Download Models for FMDV transmission in Australian feral goats

Models for FMDV transmission in Australian feral goats and merino
sheep.
Fleming, P.J.S., Tracey, J.P., and McLeod, S.R.
Vertebrate Pest Research Unit, NSW Department of Primary Industries, Orange, Australia
Abstract
Feral goats and sheep commonly co-occur in Australia and models are the most effective means of
examining the dynamics of exotic disease transmission within and between the species. This paper
discusses appropriate models given the social behaviour, population dynamics, contacts within and
between species, and habitat use of feral goats and merino sheep. Both species occurred at high
density at a site in central eastern New South Wales used to parameterise models of foot-and-mouth
disease (FMD) dynamics, and hence contacts were likely to approach maximal values and the
models were likely to represent the upper extreme of transmission.
Simple temporal models with homogenous mixing and a lattice-based spatial model reflecting the
social and movement ecology of free-ranging feral goats and sheep were constructed. The temporal
models predicted that FMD would spread rapidly throughout infected herds of feral goats and flocks
of sheep and become endemic if no controls were exerted. In contrast, the spatial model
incorporating the social structure and habitat use of feral goats and paddock use by sheep predicted
that FMD would die out in a mixed species community in less than 90 days. This was because of
inadequate contact between higher order groups such as herds, flocks and populations. Our paper
emphasises the difference in outcomes that may result from models that ignore or incorporate
animal behaviour.
Introduction
“Make everything as simple as possible, but not simpler.” (Albert Einstein)
Epidemiological models can aid contingency planning for controlling exotic disease outbreaks. The
OIE-listed foot-and-mouth disease (FMD) is exotic to Australia where livestock production is
important to the economy. Sheep (the most numerous of Australian livestock) and goats have been
implicated in the spread of FMD virus (FMDV) and in the maintenance of FMD in countries where
FMD is endemic (Barnett & Cox 1999), particularly North African epidemics in sheep caused by
FMDV type O (Samuel et al. 1999). Feral goats (Capra hircus) and sheep commonly co-occur in
high rainfall, temperate eastern Australia, where climatic conditions are believed likely to favour
transmission of FMDV and maintenance of FMD (Fleming 2004) if unchecked.
The assumptions of models are of critical importance to both model structure and outcomes. Most
published models of FMDV transmission for Australian conditions have assumed the priority of
feral pigs (Sus scrofa) as FMDV sources (e.g. Hone & Pech 1990), the equivalence of contact rates
and transmission rates (e.g. Pech & Hone 1988, Pech & McIlroy 1990, Dexter 2003), densitydependent transmission (all models), homogenous mixing of individuals (e.g. Dexter 2003) or
groups (Caley 1993), and then not modelled interactions between the wild and domestic ungulates.
Livestock interaction models have treated a property as either a “population” or an individual (i.e.
one infected, all infected; e.g. Garner and Lack 1995), which makes it difficult to incorporate feral
ungulates with dispersions that overlap property boundaries into property-based models. The one
exception is the work of Doran and Laffan (2005) where regional livestock (sheep and cattle) and
feral pig densities were averaged, the cells in a lattice superimposed on the region and a cellular
automata framework used to simulate interactions between “herds” of pigs and livestock (Doran &
Laffan 2005).
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz
In our study, the population dynamics, contacts within and between species, and habitat preferences
of feral goats and paddock use of merino sheep were used to build models of FMDV transmission.
This paper discusses the modelling of FMDV transmission of feral goats and merino sheep given
their social behaviour, their habitat use, contacts within and between the species, and the draws
conclusions for FMD management contingencies.
Modelling processes
Basic models
A simple compartmental model of transmission of a pathogen in a population of animals identifies
four states to which an animal can belong; susceptible (S), latent (L), infected (I) and removed/
recovered (R), (Anderson & May 1992). The traditional deterministic SLIR models use a set of
differential equations that describe the rate of movement of animals between states of disease and
often assume logistic growth of the population (Anderson & May 1992, Begon et al. 2002). The
rate of change in the infected proportion of the population is the most important in the dynamics of
disease (described in equation 1): after initial infection of a susceptible individual with disease
propagules from outside the population, the number of susceptible individuals in the population
declines as individuals become infected.
