Dr Michael Hutchings, Animal Health, SAC, Bush Estate, Penicuik EH26 0PH, UK. Tel: 0131 5353231; Fax: 0131 5353121; E-mail: firstname.lastname@example.org
1Paratuberculosis (Mycobacterium avium subspecies paratuberculosis; Map) is a widespread and difficult disease to control in livestock populations and also has possible links to Crohn's disease in humans. Rabbits (Oryctolagus cuniculus) have been identified recently as the key wildlife species in terms of paratuberculosis transmission to the wider host community. Here, we test the hypothesis that Map can persist in rabbit populations for extended periods of time in the absence of any external source of infection.
2A spatially explicit stochastic simulation model of a generic host–disease interaction was developed to quantify the interplay between vertical and horizontal routes of transmission needed for the persistence of Map in rabbit populations and to test the hypothesis. The model was parameterized based on empirical studies on rabbit population dynamics and on rabbit-to-rabbit routes of Map transmission.
3Predictions from the model suggest that any disease with susceptible–infected (SI) dynamics without disease-induced mortality can persist within a rabbit population in the absence of vertical transmission, providing the horizontal transmission coefficient, β, is greater than approximately 0·012. The inclusion of any vertical transmission reduces the value of β that is necessary for infection to persist.
4Paratuberculosis persists in rabbit populations at all values of the horizontal and vertical transmission parameters in the range estimated from the field data and in many cases at all values within 95% confidence intervals around this range. The persistence of Map infection in rabbit populations in the absence of external sources of infection suggests that they may act as a reservoir of infection for sympatric livestock.
5Synthesis and applications. Our findings, in combination with the ubiquitous distribution of rabbits in the United Kingdom and elsewhere, suggests that if Map becomes established in rabbit populations they are likely to provide widespread and persistent environmental distributions of infection and thus disease risk to livestock and potentially humans. Where local rabbit populations are infected they should be included in any future paratuberculosis control strategies. Because eradication of rabbits is often not a realistic option, control strategies should include reducing interspecific transmission risk from rabbits to livestock via the faecal–oral route.
Paratuberculosis (also known as Johne's disease) is a chronic, usually fatal, enteritis of wild and domestic ruminants, with purported links to Crohn's disease in humans (Naser et al. 2004), caused by Mycobacterium avium ssp. paratuberculosis Bergey (Map). It causes not only great economic losses, but also welfare issues, for the agricultural industry world-wide (Chiodini, van Kruiningen & Merkal 1984; Sweeney 1996). The disease is notoriously difficult to control in ruminant livestock populations and this, coupled with the recent detection of the presence of the causal bacteria in a number of non-ruminant wildlife species, including the fox Vulpes vulpes Linnaeus, stoat Mustela erminea Linnaeus, rat Rattus norvegicus Berkenhaut, wood mouse Apodemus sylvaticus Linnaeus, crow Corvus corone Linnaeus and rabbit Oryctolagus cuniculus Linnaeus (Greig et al. 1997, 1999; Beard et al. 2001a,b), has led to the suggestion that there may be a wildlife reservoir for the disease. If a wildlife reservoir of Map is confirmed (i.e. the disease persists in wildlife populations in the absence of external sources of infection), any disease control strategy aimed at controlling or eradicating the disease in domestic livestock must include control or eradication of the infection in the wildlife host.
Carnivorous species (e.g. foxes) have higher prevalence of Map infection than their prey species (e.g. rabbits) (85% and 22%, respectively; Beard et al. 2001a,b). However, despite the high prevalence in carnivores, the level of infection (i.e. parasite burden) is far lower than that in their prey species, suggesting that carnivores are dead-end hosts for paratuberculosis (Daniels et al. 2003). It is thought that the main route of paratuberculosis transmission to carnivore species is through the ingestion of infected prey species (Daniels et al. 2003). Rabbits are a major prey item for species such as the fox in Scotland (Harris & Lloyd 1991; King 1991a,b; Leckie et al. 1998); therefore, it is suggested that rabbits are the key species in terms of transmission to other wildlife hosts.
