. A policy in which the proportion of animals genotyped is reduced as the ARR prevalence in that breed increases is efficient. The most-effective policy was targeting the hill sector in the early years and gradually switching to genotyping more terminal-sire and longwool rams as the resistance of the hill sector increases.

The potential size and duration of an epidemic of bovine spongiform encephalopathy in British sheep

Because there is a theoretical possibility that the British national sheep flock is infected with bovine spongiform encephalopathy (BSE), we examined the extent of a putative epidemic. An age cohort analysis based on numbers of infected cattle, dose responses of cattle and sheep to BSE, levels of exposure to infected feed, and number of BSE-susceptible sheep in the United Kingdom showed that at the putative epidemic peak in 1990, the number of cases of BSE-infected sheep would have ranged from fewer than 10 to about 1500. The model predicts that fewer than 20 clinical cases of BSE in sheep would be expected in 2001 if maternal transmission occurred at a rate of 10%. Although there are large uncertainties in the parameter estimates, all indications are that current prevalence is low; however, a simple model of flock-to-flock BSE transmission shows that horizontal transmission, if it has occurred, could eventually cause a large epidemic.

Modelling the national scrapie eradication programme in the UK

In accordance with a policy to eliminate all transmissible spongiform encephalopathies from the food chain, a national untargeted ram breeding programme to eliminate scrapie in the UK is in the final stages of planning. Here we formulate a model of flock-to-flock scrapie transmission, in order to consider the effect of a targeted breeding programme which is in the early stages of consideration. We estimate the size of the susceptible flock population, and discuss implications for potential control programmes. Targeting all rams and ewes in highly susceptible flocks rather than rams in all flocks will eradicate scrapie more quickly, and so is likely to be beneficial as long as suitable penalties or incentives are available to facilitate their identification. A more restricted programme aimed only at highly affected flocks would be much easier to implement and crucially will eradicate scrapie just as quickly. This will leave behind a residue population of susceptible sheep, which could then be gradually removed by a more general breeding programme.

The sustainability, feasibility and desirability of breeding livestock for disease resistance

Selective breeding for disease resistance utilises proven animal breeding methods to improve animal health, welfare and productivity. Unsurprisingly, it is receiving more and more attention from livestock breeders. However, there are a number of largely theoretical arguments that have been raised as potential problems in selection for disease resistance. These can be classified under sustainability, feasibility and desirability. This review considers each of these areas in turn. Several examples show that enhanced resistance to disease is stable under natural selection and therefore deliberate selection for disease resistance should also be stable and sustainable. The feasibility of selective breeding depends in part upon the heritability of the trait or traits used to measure disease resistance, as well as the amount of variation among animals. The heritability of traits associated with resistance to many important diseases is often high and considerable variation among animals exists. Consequently, selective breeding for enhanced disease resistance is certainly feasible. The desirability of breeding for disease resistance depends upon whether there are trade-offs with other economically important traits. By and large these remain to be defined. However, even if unfavourable associations exist, breeders can create selection indices that include traits with unfavourable associations and maximise the desired responses while attempting to minimise undesirable effects. In conclusion, so long as one or more diseases exert a significant influence on livestock production, selective breeding will be a useful tool to assist in disease control.

The transmission dynamics of the aetiological agent of scrapie in a sheep flock

We formulate and investigate the properties of a model framework to mimic the transmission dynamics of the aetiological agent of scrapie in a sheep flock. We derive expressions for summary parameters that characterize transmission scenarios, notably the basic reproduction number R(0) and the mean generation time T(g). The timescale of epidemic outbreaks is expressed in terms of R(0) and cumulants of the generation time distribution. We discuss the relative contributions to the overall rate of transmission of horizontal and vertical routes during invasion and in endemicity. Simplified models are used to obtain analytical insight into the characteristics of the endemic state.

Scrapie transmission in Britain: a recipe for a mathematical model

Responses to an anonymous postal survey concerning scrapie are analysed. Risk factors associated with farms that have had scrapie are identified as size, geographical region, lambing practices and holding of certain breeds. Further analysis of farms that have scrapie only in bought-in animals reveals that such farms tend to breed a smaller proportion of their replacement animals than farms without scrapie. Farms that have had scrapie in home-bred animals have attributes associated with breeding many animals: large numbers of rams bought, few ewes bought, and many animals that are home-bred. The demography of British sheep farms as described by size, breeds, purchasing behaviour, age structure and proportion of animals that are home-bred is summarized. British farms with scrapie reveal certain special features: they have more sheep that are found dead, more elderly ewes and more cases of scab.

