Control of a highly pathogenic H5N1 avian influenza outbreak in the Download

Transcript
Modelling H5N1 transmission in UK poultry
Control of a highly pathogenic H5N1 avian influenza outbreak in the GB poultry
flock
Electronic Supplementary Material
James Truscott*1, Tini Garske*1,2, Irina Chis-Ster1, Javier Guitian3, Dirk Pfeiffer3, Lucy
Snow4, John Wilesmith2,5, Neil M Ferguson1, Azra C Ghani2+.
1. Department of Infectious Disease Epidemiology, Imperial College London
2. Department of Epidemiology & Population Health, London School of Hygiene &
Tropical Medicine
3. Epidemiology Unit, Royal Veterinary College
4. Centre for Epidemiology and Risk Analysis, Veterinary Laboratories Agency
5. Department for the Environment, Food and Rural Affairs
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Modelling H5N1 transmission in UK poultry
1.
Analysis of the Structure of the GB Poultry Flock ............................................... 3
1.1.
1.2.
2.
Natural History & Epidemiological Parameters ................................................... 6
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
3.
2
Incursion scenarios ................................................................................................ 27
Proportion of spatial and periodic group transmission ........................................... 31
Scaling of infectiousness with number of birds at a premise ................................. 33
Density-dependent spatial transmission ................................................................ 35
Additional Results & Sensitivity Analyses: Impact of interventions ................... 36
5.1.
5.2.
5.3.
5.4.
5.5.
5.6.
6.
Spatial transmission ............................................................................................... 18
Network transmission ............................................................................................. 20
Fixed network transmission .................................................................................... 20
Model calibration and risk calculation .................................................................... 25
Sensitivity Analyses: Scenarios without controls .............................................. 27
4.1.
4.2.
4.3.
4.4.
5.
Course of infection in individual birds........................................................................6
Susceptibility to infection and asymptomatic infection ..............................................7
Duration of infection, viral shedding and mortality ....................................................7
Effect of vaccination ..................................................................................................9
Within-farm dynamics ............................................................................................. 11
Interventions ........................................................................................................... 15
Model Details ................................................................................................... 16
3.1.
3.2.
3.3.
3.4.
4.
Poultry Register Data ................................................................................................3
Network Data.............................................................................................................4
Single incursions .................................................................................................... 36
Proportion of spatial and periodic group transmission ........................................... 40
Density-dependent spatial transmission and size-dependent contact rate............ 41
Shortening the infectious period through faster implementation of interventions .. 42
Sensitivity to intervention parameters .................................................................... 44
Sensitivity to vaccine parameters........................................................................... 45
References....................................................................................................... 47
Modelling H5N1 transmission in UK poultry
1.
Analysis of the Structure of the GB Poultry Flock
1.1. Poultry Register Data
The GB Poultry Register Data (PRD), provided by the Department for the
Environment, Food and Agriculture (Defra), contains details of the spatial location,
husbandry practices and types of animals kept for poultry premises in Great Britain. It
was a legal requirement that all commercial poultry premises keeping 50 or more
birds register with Defra by 28th February 2006. This database should therefore be
an accurate representation of the commercial poultry population of GB. However, the
extent to which this has been achieved is not known. The database also includes
3292 (14%) premises reporting less than 50 birds. These premises are included in
our analyses and in model parameterisation (except where explicitly stated
otherwise). However it should be noted that it is not known how representative this is
of this population of small holdings since registrations of holdings with less than 50
birds were voluntary and it is likely that there are many more small holdings not
registered.
The dataset records information on 23,516 premises holding 271 million birds. The
spatial location is known for 23,407 (99.5%) premises; in the analyses presented
here we restrict to those with known spatial location. There were statistically
significant differences between the characteristics of those with and without spatial
location data; those without location data were significantly less likely to keep layer
chickens (p=0.003), more likely to keep broiler chickens (p=0.01), more likely to have
50 or less birds (p<0.0001) and less likely to be free range (p=0.03) than those with
location data. However, as the overall proportion of premises with missing location
data is small we do not believe this substantially biases our analyses.