Rabbits have a high prevalence of Map and a relatively high level of infection in their tissues compared to other non-ruminant wildlife hosts (e.g. foxes), excreting up to 106 colony-forming units per gram of faeces (Beard et al. 2001c; Daniels et al. 2003). Furthermore, livestock pastures often have high levels of rabbit faecal contamination. This combination presents a risk of transmission of Map from rabbits to livestock via the faecal–oral route. This risk is especially high due to the lack of behavioural avoidance of rabbit faecal pellets by cattle when grazing, resulting in cattle ingesting a similar proportion of rabbit faecal pellets across a range of levels of contamination (Judge et al. 2005a). This is unusual, as in all other cases, all else being equal, livestock avoid the faeces of their own and other species while grazing (Hutchings & Harris 1997; Bao, Giller & Stakelum 1998; Hutchings et al. 1998; Cooper, Gordon & Pike 2000; van der Wal et al. 2000). Risk of paratuberculosis transmission from rabbits to cattle is therefore proportional to rabbit density. For example, on Scottish farms with a history of paratuberculosis in wildlife and livestock, this lack of avoidance results in cattle ingesting up to 3700 rabbit faecal pellets each per hectare grazed, of which up to approximately 1300 could be infected (Judge et al. 2005a). All the current evidence therefore points to rabbits as the key wildlife host in terms of interspecific transmission of the disease to both wildlife and livestock (Judge et al. 2005b).
Recent research suggests that transmission of Map may occur within rabbit populations via vertical, pseudo-vertical and horizontal routes (Judge et al. 2006). The presence of these routes will help to maintain the infection in rabbit populations. For a host to be considered a reservoir for a disease, the infection must show evidence of persistence within the host (Cleaveland & Dye 1995). Assessing the host status in the epidemiology of a disease is crucial to disease control (Caley & Hone 2006). Here, we use a spatially explicit stochastic disease–host simulation model to address this. The model is parameterized for the rabbit–Map interaction using rabbit demographic rates from the literature combined with empirical field studies of the routes of Map transmission. The model incorporates the aspects of the behavioural ecology of rabbits that potentially affect the routes of Map transmission identified previously. The structure of rabbit populations creates heterogeneities in intraspecific social contact rates as rabbits live in small social groups (Bell 1983) and the majority of social interactions occur between members of the same group, rather than between members of neighbouring social groups (Cowan 1987). These types of interactions, whereby individuals spend the majority of their time in spatially defined subpopulations, regularly contacting the same, small number of individuals, are best captured using spatial stochastic modelling techniques (de Jong et al. 1994; Mollinson & Levin 1995). The aim of the study is therefore to use this type of modelling approach to determine whether Map infection can persist in rabbit populations, and specifically to address the interplay between the horizontal and vertical components of Map transmission in enhancing its persistence.
The model is a continuous time, stochastic process, with state-space defined by the sex, age class, disease status and location (social group) of each animal, and in any given time each possible event (e.g. birth, maturation, death, infection and movement of individuals) may occur with a specified probability. Individuals spend a fixed amount of time t0 in the infant age class, but all other events are Markovian with associated probability distributions defined solely in terms of the relevant rates (see, e.g. Renshaw 1991). In brief, this stochastic process is simulated by specifying rates for the various event types and calculating their sum. The time step is then set such that the probability of two events occurring in a single step is negligible. The unit interval is then divided into segments in the ratio of the rates. Stochastic event simulation occurs by picking a random number between zero and one which triggers the corresponding event. In this type of stochastic process, for any given model run (realization of the stochastic process) the actual number of occurrences of a particular event need not coincide exactly with the specified rate for that event type, but none the less the average number over many realizations will converge to the event rate. For this reason many realizations must be generated in order to present meaningful results (e.g. means, variances or distributions) from a stochastic model. Below we describe the formulation of the model in more detail in terms of its demographic and epidemiological components. We then discuss the parameterization and describe the model runs performed.
rabbit population dynamics
Rabbits live in small social groups (Bell 1983), therefore the population in the model is divided into distinct social groups, each with an adult carrying capacity. Males and females belong to one of three age classes (infant, adolescent and adult), as shown in Fig. 1. Adult females give birth at a rate Rb. Newborns spend a fixed amount of time t0 in the infant class, after which they are promoted into the adolescent class. Once in the adolescent class each individual has a rate κmm (males) or κmf (females) at which they mature into the adult class. Individuals in all three classes have death rates µi, µam (µaf), and µmm (µmf) for infants, adolescent and mature males (females), respectively. There is no disease-induced mortality as rabbits appear to be asymptomatic (Beard et al. 2001b).
Individuals in the adolescent class leave it by selecting a waiting time from an exponential distribution with rate constant ram for males or raf for females. Upon entering the adult class they may either enter the mature class of their natal group, with probability πm (πf), or disperse probability rmm (rmf). The majority of dispersal events are to other social groups within a relatively small distance of the natal group (in real terms up to approximately 250 m; Cowan 1991a). However, within this ‘local’ dispersal, individuals and especially males tend not to disperse to neighbouring groups. This is thought to be a mechanism to avoid inbreeding (Webb et al. 1995) and is simulated using spatial effects in the local dispersal mechanism whereby each group is assigned a position in a two-dimensional domain augmented with periodic boundary conditions. In the case of a local migration event, an individual chooses a group other than the one it has just left, with selection probabilities weighted by a distance-dependant factor
f(x) =Cxe−αx( eqn 1)
where x is the distance between the two groups and α is the mean dispersal distance.
