SE3108Badger Perturbation
Appendix A. Badger perturbation model
Summary
The badger-TB model simulates spatial badger population dynamics in any region of the UK for which land-cover data is available. Given certain assumptions about the incidence of TB infection in groups, and the prevalence within an infected group, the model will simulate the spread of TB through the badger population. It can simulate the effects of a number of TB-control strategies, including culling on reactor land, with or without a live test to confirm TB presence before culling. The control options also allow removal of the whole group, or just infected badgers if a live test is implemented. The frequency and efficiency of culling (and sensitivity of testing) may also be varied in the model.
Introduction
Modelling techniques have been used extensively to analyse TB dynamics in badger populations; largely due to the impracticality of field experimentation. Models have been of two major types: analytical modelling and simulation modelling. Deterministic analytical approaches, such as Anderson and Trewhella (1985), Swinton et al. (1997) and Smith and Cheeseman (2002) are primarily strategic models, giving insights into the factors which control changes in the population structure. These models are useful for understanding principles of the disease dynamics, such as cyclicity and threshold population densities, but ignore badger social structure by assuming homogeneous mixing of populations. Furthermore, these models do not include stochasticity or environmental heterogeneity that are likely to be important in real landscapes in which badger-TB is a problem.
The second approach has been based on stochastic simulation modelling, (Smith et al., 1995; Smith et al., 2001; White and Harris, 1995). These are tactical models, attempting to deal with the detailed practicalities of TB control, and were spatially explicit in that the dynamics of the badger population and disease were simulated in a landscape of grid cells, between which animals were allowed to disperse. These authors analysed the conditions under which TB could remain endemic within badger populations and concluded that group size was important in determining spread. Smith et al. (1995) and Smith et al. (2001) went on to investigate the role of heterogeneity in group structure on the dynamics of the disease, and demonstrated that epidemiological models for homogeneously mixing populations were inappropriate because of the social structuring of badger social groups.
While these models have been used to predict disease dynamics of bovine TB in badgers and to investigate different control strategies (e.g. Smith et al., 1997; White et al., 1997; Smith et al., 2001), none of them have considered the disease problem in real landscapes. Dispersal and disease epidemiology is non-homogeneous in natural populations. The social and territorial organisation of badgers (Kruuk & Parish, 1987; Rogers et al., 1997; Rogers et al., 1999; Delahay et al., 2000) results in differential rates of contact between individuals of different social groups, and reduced rates of contact between territories separated by distance or landscape features. Since contact rates are dependent on spatial organisation of badger territories, there is clearly a need for a spatially explicit model which examines the relationship between the behaviour of individuals and the spread of TB (Ruxton, 1996).
Aims and objectives
The aim of this project was to integrate modelling approaches with fieldwork on the perturbation of badger populations to understand better disease transmission over wide spatial scales, and to assess the effectiveness of different control strategies. All existing models of the badger-TB system agree that the effectiveness of different control strategies on the social-spatial organisation of badgers should be known, or at least considered, as they might seriously influence the success of the strategy employed. However, no single model accurately simulates the perturbation effects or the disease dynamics as observed in Nibley. This is largely due to the lack of data to parameterise the models and the poor feedback between theoretical models and the data from the field.
In this project we developed a spatially explicit model to investigate the dynamics of TB and badger populations, based on the approach by Smith et al., (1997). Spatially articulated models have been used to investigate the effects of disease transmission between sympatric species of squirrels in the UK (Rushton et al., 2000), and control strategies such as immunocontraception to control grey squirrels (Rushton et al., 2002) and possums (Barlow, 1994). In contrast to previous approaches, the model relies on observed social group boundaries to simulate population and disease dynamics rather than a grid-based representation of social structure. The portability of the model was also a key issue, so a user interface (integrated with a Geographic Information System) was added to allow the user to specify any region within the UK to run the model; and to accommodate the spatial distribution of badger populations and herd breakdowns. It is possible to use the model to provide real-time decision support, but its primary purpose is in the planning of a management strategy for bovine tuberculosis.
Description of the model
Upon starting the model, it launches a user interface which guides the user through the parameters needed to achieve the desired scenario.
Screen-grab of the main menu
The six groups of parameters are described in the following sections.
1) Location
The model will operate anywhere in the UK for which habitat data are available (Figure 1). Currently, simulations have been confined to the Thames valley, for which GIS land cover data of habitat type is available. The region modelled can be of practically any size, although most simulations have been conducted on a 8 km x 8 km square (Figure 1, highest resolution image, on right)
The easting and northing of any location for which GIS information if available can be input by the user. These co-ordinates represent the centre of a square in which the simulation will take place; and the width/height of the square must also be provided. The model then extracts the entire habitat in this square which is usable by badgers into a separate map.