For model parameterisation the species and husbandry purposes were combined
into a single set of categories (Table S1). Where more than one category was
present at a single premise the premise was assigned to be in the category with the
largest number of birds. The data were further stratified according to the party
information supplied in the dataset into those belonging to multi-site companies (595
premises from 11 multi-site companies holding 45 million birds) and single-site
premises. This structure (primarily relating to broiler and layer chickens) is included in
the models.
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Modelling H5N1 transmission in UK poultry
Table S1: Species/husbandry classification used in the models. Premises are included once in this table
if they keep multiple species/husbandry types and are listed in the classification in which they keep the
largest number of birds. The number of birds is the total number at the premise.
Classification
Company
Number (%) of
Number of Birds
Premises
Chicken Broilers
Chicken Layers
Turkeys
Reared for shooting
Ducks & Geese
Other
10
286 (1.2%)
26.4 million
30
119 (0.51%)
17.7 million
40
138 (0.59%)
17.5 million
50
64 (0.27%)
7.2 million
140
207 (0.88%)
20.6 million
independent
985 (4.2%)
60.8 million
small holdings
264(1.1%)
31,600
70
101 (0.43%)
5.4 million
80
20 (0.09%)
1.8 million
90
14 (0.06%)
1.7 million
130
223 (0.95%)
12.2 million
independent
1197 (5.1%)
19.2 million
small holdings
5562 (24%)
0.47 million
110
45 (0.19%)
3.5 million
independent
636 (2.7%)
7.4 million
small holdings
287 (1.2%)
57,100
independent
6720 (29%)
53.9 million
small holdings
2389 (10.2%)
0.63 million
independent
265 (1.1%)
4.9 million
small holdings
751 (3.2%)
73,100
independent
419 (1.8%)
9.3 million
small holdings
2713 (11.6%)
0.27 million
1.2. Network Data
Network data were obtained from a sample of single-site premises, multi-site
premises, poultry slaughterhouses and catching companies through self-completed
questionnaires. The information was collected through postal questionnaires
completed by personnel at the premises. Given the rapid timescale under which the
research was taken, it was not possible to pilot or validate these questionnaires.
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Modelling H5N1 transmission in UK poultry
In total, 3989 poultry premises, 95 slaughterhouses and 45 catching companies are
included, although some of these did not complete questionnaires (for example,
slaughterhouses reported as used by poultry premises may not themselves have
completed a questionnaire). The data were cross-checked with the Poultry Register
Database. A total of 1822 (46%) premises represented in the network data could not
be identified in the PRD; of these only 10 had 50 or more birds and hence were
legally obliged to register. These 10 premises belonged to a single owner.
Information taken from the slaughterhouse questionnaires was used to derive the
distribution of the number of premises served by each slaughterhouse and the
distance distribution between poultry premises and slaughterhouse. Ten
slaughterhouses were excluded because they did not report any premises. A further
24 slaughterhouses did not complete the questionnaire, leaving a distribution based
on 61 slaughterhouses. A similar process was undertaken for catching companies
(n=45) and bird supplier premises (n=204). Exponential distributions provided the
best fit to these data and were used for model parameterisation.
Premises on average send birds to slaughter 6 times a year i.e. every 2 months.
Table S2 shows the statistics obtained for the main recorded contacts in the data.
There is some uncertainty over the interpretation of these data as about 85% of
premises recorded with zero contacts are actually non-responders. The data
presented, limited to those with a response in each category, may therefore overrepresent the true frequency of contact.
Summing over these possible modes of contact (for those premises that recorded
feed delivery contacts) a single premise has a median of 66 contacts in a year (90%
range 6-406) or 1.3 contacts per week. This is positively correlated with the number
of birds at the premise (Pearsons correlation coefficient r=0.27, p<0.001). These
parameters are used to define the mean node degree in the network model and for
the contact frequency for group transmission in the spatial simulation model.
