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Assessing risks of disease transmission between wildlife
and livestock: The Saiga antelope as a case study
E.R. Morgana,*, M. Lundervoldb, G.F. Medleyb, B.S. Shaikenovc, P.R. Torgersond,
E.J. Milner-Gullande
a
School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK
Ecology and Epidemiology Group, Department of Biological Sciences, University of Warwick, Coventry CV4 7AL, UK
c
Institute of Zoology, Ministry of the Environment, Akademgorodok, Almaty, Kazakhstan
d
Institute of Parasitology, University of Zürich, Winterthurerstrasse 266a, CH-8057 Zürich, Switzerland
e
Division of Biology, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, Berkshire SL5 7PY, UK
b
A R T I C L E I N F O
A B S T R A C T
Available online 5 June 2006
Disease transmission between wildlife and livestock can undermine conservation efforts,
either by challenging the viability of threatened populations, or by eroding public tolerance
Keywords:
of actual or potential wildlife disease reservoirs. This paper describes the use of transmis-
Model
sion models to assess the risk of disease transfer across the wildlife–livestock boundary,
Foot and mouth disease
and to target control strategies appropriately. We focus on pathogens of the Saiga antelope
Nematode
(Saiga tatarica) and domestic ruminants in Central Asia. For both foot and mouth disease
Migration
and gastrointestinal nematodes, the main risk is associated with infection of saigas from
Seasonality
livestock, and subsequent geographical dissemination of infection through saiga migra-
Kazakhstan
tion. The chance of this occurring for foot and mouth disease is predicted to be highly
dependent on saiga population size and on the time of viral introduction. For nematodes,
the level of risk and predicted direction of transmission are affected by key parasite life history traits, such that prolonged off-host survival of Marshallagia in autumn enables infection of saigas and transfer northwards in spring. Field estimates of parasite abundance
provide qualitative support for model predictions. The application of models as tools for
the early evaluation of disease transmission between wildlife and livestock is discussed.
Ó 2006 Elsevier Ltd. All rights reserved.
1.
Introduction
Many pathogens and parasites of wildlife also infect sympatric domestic animals. The role of different host populations in
the maintenance and spread of infection then becomes
important to conservation. Disease transmission from a
domestic animal reservoir to wildlife can directly threaten
population viability, as for rabies in Ethiopian wolves (Randall
et al., 2006). Where wildlife is the reservoir of infection for
domestic animals, on the other hand, control strategies
might include culling or curtailing the movement of wildlife,
which itself could have conservation implications. The relatively free movement of wild animals gives them the potential
to act as vectors for the geographical spread of disease, even if
infection does not persist for a long time in the wildlife population. In Africa, the importance of buffalo Syncerus caffer as
a source of foot and mouth disease virus (FMDV) for livestock
is enhanced by its ability to persist in this species (Vosloo
et al., 2002), but other wild ruminants such as impala Aepyceros melampus might also act as a vector for transmission
* Corresponding author: Tel.: +44 1179 287485; fax: +44 1179 257374.
E-mail address: [email protected] (E.R. Morgan).
0006-3207/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.biocon.2006.04.012
B I O L O G I C A L C O N S E RVAT I O N
between buffalo and cattle (Bastos et al., 2000; Hargreaves
et al., 2004). Many other important infectious diseases including rift valley fever, malignant catarrhal fever and tuberculosis infect both wild and domestic ruminants and may be
transmitted between them (Worthington and Bigalke, 2001).
The willingness of landowners and other agricultural stakeholders to support wildlife conservation efforts is likely to
be affected by assessment of the risk of disease transmission
to livestock, and on the control strategies available should
this risk be high.
Unfortunately, assessing the risk of disease transmission
between wildlife and livestock is usually extremely difficult.
Data on levels of infection in wildlife are often scarce and
open to bias, and are not in themselves sufficient for
assessment of cross-species transmission. Thus, wild animals can be infected at a high level, but if most infection
is from surrounding livestock, and there are limited opportunities for onward transmission, their role as a reservoir
of disease might be negligible. The conclusion that high
point prevalence indicates a source of infection is then
incorrect (Haydon et al., 2002a). Crab-eating foxes in Brazil,
for instance, have high seroprevalence for Leishmania infantum, but are not infective to the insect vector, and do not
therefore contribute to infection of dogs and humans (Courtenay et al., 2002). Even if wild animals are infective to their
domestic counterparts, the extent of cross-species transmission will depend on contact patterns, which are rarely
straightforward. Where contact is seasonal or sporadic, for
instance, its timing might be more important than relative
levels of infection to the direction of disease transmission
(Morgan et al., 2004). Climatic factors can significantly affect
contact rates, for example through increased density and
species range of ungulates around water holes in droughts
(Redfern et al., 2005), as well as directly affecting the persistence of pathogens outside the host, and the development
of parasites to the infective stage in the environment or in
invertebrate intermediate hosts. Variation in the weather
within and between years is then likely to influence risks
of disease transfer between species. Disease data restricted
to short sampling periods might miss key events in disease
dynamics, and give an inaccurate picture of cross-species
infection.