As an example, we will present model output in this report for the 8km x8km square indicated in Figure 1, which is situated between Swindon and Oxford.
Figure 1: The landscape of the Newcastle badger-TB model
2) Badger populations
Badgers exhibit great variation in their social behaviour, which is believed to be adapted to the landscape in which they live, and the availability of food (Kruuk and parish, 1982). In Scotland, they achieve maximum densities of 8 km-2, whereas in south-west England, the densities are much higher (up to25.3 km-2, Rogers et al., 1997). In sub-optimal habitats, badgers may be solitary, or live in pairs rather than living in social groups (Kruuk and Parish, 1982).
The badger modelling system allows all these variations to be taken into account through the first three parameters on the “Badger Populations” screen.
Screen-grab from the Population option of the main menu
The density of badger groups, the minimum distance between setts and the average number of badgers per group sum up the socio-spatial pattern of badger groups.
First, all habitat in the chosen area which is not suitable for badgers is removed from the map.
Next, random points are uniformly distributed across the badger-suitable landscape map, at the density chosen by the operator.
Then, Thiesson polygons are created around each random point, and limited to a maximum size by drawing a radius from the central point equal to the inter-sett distance chosen by the operator. These polygons represent the badger territories.
From this map, group-neighbourhood files are created, describing which groups have contiguous boundaries with others.
Finally, the groups are filled with badgers. The average group size is a user-defined input, and the age/sex distributions observed in the high density badger population of WoodchesterPark were used to determine the composition of each group. Additionally, the TB-prevalence input is used to determine the TB status of each badger; those that are determined to be infected are set at the excretor phase of infection.
3) Badger Removal Operation implemented
A number of different control strategies have been included in the model, and their effects can be compared in terms of TB prevalence, incidence and badger social behaviour.
The following Badger Removal Operations (BROs) are possible:
A proactive cull, in which badger populations are monitored, and periodically culled in an attempt to control TB incidence. Under this option, badgers may be culled without monitoring their disease status; or else the effects of a live ELISA test for M. bovis may be simulated. Under the latter option, either individuals with TB may be targeted by the badger removal operation, or all members of a group with an ELISA-positive badger may be culled. In the proactive cull scenario, the frequency of the monitoring program, the efficacy of catching badgers, and the sensitivity of the live test (if used) can all be varied.
A reactive cull is implemented in response to a herd breakdown. To simulate this procedure, the user must supply the year in the simulation in which the breakdown occurs. Once again, the simulation of a live test is possible, and the results of the test deciding which badger will be culled. The efficacy of catching badgers and the sensitivity of the live test (if used) once again may be varied.
The region in which the BRO takes place can be supplied in three forms. Firstly, if simulating the effects of culling in the 10km x 10km “hotspots” suggested by Krebs (1997), or implementing a wide-scale control of badger populations, the whole region may be chosen. If the intent is to investigate the effects of different control strategies, then a random region of the map can be the focus of badger control strategies. Finally, the user can provide the co-ordinates of a specific point in the map in which the BRO takes place. This option is useful when investigating the effects of a specific herd breakdown. For the latter two options, the user must supply the size of the area to be affected by the control strategy.
Screen-grab from the BRO option of the main menu
4) Life history variables
The life history variables in the model control the individual processes of badger populations – fertility, fecundity, mortality and dispersal probability. These variables vary according to the sex and age of the individual badger, and the time of year. There are therefore 23 life-history variables in the model.
These variables have only been measured in detail at WoodchesterPark, and currently, the model does not allow the values of these variables to be altered by the user.
5) TB transmission variables
The transmission of TB in badger populations is poorly understood, and data on the probability of passing from one state of infection to another is only available for a single population, that of WoodchesterPark. In addition, the additional mortality incurred by a TB infection is only available from the WoodchesterPark population. Furthermore, the initial infection rate (either between or within groups) has proved impossible to parameterise empirically. Shirley et al. (2003) derived values for infection rate in this simulation model that produced a pattern of TB spread that most closely matched that observed in the field data; these are the only values available for these parameters. Consequentially, it is not possible for the user to input TB transmission rates; instead these are set at the values given in Table 2.
The user can choose from three scenarios of between-group transmission of TB, which depends on the assumptions about the temporary movements of badgers throughout the year, and the territorial behaviour of badgers (and whether these behaviours can result in TB transmission, through aggression or territory marking). The three possible behaviours are a) transmission of TB only to direct neighbouring groups (accounting for territorial behaviour only); b) transmission both to their neighbouring groups and their neighbour’s neighbours (which is the observed limit of temporary movements of badgers between groups); or c) transmission to any group in the modelled area. These three scenarios will affect the speed of transmission.