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Modelling H5N1 transmission in UK poultry
Table S2: The median and 95% range of rate of contact for the main reasons that a premise has contact
with others in the poultry industry.
Type of contact
Number Premises
Median (90% range) number
Reporting
of contacts per year
Feed delivery
469
30 (4-204)
Slaughterhouse visit
2330
6 (1-21)
Catching Company
220
4 (1-42.5)
Vaccination
21
6 (1-20)
Cleaning
171
3 (1-24)
Other
397
30 (3-310)
2. Natural History & Epidemiological Parameters
As data on the natural history parameters at the flock level in the case of uncontrolled
outbreaks are scarce, we use data on bird-level parameters and a within-farm model
to translate these estimates into farm-based parameters. In the following sections we
provide justification from the literature for the bird-level parameters and detail the
within-farm model used to translate these estimates into farm-based parameters.
2.1. Course of infection in individual birds
Information on the course of avian influenza virus infections within individual birds
has been extensively studied using experimental infections, the majority as control
arms in vaccination studies. Because of the high doses and the route of infection
(mostly through direct inoculation of the virus although a small number of studies
report attack rates in contacts of infected birds) it is not possible to directly
extrapolate these results to infection in the field. However, in the absence of detailed
data on field infections, we have chosen natural history parameters based on these
experimental infections.
A second limitation to the review detailed below is the heterogeneity in the strains
and types of avian influenza considered. For completeness we present some results
from LPAI studies although it should be appreciated that the duration of infection may
well be longer and the severity less than for HPAIs. Furthermore, because of the
relative paucity of data on H5N1, we also consider other HPAI data. Finally, it has
been noted that the pathogenicity of the H5N1 strain of HPAI has changed over time.
This change has been documented in detail in ducks. For example, ducks infected
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Modelling H5N1 transmission in UK poultry
with H5N1 in Hong Kong between 1997 and 2002 show either no clinical signs or
only very mild disease (Hulse-Post et al., 2005). In contrast, more recent
experimental studies in ducks with H5N1 viruses obtained in 2002 from Vietnam and
China have killed ducks and other aquatic poultry (Ellis et al., 2004; Sturm-Ramirez
et al., 2004; Sturm-Ramirez et al., 2005). These differences between strains within
the H5N1 type can also therefore impact on observations of the natural history within
individual birds.
2.2. Susceptibility to infection and asymptomatic infection
Experimental studies have demonstrated that chickens are always susceptible to
H5N1 infections and there is a near 100% mortality rate. Turkeys appear to be more
susceptible to other HPAI and LPAI infections (Capua and Marangon, 2004; Tumpey
et al., 2004) and recent experimental data using an H5N1 strain from outbreaks in
Turkey in 2005 suggest that this is also the case for that subtype (McNally et al.,
2006). Asymptomatic infection has not been reported in chickens or turkeys.
The degree to which ducks are susceptible to infection and onset with clinical signs
varies by strain, even within the H5N1 subtype. The most comprehensive study of
H5N1 in ducks shows some recent H5N1 viruses retrieved from a variety of locations
in South-East Asia can be highly pathogenic and result in clinical signs and death in
mallard ducks whilst other only result in asymptomatic infection or mild clinical
disease (Hulse-Post et al., 2005). These results are in contrast with earlier studies of
H5N1 from the Hong Kong outbreak in 1997 in which all ducks showed few clinical
signs (Ellis et al., 2004; Sturm-Ramirez et al., 2004; Sturm-Ramirez et al., 2005).
2.3. Duration of infection, viral shedding and mortality
The data in Table S3 summarise the information obtained from the literature on the
duration of infection (days from inoculation to death) as well as any information
provided on viral shedding over this period.