1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4
245
It is clear that existing field data on wildlife disease will, in
most cases, not enable reliable assessment of future risks of
transmission from and to sympatric livestock populations.
This will be particularly true for new and emerging disease
threats, for which data are especially scarce, or when perturbations to host populations or the environment might affect
disease dynamics in unknown ways. In these situations,
understanding of general disease dynamics, formalised as
mathematical models, could be applied to the specific system
in question in order to predict likely transmission patterns,
and investigate potential control strategies. Models have been
used successfully in this way for several important livestock
diseases (e.g., French et al., 1999; O’Callaghan et al., 1999;
MacKenzie and Bishop, 2001; Smith, 2001; Keeling, 2005).
However, additional complexities in wildlife systems limit
the applicability of livestock-based models. These include
host movement, variation in host population size, density
and contact rates, unpredictable variation in climate, and
species differences in the host–parasite relationship. Considerable adaptation is therefore necessary before such models
can be successfully applied to disease transmission across
the wildlife–livestock boundary. Nevertheless, mathematical
modelling could be a useful first step in the investigation of
risks of disease transmission between wild and domestic animals, if it is able to focus attention on likely drivers of disease
dynamics, and on key areas of data scarcity. This paper attempts to illustrate the benefits and limitations of such an approach with respect to saiga antelopes and domestic
ruminants in Kazakhstan, a system which includes many
complexities that are common in other wildlife situations.
2.
Saiga antelopes and livestock in
Kazakhstan
Until recently, the saiga antelope (Saiga tatarica) was common
in Kazakhstan, reaching total numbers of around one million
in the 1970s. It is a commercially valuable species, supplying
meat, horns and hides to domestic and international markets
(Fadeev and Sludskii, 1982; Bekenov et al., 1998). The species
is nomadic, undertaking extensive seasonal migrations
(Fig. 1). Large aggregations form in the spring, when females
give birth over a 10 day period (Bekenov et al., 1998). Saigas
Fig. 1 – Migrations of the saiga antelope in the Betpak-Dala region of Kazakhstan. Saigas spend the winter in the south (1),
calve on the northward migration (2), and graze northern pastures in the summer (3), before migrating south in autumn (4).
The other saiga populations are not shown.
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graze on the open plains, and come into contact with domestic livestock by sharing pasture and water sources. This contact is uneven because of the patchy distribution of both
livestock and saigas. In the Betpak-dala population of Central
Kazakhstan, contact is likely to be closest in the winter, when
saigas and livestock are concentrated on limited pasture in
the south, and also occurs in the summer in the north. During
the spring and autumn, saigas migrate through the central
part of their range, which has become denuded of livestock
in recent years. Additionally, most livestock is grazed close
to villages at this time of year, and contact is less likely,
although much of the pasture used by saigas will have been
previously grazed by livestock.
Saiga herds vary in size through the year, from huge aggregations during calving to small groups during summer grazing, with intermediate group size during migration and
mating. Herd structure is also quite labile, and individuals
can leave and join different groups through the year (Grachev
and Bekenov, 1993). Total saiga population size is highly variable between years, and even in the absence of hunting severe
winters can cause up to 50% mortality, with recovery over the
next 2–3 years (Bekenov et al., 1998).
Cattle, sheep, goats, camels and horses are present in the
saiga range, but sheep are by far the most numerous and tend
to graze the more remote pastures, and are therefore the
most likely to share parasites and diseases with saigas. Recent changes have affected the numbers and grazing patterns
of both saigas and livestock. Excessive hunting has pushed
saiga numbers down to critical levels in much of its range
(Milner-Gulland et al., 2001), while collapse of the agricultural
economy in the 1990s has decimated livestock numbers and
dramatically reduced grazing on the remote open plains, as
well as inhibiting veterinary care and disease prevention
(Lundervold et al., 2004). Impoverishment linked with reduced
livestock production has been a major cause of increased saiga poaching (Robinson and Milner-Gulland, 2003). The likely
effect of these changes on disease transmission between saigas and livestock, and the risks of disease to a declining saiga
population, are unknown.
Saigas and domestic ruminants are susceptible to many of
the same parasites and diseases. Foot and mouth disease
virus (FMDV) is known to infect saigas and appears to cause
more severe disease than in domestic ruminants. Mortality
in saigas experimentally infected with FMDV can be up to
75%, and as much as 10% of the free-living population has
died during natural outbreaks (Sokolov and Zhirnov, 1998).
Outbreaks of FMD in domestic ruminants involving viral
types A and O have occurred regularly in Kazakhstan over
the past few decades, with increasing frequency in border
areas in recent years as veterinary controls and vaccine coverage have deteriorated (Lundervold, 2001). Brucella melitensis,
a common cause of ovine abortion in Kazakhstan, can also infect saigas, though its clinical consequences in this species
are not well known (Lundervold, 2001). Of the 38 helminth
species found in saigas in Kazakhstan, 35 have also been
found in domestic ruminants (Morgan et al., 2005). These
organisms are important causes of lost agricultural production in Kazakhstan, and have also been shown to adversely
affect wildlife populations in other parts of the world. Previous work catalogued nematode species in saigas and high-
1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4
lighted the possibility of infection across the wildlife–
livestock boundary, but did not quantify this risk (Berkinbaev
et al., 1994).