As, in some cases, dispersal further afield does occur (Cowan 1991a), there is a second, ‘global’, dispersal mechanism. When global dispersal occurs, the individual chooses a group other than that from which it came at random. Individuals disperse either locally or globally with a probability pl. For both local and global dispersal, once a group has been selected the animal enters the mature age class of that group with probability
( eqn 2)
in which n is the number of individuals in the mature age class of the group and N is its carrying capacity. If the individual is not accepted it dies. This acts as a density-dependent mechanism limiting population size.
The model assumes a simple susceptible–infected (SI) dynamic for the disease, with individuals being either susceptible (S) or infected (I) without the possibility of recovery or immunity. This is because hosts are not thought to recover from Map infection (Chiodini, van Kruiningen & Merkal 1984), and there is no disease-induced mortality as rabbits appear to be asymptomatic (Beard et al. 2001b).
Vertical (i.e. transplacental) and pseudo-vertical transmission (e.g. via milk or faeces ingestion from the mother) are combined into a single process, referred to subsequently simply as vertical transmission, modelled by specifying a probability pv with which an infected individual emerges into the population post-weaning conditional upon it having an infected mother. Individuals emerge at an age α0, generally set to be equal to 1 month. Vertical transmission can occur only from an infected adult female to her offspring. Individuals in the infant age class cannot become infected nor pass on infection via horizontal transmission as they are not mixing with the rest of the social group at this age. Horizontal disease transmission can occur only between post-infant members of the same social group as the vast majority of social interactions, and therefore opportunities for disease transmission, occur within social groups. Within each social group the horizontal transmission rate per susceptible member is proportional to the number of infected post-infant individuals and the coefficient β. The intersocial group route of transmission (not including dispersal) was expected to occur infrequently and was set to zero to ensure a conservative test of our hypothesis.
The rabbit population dynamics and disease parameter values are given in Table 1. All rates are expressed as per month and therefore 1 unit of model time corresponds to 1 month real-time. The parameters defining rabbit demography were obtained from the literature sources noted in Table 1. The estimations of the disease transmission parameters are taken from data collected in a previous study from a low- to moderate-density wild Scottish population of rabbits naturally infected with Map, in which a maximum likelihood fitting procedure was used to derive probabilities of vertical and horizontal transmission from the field data (Judge et al. 2006). The probability of transmission via vertical routes pv is 0·326. The horizontal transmission coefficient per month (β) based on the monthly per capita rate of infection from the empirical study was estimated to be in the range between 0·013 and 0·046 (Judge et al. 2006). For a two-parameter maximum likelihood inference procedure, we obtain 95% confidence ellipses around the minimum, middle and maximum β-values by assuming that the deviation of the likelihood function (used by Judge et al. (2006) to estimate β) from its maximum value is χ2 distributed (Kendall 1999).
Table 1. Model parameter definitions and value estimates. Rates are given for a time interval of a month
The model was run using the parameter values listed in Table 1, initializing the population by allowing new individuals to migrate into the system for an initial period at a mean rate of 50 individuals per time step for 10 time steps, after which the system was isolated from external influences. After the external immigration was stopped the model was run until the population reached equilibrium. Next, a sample of individuals was infected and once again the model was allowed to reach equilibrium. Both the population and disease prevalence reached average equilibrium levels that were independent of the parameters associated with these initialization processes as long as they were not chosen to be too small. Excessively small initial values may give rise to a non-negligible probability that the disease or population may die out before equilibrium is reached.
In order to obtain statistics describing the output of the stochastic model, 100 simulations of each combination of the vertical and horizontal transmission parameters were carried out. As the initial population dynamic parameters were taken mainly from studies of unmanaged populations, whether natural or captive, the population reaches equilibrium at near to carrying capacity. However, rabbit populations on agricultural land are often far from carrying capacity. Therefore, the death rates were increased to 0·141 for adults, 0·734 adolescent males and 0·275 for adolescent females to provide a population that reached equilibrium at approximately 50% of the carrying capacity. Re-running the model with all other parameters remaining the same then produced an alternative more conservative set of results.