6) Model specifications
This section allows the user to specify how many years of simulation to perform, and how many replicates of each model run are desired.
Screen-grab of the default program parameters
The Simulation model
The user-defined inputs are then used by a number of different processes to produce the input for the badger-TB core simulation model, as described by the diagram below.
The model is an individual-based model with the age, TB status and sex of each badger in each social group as the state variables (Figure 3). The model interrogates each badger at six-month time steps to determine stochastically the life history of the individual. Life history ‘decisions’ are made using a probabilistic approach, each individual having a particular chance that it will become infected or pass into the next stage of the disease (depending on TB status), change social groups and die (both based on age and sex), and, if female, breed.
The first 6-month season each year is the spring / summer season, and includes subroutines governing reproduction, TB transmission, TB-induced mortality, natural mortality and movement (Smith et al., 1995; Smith et al., 1997). The second season, representing autumn / winter, includes all these subroutines except for reproduction, which in badgers only occurs once a year. Values for each of the life history and disease transmission parameters (Tables 1 & 2) all operated on a six month timestep.
Female badgers produce only one litter each year (usually one to five cubs), with the majority giving birth between mid-January and mid-March (Neal & Cheeseman, 1996). In high density populations usually only one female per social group produces a litter, although others may also breed if sufficient setts and resources are available (Cresswell et al., 1992; Woodroffe & Macdonald, 1995). To this end, the process of reproduction is modelled as a sequential Markov chain: there is a base probability that a female will produce a litter and if she does, the model checks to see if a second female (if present) produces a litter, and so on. This allows for variation between years based on the assumption that there is a fluctuating resource to support multiple breeding females in a social group. The number of cubs in each litter is determined by a cumulative probability distribution, based on field data collected at WoodchesterPark (unpublished).
Dynamics of bovine tuberculosis
Amongst badgers, bovine tuberculosis is thought to be spread in four major ways: as a respiratory aerosol; during aggressive encounters involving bite wounds; at latrine sites and by vertical (or pseudo-vertical) transmission between mother and cubs (Anderson & Trewhella, 1985; Cheeseman et al., 1988). When healthy badgers become infected, they are assumed to undergo a latent period before becoming infectious themselves. A tracheal aspirate taken from an infectious badger has a positive reaction in an ELISA test for Mycobacterium bovis; although no other bodily fluids contain the bacillus. A small proportion of badgers (particularly adult males) become ‘super-excretors’ (Smith et al., 1995); who test positive for the TB bacillus in saliva, urine, faeces, semen and in open bite wounds, in addition to the tracheal aspirate; and therefore have a higher transmission rate than normal excretors.
Following Smith et al. (2001; 2001) all badgers in the model are assumed to be in one of four health stages: healthy (i.e. uninfected), latent (i.e. infected but not infectious), excretor, or super-excretor (Figure 4). Only the last two stages can infect other badgers. Since super-excreting badgers shed such a high amount of M. bovis in all bodily fluids, it is assumed that badgers have twice the probability of becoming infected with TB from a super-excretor than from an excretor (Smith et al., 2001). Healthy badgers become latent by one of two transmission mechanisms, one governing within social-group infection (where an excretor or super-excretor could infect any healthy member of the same social group, with frequency HLwithin/2 and HLwithin respectively) and the other governing between social-group infection (where an excretor or super-excretor could infect any healthy member of any social group determined by the neighbourhood designated by the user, with frequency HLbetween/2 and HLbetween respectively). Latent badgers can become excretors or super-excretors (at frequencies LE and LS); and excretors can become latents or super excretors (with frequency EL and ES).
Figure 4: The interaction between the TB state-transition parameters in the model
Mortality
Natural mortality data for the model varies according to age, sex and season (Table 1). Only super-excreting badgers suffer life-history consequences from TB infection (Wilkinson et al., 2000). Mortality due to TB infection is assumed to be additive and was assessed before natural mortality.
Movement
High density badger populations such as the one at WoodchesterPark are typified by a low level of movement of individuals between social groups (Cheeseman et al., 1988; Woodroffe & Macdonald, 1993). Rogers et al. (1998) found that 73.1% of badgers (n = 208) that changed social groups between 1978 and 1995 were ‘occasional movers’ and 22.1% were ‘permanent movers’. Of the 703 recorded movements of badgers between social groups in the study area, the majority occurred between neighbouring groups. Consequentially, badgers in the model could move to social groups whose territories where adjacent to the territory of their current social group.