Evidence of mutual susceptibility gives us no indication of
how important transmission between saigas and livestock
actually is in nature, or how it might be prevented. However,
the biology of the main pathogens and parasites of saigas is
fairly well known, albeit in other host species, and we should
be able to make sensible predictions about their behaviour in
this more complex epidemiological setting. In this paper we
use exploratory mathematical models to predict patterns of
disease transmission within and between saiga and livestock
populations. We focus on FMDV and gastrointestinal nematodes because they are important pathogens, and also because they illustrate the contrasting approaches to
modelling infection patterns in microparasites (e.g., viruses)
and macroparasites (e.g., helminths). The details of the models are published elsewhere: here we use them to illustrate
how established model frameworks have to be adapted to
take account of the additional complexities of the saiga–
domestic ruminant (and, in general, the wildlife–livestock)
interface.
3.
Model 1: Foot and mouth disease (FMD)
Saigas are known to be susceptible to FMD, and to excrete the
virus for some days after infection. It has been widely assumed that saigas become infected from domestic ruminants, and there is also anecdotal evidence suggesting
transmission from saigas to livestock. This is of particular
concern because saigas could promote geographical dissemination of infection through their seasonal migrations. It is not
known when saigas are most likely to be infected from livestock, how long the virus could persist in saiga populations,
or under what conditions there is a significant risk of onward
transmission to livestock. The model was designed to address
these questions using existing knowledge of FMD
epidemiology.
3.1.
Model structure
The model is based on the established SLIR framework
(Anderson and May, 1991), whereby individuals are placed
into mutually exclusive categories representing susceptible,
latent infected, infectious and recovered (immune) states.
The model architecture is shown in Fig. 2, and a detailed
description can be found in Lundervold (2001). Similar models have been used to assess control strategies for FMD in
domestic ruminants (Keeling, 2005), and to predict risks of
FMDV establishment in wild pig populations (Pech and
Hone, 1988; Pech and McIlroy, 1990). Additional complexities
that might be important in the saiga–domestic ruminant
system but are generally ignored in previous models include
multiple host species, complex host movement patterns,
and dramatic fluctuations in population size and density.
These give rise to regional and seasonal differences in contact rates between saigas, and between saigas and domestic
ruminants. Key points of infection risk are therefore likely
to vary widely between different geographical locations
and times of year. Fluctuations in saiga population size
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Nat_Death
Ra
Ω
Adults
Sa
Calves
Sc
ν
β
La
Ia
σ
Lc
α
FMD_Death
FMDDeath_C
Ic
Births
IM c
Rc
Nat_DeathC
Fig. 2 – Schematic representation of the flow of hosts
between classes, which records the dynamic interaction
between the directly transmitted microparasite FMDV and
its host population, the saiga antelope. Compartments
represent susceptible (S), latently infected (L), infective (I)
and recovered immune (R) individuals. Infection can lead to
recovery or death (FMD__Death) at rate a, and all classes are
subject to natural background mortality (Nat__Death). Suffix
a = adult, c = calf. b represents the transmission function, r
the latent period, m the infectious period, and X the duration
of immunity. Calves may be born susceptible (Sc) or immune
through maternal antibodies (IMc) (Lundervold, 2001).
and density will also cause infection risk to vary greatly
within and between years.
These complexities were addressed by adaptations to the
basic SLIR model. Most models of FMD in domestic ruminants
focus on inter-herd spread, and consider each herd to be a
unit. Because of variation in saiga herd size and structure, it
is more appropriate to consider the individual saiga as the
unit. Previous models of FMD and many other viruses also assume a linear relationship between population density and
virus transmission. If the range of a population is fixed, then
an increase in population size will lead to an increase in population density and increased contact rates. However, there is
no fixed edge to the saiga range, which can expand when
numbers increase, so the relationship between population
size and density is not straightforward. Additionally, saigas
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come together into groups to mate, calve and migrate even
at low population density, and so the chances of an individual
encountering other saigas (and passing on or contracting
infection) is unlikely to vary linearly with population density.
Consequently, we assume frequency-dependent rather than
density-dependent transmission (McCallum et al., 2001).
The seasonal dynamics of saiga populations present further challenges. Saigas give birth over a period of around 10
days, leading to a massive influx of susceptible individuals
into the population. These large fluctuations in available
hosts mean that infectious disease may spread more rapidly
at certain times of year. Additionally, saiga migration leads
to seasonal contact with different livestock populations, and
consequently variation in the risk of cross-species transmission. Rather than attempting to simulate spatial variations
in saiga–livestock contact explicitly, they are subsumed into
temporal variation in the contact rate, b. This is possible because saigas generally migrate en masse and so geographical
variation in infection risk is implicitly included by varying b
(the effective contact rate) in time. b is split into saiga and
livestock components to reflect the two sources of infection,
and the livestock component is weighted according to
livestock density at different times of year (=different parts
of the saiga range) and monthly relative humidity (=ability of
the virus to survive in the air). The seasonal forcing effect of
mass saiga calving is included by splitting the saiga population into separate adult and juvenile compartments, with
transfer from juvenile to adult compartments occurring at 6
months of age. Calves are assumed to carry maternal antibodies for the first 5 months of life, based on estimates of
3–7 months for the duration of maternal immunity in domestic cattle and buffalo (Lundervold, 2001).