The model suggests that any disease with SI dynamics without disease-induced mortality can persist within rabbit populations in the absence of vertical transmission as long as the horizontal transmission coefficient (β) is greater than 0·012 (Fig. 2). In rabbit populations at approximately 50% of carrying capacity, β must be above approximately 0·025 for disease to persist with only horizontal routes of transmission (Fig. 3). The inclusion of any vertical transmission reduces the amount of horizontal transmission necessary for persistence.
Disease prevalence increases non-linearly as the vertical transmission probability and the horizontal transmission rate increase. Increases in β have a much greater effect on overall prevalence at values up to 0·01 at high and 0·03 at low rates of vertical transmission, respectively. Above these values, increases in β have relatively little effect on the overall prevalence. Conversely, an increase in the vertical transmission rate has a notable effect on overall prevalence at all β-values (Figs 2 and 3). A 0·1 increase in the vertical transmission probability has a roughly equal effect on the increase in overall prevalence; this increase is slightly higher at lower levels of β than at higher levels. For example, at a β of 0·02 a 0·1 increase in vertical transmission leads to an increase in prevalence of approximately 7·5% and at a β of 0·05 the same increase in vertical transmission leads to an increase in overall prevalence of approximately 5% (Fig. 2).
The interactions between the vertical transmission probability and the horizontal transmission coefficient have different effects on the pattern of prevalence in the three age classes (Fig. 4). For all age groups, at β-values up to 0·01 a small increase in β leads to a large increase in disease prevalence. As would be expected, changes in the vertical transmission rate have a much greater effect on prevalence in infants than the other two age groups. For infants an increase in the β-value above values of 0·02 has almost no effect on the prevalence of disease; however, a 0·1 increase in the vertical transmission rate leads to an approximately 10% increase in prevalence. At lower levels of β, the same increase in vertical transmission leads to a slightly higher, non-linear, increase in prevalence (Fig. 4a). With the adolescents, again once the β-value is above 0·02 any increase in β has a relatively small effect on the increase in prevalence, although the increase is greater than for either infants or adults (Fig. 4b). In adults, by a β-value of 0·02, prevalence has already reached 55% without any input from vertical transmission. An increase in β above this value leads to a small increase in prevalence (Fig. 4c).
In the case in which the population is near carrying capacity, the entire estimated range of transmission parameters as well as all of the 95% confidence regions surrounding each point within that range lie in the area corresponding to a stable infection. The lower end of this range represents highly conservative estimates for these parameters (Judge et al. 2006). For the case where the population is maintained at approximately half that of the carrying capacity, the confidence intervals around the conservative end of the range of estimates reaches into the unstable region.
The results of this study provide a general framework to determine the persistence and prevalence of infections (following SI dynamics) in rabbit populations for which the rates of vertical and/or horizontal transmission are known. Rabbit population dynamics are well studied, providing robust parameter estimates (see Table 1). However, there will be some variation in parameter values according to specific geographical locations (e.g. environmental and management conditions). To account for this, a highly conservative approach was built into the design of the model (for example, restricting intersocial group transmission routes to dispersal only) and into the model parameter estimates (for example using full 95% confidence intervals around the conservative extreme of the range of β-values). This conservative modelling approach should compensate for the effects of minor variations in parameter values on disease dynamics and to ensure a robust test of the hypothesis for rabbit populations in the United Kingdom and populations elsewhere with similar social structures.
The prevalence of disease in rabbits at the different rates and combinations of rates of transmission shown in Figs 2 and 3 would apply for any disease with SI dynamics without disease-induced mortality affecting rabbit populations. The interaction between the two transmission rates has the greatest effect on overall prevalence at lower horizontal transmission rates, particularly at β-values below 0·01, which results in the pattern of the isopleths seen in Figs 2 and 3. Small increases in β combined with vertical transmission rates above approximately 0·4 result in large increases in overall prevalence. This is because as the number of infected adults increases with the increase in β, a much greater number of individuals are infected through vertical transmission. This increases the mean prevalence in all age groups (Fig. 4) and therefore the overall prevalence. Once β is greater than 0·02 at any vertical transmission rate the adult age group is already saturated with infected individuals; therefore, even a relatively large increase in β leads to only a small increase in individuals infected via horizontal transmission.
At lower vertical transmission rates, increases in β have a relatively large effect on overall prevalence up to β-values of approximately 0·03. After this point, once again the adult age group is reaching approximately 85% infection prevalence; therefore, increasing the rate of horizontal infection does not result in a notable increase in the proportion of infected individuals (Fig. 4c). However, at these low rates of vertical transmission the prevalence in the infant and adolescent age groups is still relatively low (Fig. 4a,b) resulting in a lower overall prevalence of infection, even though the prevalence of infection in adults is similar to the situation described above. Increases in vertical transmission have a relatively large effect on overall prevalence at all rates of β.