The rate of change of the infected proportion of the population (I) is often described by the basic
differential equation:
dI
= β SI − αI
dt
,
equation 1
where • is the transmission coefficient and • is the per capita death rate caused by the disease
(Begon et al. 2002). The transmission term, •, determines the rate at which the disease is
transmitted from infectious individuals to susceptible individuals. This basic model assumes
homogenous mixing within the population, homogeneity of host susceptibility, and that
transmission is density-dependent (Begon et al. 2002).
The rate of change from susceptible class to infected class can also be written:
dI
= λS ,
dt
equation 2
where •, the “force of infection”, is the static per capita rate of acquisition of infection and is the
rate at which susceptible individuals will become infected on contact with an infectious individual
(Anderson & May 1992). Now, the force of infection is the product of the per capita contact rate
(c), the probability that the individual contacted by an infectious individual is susceptible (p, which
is equivalent to the prevalence of the disease, Hyman et al. 1999), and the infectivity of the disease,
(•, the probability that the contact will lead to transmission).
However, prevalence changes as animals move in and out of the infected class and these changes
can be reflected in a dynamic force of infection, •t, that is:
λt = cp tν ,
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
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equation 3
where c and • are as previously defined and pt is the prevalence at time t.
The dynamic force of infection is useful for predicting disease dynamics in the absence of disease
because, if the contact rates are measured, then any disease for which the probability of successful
transmission (v) is known can be modelled by substituting the known values into equation 3. The
dynamic force of infection also encapsulates individual heterogeneity of susceptibility (Dwyer et al.
1997) because it uses the empirically-derived probability of a contact being with a susceptible
individual in its formulation. This approach also allows the contact rate to be varied (e.g. between
and within species) in the model using empirically-derived data. In addition, c is not assumed to
scale with density.
Australian wildlife disease models
In modelling of exotic disease transmission in Australia density-dependent transmission and
homogenous mixing has been assumed (e.g. the models of exotic diseases in feral pigs: Dexter
2003, Pech & Hone 1988, Pech & McIlroy1992, Caley 1993, Doran & Laffan 2005). These models
all assumed that contact was analogous to transmission and used equation 1 or variants to describe
disease dynamics. Contact rate is often assumed to increase directly with population density (Begon
et al. 2002) and hence transmission in these models is density-dependent.
At high densities, contacts being saturated, density-dependent transmission to be an inaccurate
description of contact rates (Mollison 1995). In frequency-dependent transmission, there is no
threshold density above which disease is transmitted and contacts and transmission occur in
proportion to the number of animals rather than their density. The only frequency-dependent
transmission for Australian wildlife (Dexter’s 2003 second stochastic model of FMDV dynamics in
feral pigs in semi-arid western New South Wales) includes the assumption that the rate of contact is
constant regardless of density. Modelling using force of infection is more apt than using those with
transmission coefficients when transmission is shown to be frequency-dependent or when it is not
known whether transmission is density-dependent or frequency-dependent or if contacts are
saturated. This is because • incorporates population size in the prevalence term (p).
Data collection and modelling of FMD dynamics in feral goats and merino sheep
Field studies were undertaken in hilly terrain in temperate, central eastern New South Wales, where
feral goat densities as high as 98.2 goats km-2 and average livestock densities of 613.5 dry sheep
equivalents km-2 were evident (Fleming 2004). Because of high densities, contacts were presumed
likely to approach maximal values and the resultant models were likely to represent the upper
extreme of transmission. Analysis of habitat preference, home range overlap and herd structure
showed that home range use by feral goats was not homogeneous (Fleming 2004). The probability
that feral goats were found in a particular space (1 ha cell) could be assigned with a log-linear
resource selection function with Poisson errors that included slope, aspect, elevation and vegetation
structure (i.e. open grassland to closed forest). Previous work (Taylor et al. 1984) had shown that
sheep habitat use in hilly terrain is heterogeneous.
We modelled FMDV transmission between feral goats and merino sheep in two ways. Temporal
models that addressed the population of feral goats and sheep as homogenously mixing with
different empirically-derived contact rates for the two species and empirically-derived life history
data. FMDV was introduced at day 0 into either feral goats or sheep and disease dynamics were
tracked with the dynamic force of infection, •t. A cellular automata structure (1 ha cells) that
reflected space use, and social and movement ecology of free-ranging feral goats and merino sheep
was used for spatial modelling. Infection was initiated randomly at single sheep camps. The spatial
models were viewed through ArcView GIS.