3.2.
Results
The aim of the model is to predict the conditions necessary
for FMD establishment and persistence in the saiga population, and hence the risk of onward transmission to livestock.
Infection is introduced to the model by adding two infected
Number of infected saigas
250000
200000
150000
100000
50000
0
0
52
104
156
208
260
312
364
416
468
Weeks
Fig. 3 – The predicted size and frequency of FMD epidemic peaks when both population size (2,300,000) and contact rate (b) are
high. The initial spike is on a much larger scale than the others; however, this is not seen on the graph as the y-axis has been
truncated for clarity. Two peaks of infection are predicted to occur each year: the first when saigas come together for calving,
and the second, higher peak when new susceptible juveniles enter the system after maternal immunity has waned in
autumn. Week 0 = January.
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Table 1 – The predicted effect of varying the time of year that infection is introduced into the saiga population
Value of b
Spring
Summer
Autumn
Winter
High (5 x 10-6)
Medium (9.3 x 10-7)
Low (5 x 10-7)
Initial population size in week 0 is at equilibrium (N = 2.3 million). Dark shading indicates cyclical epidemics, light shading one epidemic. b is
the effective contact rate.
adults to the population, and the main model output is the
predicted number of infected saiga individuals through time.
There are three possible consequences: no epidemic (the
virus does not propagate successfully within the population
and dies out), a single epidemic peak which is unsustainable
and then dies out, or sustained cycles of infection. From the
point of view of disease management in livestock, cyclical
epidemics in saigas are the most dangerous because the virus
can then persist until contact with other livestock populations occurs.
We first explore the behaviour of a simple version of the
model, with contact rate constant throughout the year. In this
case, the outcome of a single infection event in saigas is
strongly affected by the effective contact rate (b), as well as population size (N). When both parameters are high and constant,
cyclical epidemics are predicted to occur, regardless of the time
of year at which infection is introduced (Fig. 3). However, when
N is reduced below 1.5 million, or b is set at a medium value,
epidemics occur only if infection is introduced in autumn
(Table 1). This is because at other times of year, infection ‘burns
out’ by depleting the pool of susceptible animals, after which it
cannot keep circulating until the introduction of new susceptible animals. When the population size is low (<750,000), there
is predicted to be no epidemic unless b is at the upper end of
its range. Thus there is a threshold minimum number of
susceptible animals required to propagate an epidemic.
The value of the contact rate b is therefore critical to model
predictions. In a more realistic refinement of the model, b is
varied seasonally to simulate fluctuating saiga herd size (largest in spring) and contact with livestock (closest in winter).
The refined model predicts that just a single epidemic peak occurs if infection is introduced in spring. This is because such a
high proportion (up to 92%) of the population is infected in the
initial outbreak that there are insufficient susceptible animals
left for the virus to persist through the rest of the year when b
is much lower. Introduction of the virus at other times of year
results in fewer than 70% of the population becoming infected,
leaving enough susceptible animals for the virus to persist. If
overall values of b are very low, the dip in contact rates in summer and autumn is such that the virus is unable to persist
through the year. Virus introduced in winter is least likely to
trigger an epidemic in saigas, as the population size at this
time of year is at its lowest. This is fortunate, because saigas
and livestock are in closest contact in winter, and infection
of saigas from livestock is perhaps most likely then, but under
these conditions the virus would disappear from saigas by the
time they moved north in spring.
Validation of model predictions is troublesome, because
few quantitative data are available from past FMD epidemics.
However, between 1955 and 1974, when saigas were relatively
abundant, 9 separate FMD outbreaks were observed in saigas
(Lundervold, 2001). Typically, large epidemics were observed
in spring and summer, which died out in summer and autumn. This matches model predictions when seasonal variation in b is included.
3.3.
Discussion
The most important conclusions of the model, as it stands,
are firstly that introduction of infection into the saiga population is most dangerous in autumn because establishment of
cyclical epidemics is most likely at this time of year, and secondly that persistence of the virus in saigas is most likely
when the population is large. These insights could be useful
when planning vaccination of livestock to prevent infection
of saigas. Thus, vaccination of livestock in saiga over-wintering areas might be preferred because contact rates are relatively high and exposure of saigas to the virus is arguably
most likely here. However, because the risk of viral persistence in the saiga population is predicted to be higher if it is
introduced in autumn, there is an argument for prioritising
vaccination of livestock in those areas through which saigas
pass at this time of year, i.e., on their southward migration.
Large scale livestock vaccination campaigns have been used
in the past in order to prevent infection of saigas. However,
changes in the agricultural economy are likely to decrease
the feasibility of such centrally funded blanket vaccination
strategies in the future, and a strategic decision on where to
best target limited resources will have to be made.