The main aim of this study was to test the hypothesis that Map infection persists in rabbit populations, the first step in identifying rabbits as a reservoir for the disease. This was confirmed for a population which has been allowed to grow unhindered to reach a level near its carrying capacity. For the most conservative estimate for β the equilibrium infection prevalence ranged within the area defined by a confidence level of 95%, from 10% to 65%. When the population is maintained continuously at around 50% of carrying capacity the overall prevalence falls. In this case a small segment of our 95% confidence region on the most conservative transmission parameter estimate lies outside the stable region.
The lowest vertical transmission rate used in the model simulations is likely to be highly conservative and much lower than the actual rate, e.g. due to the low sensitivity of the culture methods at the low levels of infection that would be expected in young individuals (Judge et al. 2006). Judge et al. (2006) concluded that the actual β-value would be towards the higher end of the estimated range. Furthermore, the conservative approach adopted at each stage of model development and parameterization and the addition of the 95% confidence interval around the already highly conservative point estimate for β supports the conclusion that infection is likely to persist in rabbit populations for extended periods.
One factor that may counterbalance the arguments for the actual β being toward the highest end of the estimated range is that the horizontal transmission rate estimated from the field data includes interspecies transmission from livestock. However, it is thought that the risk of interspecies infection is likely to be very low (Judge et al. 2006). The main route of interspecies transmission is the faecal–oral route; as rabbits are highly selective grazers, with the ability to select individual blades of grass (Foran, Low & Strong 1985), it seems unlikely that they would ingest faeces accidentally while grazing. The inclusion of interspecific transmission is therefore thought to have a negligible effect on the transmission coefficient (β-value); however, an effect of interspecific transmission cannot be ruled out.
The prevalence of Map infection in the study site from which the transmission rates were estimated was 39·7%. This falls well within the ranges of prevalence produced by the model for the estimated range of transmission values at both simulated population levels. The evidence points to an infection which could persist permanently without disease input from any other source, fulfilling the criteria for being a reservoir set out by Cleveland & Dye (1995) and Haydon et al. (2002). Therefore, it is imperative that the role of rabbits in the transmission and persistence of this disease are taken into account in any paratuberculosis control or eradication strategy for livestock. For example, de-stocking is often considered as a means of disease control in livestock populations, and is being used to attempt to control paratuberculosis in livestock in Australia under the National Ovine Johne's Disease Control and Evaluation Program (Sergeant 2001; Whittington et al. 2003). However this strategy fails to include rabbits and, in particular, the longevity of the disease in rabbit populations and is therefore likely to be unsuccessful if the rabbits are infected. Furthermore, the possibility of the disease spreading from infected livestock farms to previously uninfected livestock areas through the dispersal of infected rabbits needs to be considered in control strategies.
It would seem unrealistic to eradicate rabbits at the scales necessary to control disease in livestock systems in the current hotspots of disease in the United Kingdom (Judge et al. 2005b). Consequently, management of any disease for which rabbits are a reservoir would most probably be restricted to rabbit population management (e.g. keeping populations densities low), managing livestock–wildlife interactions (e.g. keeping animals, especially the most susceptible animals, away from areas with high rabbit densities) and good livestock management practices in terms of husbandry and movement between herds. The persistence of Map infection in rabbit populations at 50% of carrying capacity predicted by our model indicates the high level of population control effort needed if disease eradication was to be attempted in rabbits. At the present time, paratuberculosis in rabbits in the United Kingdom is thought to be confined largely to the eastern regions of Scotland (Greig et al. 1999). If the disease could spread through rabbit-to-rabbit transmission, as suggested above, and rabbit control is a feasible option, with no counter-productive effects such as disturbance of the social structure leading to potential increases in contacts and disease spread (see Woodroffe et al. 2006), it should be implemented in these areas sooner rather than later before significant spread of the disease via this route occurs. World-wide, rabbit population structure varies according to environmental and climatic conditions (Cowan & Garson 1985; White et al. 2003). Such variation will have an impact on contact networks and therefore also on the threshold population densities required for Map persistence. Improved knowledge of the variation in behavioural ecology of rabbits throughout their distribution will allow models such as the one used here to be parameterized according to specific local conditions, enhancing their usefulness for strategic wildlife management planning.
This project was part-funded by the European Union (Qlkzct-2001-00879). SAC and BioSS receive support from the Scottish Executive Environment and Rural Affairs Department (SEERAD). M. R. Hutchings holds a SEERAD Senior Research Fellowship. We thank two anonymous reviewers for helpful comments on the manuscript.