Mathematical models of Neospora caninum infection in dairy cattle: transmission and options for control

The transmission and control of Neospora caninum infection in dairy cattle was examined using deterministic and stochastic models. Parameter estimates were derived from recent studies conducted in the UK and from the published literature. Three routes of transmission were considered: maternal vertical transmission with a high probability (0.95), horizontal transmission from infected cattle within the herd, and horizontal transmission from an independent external source. Putative infection via pooled colostrum was used as an example of within-herd horizontal transmission, and the recent finding that the dog is a definitive host of N. caninum supported the inclusion of an external independent source of infection. The predicted amount of horizontal transmission required to maintain infection at levels commonly observed in field studies in the UK and elsewhere, was consistent with that observed in studies of post-natal seroconversion (0.85-9.0 per 100 cow-years). A stochastic version of the model was used to simulate the spread of infection in herds of 100 cattle, with a mean infection prevalence similar to that observed in UK studies (around 20%). The distributions of infected and uninfected cattle corresponded closely to Normal distributions, with S.D.s of 6.3 and 7.0, respectively. Control measures were considered by altering birth, death and horizontal transmission parameters. A policy of annual culling of infected cattle very rapidly reduced the prevalence of infection, and was shown to be the most effective method of control in the short term. Not breeding replacements from infected cattle was also effective in the short term, particularly in herds with a higher turnover of cattle. However, the long-term effectiveness of these measures depended on the amount and source of horizontal infection. If the level of within-herd transmission was above a critical threshold, then a combination of reducing within-herd, and blocking external sources of transmission was required to permanently eliminate infection.

The basic reproduction number for scrapie

The basic reproduction number R0 provides a quantitative assessment of the ability of an infectious agent to invade a susceptible host population. A mathematical expression for R0 is derived based on a recently developed model for the spread of scrapie through a flock of sheep. The model incorporates sheep demography, a long and variable incubation period, genetic variation in susceptibility to scrapie, and horizontal and vertical routes of transmission. The sensitivity of R0 to a range of epidemiologically important parameters is assessed and the effects of genetic variation in susceptibility are examined. A reduction in the frequency of the susceptibility allele reduces R0 most effectively when the allele is recessive, whereas inbreeding may increase R0 when the allele is recessive, increasing the chance of an outbreak. Using this formulation, R0 is calculated for an outbreak of scrapie in a flock of Cheviot sheep.

Population dynamics of scrapie in a sheep flock

A detailed analysis of an outbreak of natural scrapie in a flock of Cheviot sheep is described. A total of 137 cases was reported over 13 years among 1307 sheep born into the flock. The epidemiology of scrapie can only be understood with reference to sheep demography, the population genetics of susceptibility to scrapie, pathogenesis during a long incubation period, and the rate of transmission (by both vertical and horizontal routes), all of which interact in complex ways. A mathematical model incorporating these features is described, parameter values and model inputs are derived from available information from the flock and from independent sources, and model outputs are compared with the field data. The model is able to reproduce key features of the outbreak, including its long duration and the ages of cases. The analysis supports earlier work suggesting that many infected sheep do not survive to show clinical signs, that most cases arise through horizontal transmission, and that there is strong selection against susceptible genotypes. However, important aspects of scrapie epidemiology remain poorly understood, including the possible role of carrier genotypes and of an environmental reservoir of infectivity, and the mechanisms maintaining alleles giving susceptibility to scrapie in the sheep population.

Epidemiology and control of scrapie within a sheep flock

Mathematical models of the transmission dynamics of scrapie are used to explore the expected course of an outbreak in a sheep flock, and the potential impacts of different control measures. All models incorporate sheep demography, a long and variable scrapie incubation period, horizontal and vertical routes of transmission and genetic variation in susceptibility. Outputs are compared for models which do and do not incorporate an environmental reservoir of infectivity, and which do and do not incorporate carrier genotypes. Numerical analyses using parameter values consistent with available data indicate that, in a closed flock, scrapie outbreaks may have a duration of several decades, reduce the frequency of susceptible genotypes, and may become endemic if carrier genotypes are present. In an open flock, endemic scrapie is possible even in the absence of carriers. Control measures currently or likely to become available may reduce the incidence of cases but may be fully effective only over a period of several years.