The default saiga population size used in the model was
the estimated carrying capacity. However, the results suggest
that when saiga populations are small, as they are at present,
the risk they present to livestock as a reservoir of infection for
FMD is extremely low, and specific control strategies are unlikely to be needed. These results are for simulations with a
constant contact rate regardless of population size. However,
population fragmentation could lead to this assumption
being violated. Furthermore, the effects of an outbreak of
FMD are potentially more devastating from a population viability perspective if the saiga population is already low. Since
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agricultural economic reform and the cessation of effective
vaccination schemes in much of Kazakhstan, localised outbreaks of FMD in domestic ruminants have become common
(Lundervold et al., 2004), and the chance of spread to saigas
has probably increased. This could be mitigated in part by
the decrease in numbers of livestock grazing the open steppe
(Robinson and Milner-Gulland, 2003). The model can be used
to investigate alternative scenarios by weighting the relative
contribution of saigas and livestock to b, and by manipulating
its seasonal variation.
The model also illustrates several points important to our
understanding of disease dynamics in wildlife populations.
The dominant features in the behaviour of the saiga-FMD
model are the strong seasonal forcing effect of saiga population dynamics, and seasonal contact with livestock populations. Predictions using seasonally varying effective contact
rates are qualitatively different to those using constant values. However, it is extremely difficult to obtain accurate estimates of contact rates in wildlife populations. This leaves us
with a dilemma: the complexities which we really ought to include in our models are the very ones that are hardest to
quantify. As a result, although model output can give us real
insight into the possible behaviour of FMDV in saigas, parameterisation and validation are too tentative to allow us to
place much confidence in practical recommendations for
control. The alternative, however, is to omit factors about
which we have little information, leading to simple, tractable
models which are liable to completely miss fundamental drivers of system dynamics. The strong effect of contact rate (b)
on the qualitative output of the model suggests that more
accurate estimation of contact rates between saigas and between saigas and livestock is a priority if we are to accurately
predict the course of disease in saiga populations. This will be
difficult, although satellite tracking studies could make an
important contribution. Serological studies of endemic
viruses transmitted by similar routes could also help to estimate b without having to wait for the next FMD outbreak,
although there are no obvious candidate viruses in saigas.
4.
Model 2: Gastrointestinal nematodes
The model of nematode dynamics considers three closely related but contrasting genera: Haemonchus, Nematodirus and
Marshallagia. The adults live in the abomasum and lay eggs
that pass out in the faeces. Larvae hatching from these eggs
undergo further development before climbing onto the herbage to be ingested by the next host. Rates of development,
mortality and migration onto herbage are dependent on climate, especially ambient temperature and moisture provided
by recent rainfall. As a result, transmission is highly seasonal.
The exact timing and extent of transmission within and between populations is also likely to differ between years
according to the weather. Data on parasite abundance and
epidemiology collected over a small number of years might
not therefore be representative of typical patterns, and such
field data cannot be relied on to guide control strategies in
the future.
The purpose of this model is to use existing understanding
of the relationships between climate and parasite vital rates
to predict the times of year when transmission is greatest.
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1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4
This is important because it will enable control strategies to
be focused appropriately. Additionally, the model can predict
how regularly significant parasite transmission is expected to
occur between saigas and domestic livestock.
4.1.
Model structure
The model is based on a framework that is well established for
domestic ruminants (Coyne and Smith, 1994; Smith and Grenfell, 1994), and its basic structure is shown in Fig. 4. The total
abundance of parasites in each life cycle stage is calculated
in successive daily time steps. There are separate parasite
populations in adult and juvenile saigas, and in sheep and
lambs in the north, centre and south of the saiga range. These
populations are linked by access of the hosts to common pools
of free-living stages in each area. Migrating hosts infected by
parasites transfer them to other areas and host populations
through contamination of pasture with eggs. The model is
deterministic, but the effect of climate is included as run-time
variation in parasite vital rates, which are drawn from probability distributions within and between years (Table 2). Further
details of the model are given in Morgan (2003).
4.2.
Results
We focus here on Marshallagia, the most common of the three
genera. The model predicts that saigas acquire Marshallagia
primarily in the winter, from the south of their range
H (i=1 to 10)
μP
(1-pe)
pe
β
μLh
Area (j=1 to 3)
P
λ
Lh
dm
L3
μL3
dL
L
μL
dh
EL
μel
de
E
μe
Fig. 4 – Schematic representation of the nematode model.
Adult parasites (P) lay eggs (E) that pass out in the faeces and
develop through successive embryonated egg (EL), early
larval (L) and infective larval (L3) stages before becoming
available to hosts on the herbage (Lh). The model tracks
losses from each stage through development (d) and
mortality (l). b represents the rate of uptake of larvae by
grazing saigas or livestock, pe the proportion of larvae that
establish successfully in the host after ingestion, and k the
rate of egg production of adult worms. The part of the
parasite life cycle that takes place within the host is
duplicated for each host population, and the part that takes
place on the ground is duplicated three times, once for each
part of the saiga range. More details are given in Morgan
(2003).