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz
Results
Contact rates
Our field studies showed that, while contacts between individuals within a group of feral goats were
very common (contacts between goats• 7.0 cGG day-1, s.e.• 1.3), contacts between herds of a
population were few (contacts between herds of goats• 0.002 cHH day-1, s.e.= 0.0002) and between
populations were extremely rare. Daily per capita contact rates were not related to herd density
(goats km-2), but were inversely related to the number of goats in a foraging subgroup of the herd.
We concluded that transmission was unlikely to be density dependent among feral goats and used
the dynamic force of infection model structure. Similarly, contacts between sheep and feral goats
(daily per capita contacts between species• 2.8 cGS day-1, s.e.• 0.4) were mostly related to subgroup
size of goats.
Temporal models
Force of infection( λ)
When homogeneous mixing was assumed, the temporal models predicted that infection spread
rapidly throughout and was maintained at a low level thereafter (Fig 1). Peaks of infection occurred
annually, corresponding with birth pulses of sheep.
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
100
200
300
400
500
600
700
Time (day)
Figure 1 Forces of infection for FMD in a population of merino sheep and feral goats, for goats ( •G,
thin black line), sheep (•S, thin grey line) and between species (•GS, thick grey line), projected past
two breeding pulses of sheep (from Fleming 2004).
Spatial models
In contrast to the temporal models, spatial models that incorporated empirically-derived, behaviourmoderated heterogeneous mixing (Fleming 2004) predicted that disease initially spread rapidly in
sheep and into feral goats when co-occurring. However, FMD always died out in both species in
less than 90 days because of inadequate contact between herds of goats and flocks of sheep. If the
initially infected sheep flock did not overlap with the home range of a herd of feral goats, then the
disease did not spread between flocks, and sometimes did not establish. These disease processes
were dominated by the high level of infectivity of FMDV (McVicar & Sutmoller 1972) and hence
high p, different contact rates within and between herds and flocks (Fleming 2004), and previously
reported long immunity (Barnett & Cox 1999), which affects the rate at which immune animals
return to susceptible class.
Discussion and conclusions
Contrasting predictions of disease dynamics were provided by our temporal and spatial models,
underlining the need to incorporate knowledge of animal socio-biology into models. The
population-level simple models were too simple and hence gave potentially misleadingly
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz
pessimistic predictions of FMD dynamics in mixed species. The prediction that FMDV would
persist at a low level in a feral goat population would require that extreme control effort be exerted
before clean livestock could be reintroduced to a destocked property.
However, social behaviour of feral goats and management practices for sheep prevented mixing of
herds and populations of goats, and flocks and populations of merino sheep to such an extent that
the more complex spatial models predicted that disease was largely contained within the originally
infected flock and the herds it overlapped. The results supported the current depopulation strategies
in AUSVETPlans (Animal Health Australia 2001) but only at the herd level within feral goats.
Broad scale reduction in abundance of feral goats may result in increased mixing of infected and
susceptible herds and populations because small remnant groups are more likely to seek other goats
whereas stable groups are unlikely to move from their home range.
We concluded that density-dependence could not be assumed for our population of feral goats and
merino sheep and that homogenous mixing within and between species was unlikely. We also
concluded that • could not be assumed equal to1.0 in sheep and goats. Therefore, model structures
that did not require these constraints were most appropriate for predicting disease dynamics here. It
is possible that contact rates may be density-dependent at lower densities (Mollison 1995) than
occurred at our site, but the observed inverse relationship between foraging subgroup size and
contact rates of feral goats would contradict this possibility.
An understanding of the social ecology of animals is necessary for adequate modelling of disease
dynamics within and between species. Where two or more species co-occur, it does not necessarily
follow that they come into contact sufficient to allow disease transmission. Indeed, some animals
may usually disassociate when free-ranging together (in our study, feral pigs did not approach feral
goats, nearest approach distance= 60m, n= 7 observations over 4 years). Contacts within
populations of other sheep breeds and between them and feral goats may well differ because some
other breeds are less gregarious than merino sheep (Lynch et al. 1992). Similarly, within-species
interactions are not homogenous and so disease transmission may be limited to part of a population
as occurs with HIV infection in Europe (Woolhouse et al. 1997).
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Acknowledgements
We particularly thank Mike Martin, Jim Hone of Applied Ecology Institute at University of
Canberra, Greg Jones and Matt Gentle for their assistance. The funding of Wildlife and Exotic
Diseases Preparedness Program and the National Feral Animal Control Program are gratefully
acknowledged.
Proceedings of the 11th International Symposium on Veterinary Epidemiology and Economics, 2006
Available at www.sciquest.org.nz