For chickens and turkeys, all experimental inoculations result in the death of the
birds. For HPAI H5N1 the duration of infection is reported to be between 3 and 5
days following infection. One study of H7N7 HPAI reported that 3 infected contact
chickens (those placed in close contact with the inoculated chickens) survived
infection (van der Goot et al., 2005) but we assume that this is unlikely for the more
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Modelling H5N1 transmission in UK poultry
pathogenic H5N1. Viral shedding typically occurs rapidly with all studies reporting
shedding by 3 days post inoculation (when first tests are typically undertaken). Only
one study reported more frequent testing; this showed viral shedding with H7N7
occuring in the buccal cavity from 24 hours post inoculation in chickens and 8 hours
post inoculation in turkeys, suggesting a potentially rapid onset of infectiousness in
individual birds (Essen et al., 2006).
Table S3: Summary of the duration of infection, mortality rate and viral shedding in experimentally
infected birds.
Species
Subtype
Country /
Days from
Year
inoculation
Viral shedding
Reference
-
(van der Goot
to death
Chickens:
HPAI H7N7
Netherlands/
2–5
2003
HPAI H5N2
U.S.
et al., 2005)
6
-
(van der Goot
et al., 2003)
HPAI H5N1
China / 2004
2 days
-
(Tian et al.,
2005)
HPAI H5N1
Vietnam
3-4
1/1 at 3 days p.i.
(Webster et al.,
2006)
HPAI H7N1
Italy/1999-
>21
2000
Buccal cavity
(Essen et al.,
from 24 hours
2006)
p.i.; Cloacal from
3 days p.i.
Turkeys:
HPAI H7N1
Italy / 1999-
Up to 8
Buccal cavity
(Essen et al.,
2000
days?
from 8 hours p.i.;
2006)
Cloacal from 24
hours p.i.
Ducks:
HPAI H5N1
China / 2004
13/15 died by
Oropharyngeal
(Tian et al.,
day 6
and cloacal
2005)
shedding from 3
days p.i.
HPAI/LPAI
Hong Kong /
6/12 HPAI
Viral shedding
(Hulse-Post et
H5N1
1997-2003,
died, 0/16
from day 7 to 17
al., 2005)
China / 2004,
LPAI died
Vietnam /
2003-2004,
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Modelling H5N1 transmission in UK poultry
Indonesia /
2004,
Singapore /
1997
HPAI H5N1
HPAI H5N1
Hong Kong /
16 hours – 4
1997
days
Hong Kong /
4 – 6 days
1997-2003
-
(Shortridge et
al., 1998)
Tracheal and
(Sturm-
cloacal shedding
Ramirez et al.,
peaks on day 3;
2004; Sturm-
drops from day 6
Ramirez et al.,
2005)
HPAI H5N1
Vietnam
No deaths
Tracheal and
(Webster et al.,
cloacal shedding
2006)
from day 3 p.i.
Geese:
HPAI H5N1
China / 2004
All died within
Oropharyngeal
(Tian et al.,
7 days
and cloacal
2005)
shedding from 3
days p.i.
2.4. Effect of vaccination
A range of vaccines have been developed against H5N1 and are in widespread use
in parts of South East Asia (notably Vietnam and China (Normile, 2005a; Normile,
2005b)). A growing number of studies have been undertaken on the effectiveness of
current vaccines with the majority based on individual birds rather than premises.
Table S4 summarises these studies. The current vaccines appear to have high
efficacy in protecting individual birds and all also report a reduction in viral shedding.
Two studies have attempted to quantify the effectiveness of vaccination at a
population level. The first was a field evaluation of the effectiveness of the Nobilis
H5N2 influenza vaccine against H5N1 outbreaks on chicken farms in Hong Kong in
2002 (Ellis et al., 2004). Three chicken farms were studied from the commercial
sector in which farms typically keep between 20,000 and 100,000 chickens which are
imported as 1 day old chicks and marketed between 80 and 100 days. The
evaluation followed the impact of vaccination on transmission from shed to shed
within each of the three farms in which H5N1 incursions occurred. In the first farm,
clinical signs of infection (death of birds) were detected in one shed 9 days after this
shed had received the vaccine and continued until day 18 post vaccination. Following
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Modelling H5N1 transmission in UK poultry
this time there were no further outbreaks, nor was there any detectable sub-clinical
infection in unaffected sheds at days 15, 22, 28, 33 or 37 post-vaccination. The
second farm was vaccinated as part of the ring vaccination program for the infection
in the first farm. In three sheds on this farm, affected chickens were detected
between 13 and 17 days post vaccination. No virus was detected in later samples.