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Table 2 – Stochastic elements of the nematode transmission model, with range of run-time variation in parameter values
Element
Governed by
Variation
Form
Time of year at which
development of the freeliving stages can begin
Time of year at which
development of the freeliving stages must end
Probability that a given dekad
is sufficiently wet for
development to take place
Peak herbage biomass
Range
Timescale
Air temperature in spring
Normal, rounded off to
whole dekad
Annual
End March–end May
Air temperature in autumn
Normal, rounded off to
whole dekad
Annual
Start September–end October
Rainfall in each dekad
Uniform
Dekadal
0.07–0.61
Cumulative early year precipitation
Lognormal
Annual
200–2000 kg/Ha
Parameters were different for each of the three areas of the saiga range and for each of the three nematode species.
Marshallagia
Saigas and sheep
S
J
F M
C
A
N
M
J
J
C
S
A
S
O N D
A
S
O N D
Saigas alone
J
F M
A
M
J
J
Fig. 5 – The peak times of Marshallagia acquisition by saigas
predicted by the model. The vertical axis represents the
daily change in the total parasite population in saigas:
shading above the horizontal axis means net parasite
acquisition, and shading below the axis net parasite loss.
Letters on the horizontal axis are months of the year, and N,
C and S indicate the periods during which saigas are in the
northern, central or southern part of their range,
respectively. In the top plot, saiga and sheep populations
were included in the model, whereas in the bottom plot only
saigas were present. The vertical axis on the lower plot is
scaled to 1/100 of that in the upper plot: at the same scale,
no parasite acquisition is discernible. The plots represent
output of simulation for a single year, but climatic
parameters typical for the region were chosen, and the
winter peak of acquisition when sheep are included was
consistently repeated.
Marshallagia eggs deposited in autumn are able to develop to
the infective stage and survive until saigas arrive in winter.
When sheep are excluded from the model, this winter peak
of larval ingestion is greatly reduced, suggesting that sheep
are the main source of infection for saigas. By tracking the
origin of ingested larvae, the model can partition infection
according to the source population (Fig. 6). It appears that
saigas indeed acquire most of their parasites from sheep.
However, sheep in northern Kazakhstan can acquire a significant proportion of total annual infection from saigas that arrive from the south in summer. This only occurs in some
years, depending on the weather conditions in relation to
saiga movement. The model predictions are therefore riskbased, and acknowledge that infection patterns differ
between years. Control strategies will not have exactly the
same results every year, but must simply aim to reduce the
overall risk of excessive parasite transmission.
Haemonchus transmission is even more strongly affected
than Marshallagia by changes in the weather between years,
and significant infection of saigas from sheep in the north
'Perc entage trans mis s ion' from s aigas
(Fig. 5). At first glance this is surprising, because conditions
at that time of year are too cold for parasite development.
However, winter transmission occurs in the model because
100
80
60
40
20
0
Saigas
Sheep
Sheep
(transhumant) North
Sheep
Centre
Sheep
South
Fig. 6 – The predicted importance of saigas as a source of
nematode infection for different host populations. For each
population, the first column is the cumulative percentage of
infective larvae ingested over the course of a year that come
from eggs egested by saigas; the second column is the
proportion of years in which more than 10% of ingested L3
come from saigas (proportion >50% from saigas shaded). All
figures are averages from 1000 stochastic simulations.
B I O L O G I C A L C O N S E RVAT I O N
Table 3 – Mean burdens of Marshallagia in saigas culled
in autumn, before visiting the winter range, and in
spring, after visiting the winter range
Autumn (n = 87, 46)
Spring (n = 5, 6)
Juvenile
Adult
p
8
178
143
160
<0.001
NS
The autumn sample was taken from Betpak-Dala in November
1997, and the spring sample from Ustiurt in May 1998. Means were
compared using the Mann–Whitney U-test (Morgan et al., 2005).
and subsequent carriage to southern pastures is predicted to
occur approximately one year in five. The time of peak Nematodirus transmission is predicted to be in spring, when saigas
are furthest from sheep pastures, and transmission between
saigas and livestock is likely to be minimal. Interestingly,
the most common Nematodirus species in saigas, Nematodirus
gazellae, is rarely observed in sheep or cattle. The model is run
using moderately high saiga numbers from the 1980s (240,000
saigas in the Betpak-Dala range); with the lower current population size, the contribution of saigas to contamination of
livestock pasture with nematode larvae is predicted by the
model to be negligible, and so no specific control strategies
to counter this are indicated.
Validation of the model would require extensive field sampling of saigas and livestock over a long period of time. However, the most interesting prediction is winter infection of
saigas with Marshallagia. Analysis of parasite count data revealed that in autumn, juvenile saigas – which have not yet
visited the winter range – were observed to carry far fewer
Marshallagia worms than adults, whereas in spring, there
was little difference in parasite burden between old and
young saigas (Table 3), suggesting that both age classes have
been exposed to a similar level of infection. These field data
provide support for the winter transmission hypothesis. To
directly test the hypothesis that sheep are the main source
of this infection, an intervention study could be developed
in which sheep are treated during the autumn to decrease
their output of eggs, and a reduction in worm burdens in saigas moving north is assessed. If burdens are reduced, treatment of sheep in autumn in the south of the saiga range
could decrease the risk of onward transmission to sheep in
the north via migrating saigas.
4.3.
Discussion
The model helps to explain observed patterns of parasite
transmission, and to focus analysis of field data (and potentially future sampling effort) onto the most important times
and places for parasite transmission. The model also allows
us to extrapolate our expectations regarding parasite epidemiology between years, in a way we could not attempt using
field data alone. To take an extreme example, saigas are predicted to provide the majority of Marshallagia infection for
sheep in the south of their range just one year in a hundred,
but if we happened to sample only in this year, we would have
a distorted view of transmission dynamics and might be
tempted to instigate inappropriate control strategies. Transmission in the other direction – from sheep in the south via
1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4
251
saigas to sheep in the north – is predicted to occur quite consistently, and would be a more suitable target for control. The
effect of control strategies can be investigated by manipulating the model, before submitting to the risk and expense of
trying them out in the field. The model output is stochastic
and the expected effect of control strategies is expressed in
terms of risk of significant transmission, rather than parasite
burdens per se. This makes more sense; other factors such as
host nutrition and immunity confound predictions of parasite
burdens, whereas what managers need to know is the chance
that parasite control in livestock will fail as a result of introduction of infection from saigas.
The nematode model is not without problems. Even
though it predicts over-winter transmission of Marshallagia,
for instance, this results from a combination of parasite life
history characteristics, weather and saiga movement patterns. Changing any of these affects the magnitude and/or
timing of the predicted transmission peak. The more complex
a model is, the less transparent are the mechanisms behind
its predictions, and the less sure we can be about what aspects of the model generate the key infection patterns. In this
case, detailed sensitivity analysis could be used not only to
identify key parameters, but also to determine the simplest
model structure that still generates the observed epidemiology. A further limitation of the model is that it is specific to
saigas, and of limited relevance to other systems. Extrapolation of its findings to other problem parasites of wildlife is
not recommended, since movement patterns and host factors
are likely to be different, and few general lessons about parasite epidemiology emerge. It is possible that parameters that
have been extrapolated from sheep, such as parasite establishment and survival rates, are very different in saigas, leading to qualitative differences in model predictions. This is a
common problem with models of wildlife disease, especially
for threatened species for which estimation of parameters
using experimental infection of captive individuals is both
impractical and undesirable.
Finally, validation of the model is difficult. The source population of ingested larvae, for instance, would be impossible
to measure, although advancing techniques in molecular
genetics might change this in future. Because transmission
is influenced by stochastic variation in climate, parasite
abundance data collected in a single year would be of limited
relevance. Validation would therefore have to be a long term
process, and recommendations might be needed before it is
complete. The outcome of control strategies based on the
model cannot be known until they are put into practice, and
so recommendations can only be made tentatively pending
thorough validation. Nevertheless, the model fulfils the aim
of providing an initial indication of the likelihood of parasite
transmission between saigas and livestock, and focusing research effort on the probable key times and places of parasite
acquisition.
5.
General discussion
For both FMD and gastrointestinal nematodes, mathematical
models based on our understanding of disease dynamics in
livestock were able to provide predictions concerning the role
of saigas in the epidemiology of livestock disease, and vice
252
B I O L O G I C A L C O N S E RVAT I O N
versa. However, this was only possible when additional complexities were included, in particular host movement and
population dynamics, multiple host species, and temporal
and spatial climatic variation. These complexities are also
likely to be important in other free-living wildlife. Observed
patterns of infection of house finches Carpodacus mexicanus
with the bacterium Mycoplasma gallisepticum, for instance,
can only be explained by transmission models that include
seasonal breeding (Hosseini et al., 2004). Seasonal host absence, which can drive macroparasite dynamics in livestock
(Roberts and Grenfell, 1991), is also likely to be a common feature in free-living wildlife populations that occupy habitat
patches for only part of the year. For the saiga diseases discussed here, increased complexity of the transmission models radically affects their predictions, and cannot be left out
without justification. However, the decision on whether and
how to include these complexities is subjective, and they also
make it more difficult to see what actually drives system
dynamics. The act of constructing a model does at least force
us to formalise our understanding in a logical way, highlighting the areas in which we know too little. These areas of
uncertainty can then be made the focus of further research,
and also warn us not to accept too readily the predictions of
simpler models.
There are many potentially important complexities that are
too difficult to parameterise. Excretion of FMDV by wild ruminants is a good example: the virus has been found in many
species, but data are observational and a transmission model
would have to use livestock-derived data on important parameters such as duration of infectiousness (Thomson et al., 2003).
In these circumstances, a complex model can still be justified.
For example, if realistic population densities and movement
patterns in a complex model produce similar qualitative results regardless of variation of some parameters within their
plausible ranges, seeking to refine those parameter estimates
is not a priority. Where parameter uncertainty is great, as in
most wildlife situations, sensitivity analysis of transmission
models can be valuable in focusing limited experimental and
field resources (McCallum and Dobson, 1995).
Model structure, and the key complexities involved in
transmission, differ for micro- and macroparasites. In both
cases, parasite persistence depends on host availability. However, microparasites generally survive for a limited period
outside the host and are subject to strong host immunity, so
patterns of contact between individual hosts, and the timecourse of immunity and re-supply of susceptible hosts, are
crucial to parasite population dynamics. Macroparasites, by
contrast, must usually undergo development outside the host
and can survive for a period in the external environment. Parasite population growth and problems for the hosts depend
on reinfection and the build-up of parasite numbers. The
dynamics of transmission and persistence then depend on
patterns of host movement in relation to infective stage
development and availability in the environment (Morgan
et al., 2004). Climatic stochasticity and its effect on parasite
vital rates is likely to be important. In both cases, spatial factors including host distribution and movement, and variation
in the environment, could influence rates of infection. However, modelling this spatial heterogeneity explicitly leads to
complex simulations that are even more difficult to para-
1 3 1 ( 2 0 0 6 ) 2 4 4 –2 5 4
meterise, explore and validate than the models presented
here. Deciding on the level of complexity to include in models
of parasite transmission is an important dilemma facing theoreticians of animal parasites in general (Cornell, 2005), but is
perhaps an even greater issue when considering wildlife disease and associated conservation management issues.
This paper aims to demonstrate that mathematical models of wildlife disease can be usefully applied to assess the
risk of transmission across the wildlife–livestock boundary,
and to guide control strategies accordingly. Earlier efforts at
modelling wildlife disease largely focused on models that
generate general patterns of disease dynamics using only a
simple structure (e.g., Grenfell, 1992; Heesterbeek and Roberts, 1995; Roberts et al., 1995; Roberts and Heesterbeek,
1998). These models have the advantage that they are transparent and analytically tractable, and they hold lessons that
can be applied to a wide range of systems. However, predictions are usually too vague to be used in relation to a specific
system. The motivation behind this class of model is the discovery of determinants of general disease behaviour, and not
the control of wildlife disease per se. As a result, a culture gap
has grown between modellers and wildlife managers. The
proceedings of an important meeting on wildlife disease targeted the narrowing of this gap as a priority for the research
community (Grenfell and Dobson, 1995), but a follow-up
meeting acknowledged that little progress had been made
in this direction (Hudson et al., 2002). More recently, models
have appeared that consider pathogen dynamics in multiple
host species (e.g., Dobson, 2004), although few explicitly consider implications for control in specific systems (but see Haydon et al., 2002b; Caley and Hone, 2004; Cox et al., 2005;
Randall et al., 2006; Vial et al., 2006).
In order to persuade field veterinarians and others with
responsibility for the control of wildlife disease of the merits
of modelling as a tool in disease control, its output must be
meaningful in terms of practical control strategies for specific
systems. This will require models that are narrower and more
applied in focus than many theoretical biologists are comfortable with. Greater biological realism will have to be incorporated. There is a danger that this will lead to a profusion of
detailed simulation models, perhaps several for each disease
system, each producing contrasting predictions in a rather
opaque way. Rather than just pointing this out and extolling
the contrasting merits of simplicity, however, the modelling
community should lead the way in standardising some of
the general model approaches and frameworks that could
usefully guide the practical control of wildlife disease. Methods for comparing different models with each other and with
patchy and imperfect field data should also be developed to
the point where they can be applied by non-specialists. For
their part, field veterinarians and biologists should realise
that models are a simplified representation of reality, and that
predictions will never be as accurate as they would like. In
most cases, there is a lack of good quality, basic data over a
sufficient period of time with which to validate models, so
that there is always a risk that model predictions will be
quantitatively and even qualitatively wrong. This should not
discourage field workers from embracing modelling as a tool
in their armoury against wildlife disease, but it should
discourage them from using models uncritically, and then
B I O L O G I C A L C O N S E RVAT I O N
complaining when control strategies based on them fail.
Modellers can help in this regard by expressing their predictions as relative risk of various events or control strategies,
rather than making concrete forecasts of disease incidence.
A major challenge for both modellers and field biologists is
to match model output with the sorts of data that can be
practically collected in the field. Validation of wildlife disease
models relies on much shorter data series than are available
for many diseases of humans and domestic livestock. To surmount this obstacle, we must either make more efficient use
of the limited data that we have, by developing advanced analytical tools, or find a way to fund longer term studies and
monitoring of wildlife disease, or preferably both. It is only
by comparing model predictions with real data that we will
advance our science and develop useful insights into disease
behaviour and practical control.
Acknowledgements
Research contributing directly to this paper was funded by INTAS (projects 95–29 The interactions between saiga and
domestic livestock in the Aral Sea region (through contact,
competition and transmission of parasites and diseases)
and KZ-96-2056 Land degradation and agricultural change
on the rangelands of Kazakhstan), and by studentships from
the University of Warwick (ML), University College Dublin
(ERM), and BBSRC (UK) (ERM).
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