The third farm was located in a separate district and therefore not part of the ring
vaccination program. Following an incursion in this farm, all other sheds were
vaccinated and H5N1 was not detected in any of these sheds.
Table S4: Summary of the effectiveness of vaccination in experimental studies.
Species
Subtype
Country
Clinical Signs /
Viral shedding /
/ Year
Death
Antibody
Reference
response
Chickens:
HPAI H5N1
HPAI H5N1
Hong
Deaths at 13-17 days
-
(Ellis et al.,
Kong /
p.v.; Protected by day
2002
30-33 p.v.
China /
Protected 2, 3 and 43
Oropharyngeal and
(Tian et al.,
2004
weeks p.v.
cloacal shedding
2005)
2004)
very low 3 days p.v.
Protected 20 days
Antibody response
(van der
p.v.
increases from day
Goot et al.,
8 p.v.
2005)
“significant
(Tumpey
reduction in viral
et al.,
shedding”
2004)
Oropharyngeal and
(Tian et al.,
cloacal shedding
2005)
Turkeys
LPAI H7N2
U.S. /
-
2002
Ducks:
HPAI H5N1
China /
All healthy
2004
very low 3 days p.v.
HPAI H5N1
Vietnam
No deaths or clinical
No cloacal /
(Webster
signs; virus continued
tracheal shedding 3
et al.,
to replicate
days p.v.
2006)
China /
Several vaccinated
Viral shedding on
(Tian et al.,
2004
died; Complete
days 3, 5 and 7
2005)
Geese:
HPAI H5N1
protection by day 30
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Modelling H5N1 transmission in UK poultry
The second study used simple SIR compartmental models to evaluate the
effectiveness of two different vaccines (H7N1 and H7N3) in an experimental study of
H7N7 transmission in chickens (van der Goot et al., 2005). In this study chickens
were housed, infection was introduced at different time points (1 or 2 weeks post
vaccination), and the birds were monitored daily using virus isolation and serology.
All unvaccinated chickens which were inoculated with the virus died within 2-5 days,
as did the majority of unvaccinated chickens which were in contact. The virus spread
rapidly in the unvaccinated setting with the reproduction number from bird to bird
estimated to 208. After 1 week of vaccination, the reproduction number was reduced
to 0.03 with the H7N1 vaccine and 1.1 with the H7N3 vaccine. Two weeks post
vaccination there was no transmission. They also estimated a reduction in the
infectious period from 6.3 days in unvaccinated chickens to 3.7 days 1 week post
vaccination with the H7N3 vaccine and 1 day for the H7N1 vaccine (though these
were based on small numbers of infected birds).
2.5. Within-farm dynamics
Since limited data exist on the detailed time-course of a typical HPAI H5N1 outbreak
on the types of poultry farms found in GB, it is necessary to extrapolate from the
natural history of infection in a single animal to that likely to be seen on a farm.
Models of within-farm transmission dynamics offer a means to do this. Here we use a
very simple model of within-farm dynamics, namely one which assumes all birds are
homogenously mixing on a single premise. In reality poultry populations in farms are
structured by house and (in the case of housed layers) cage, but the theory of
epidemics in metapopulations tells use that such structuring is only likely to have a
major effect if it results in a greater than 3 orders of magnitude variation in the risk of
infection between different birds (Hagenaars et al., 2004; Lloyd and May, 1996).
Thus a premise with multiple poultry houses and good biosecurity between them may
see somewhat slower outbreak progression than a premise with the same number of
animals in a single shed. However, the progression of an epidemic in a single poultry
house with birds structured into cages where within-cage transmission is, say, 10-fold
greater than between-cage transmission will occur at almost exactly the same rate as
an outbreak in a poultry house with no cages and the same overall within-premise
R0.
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Modelling H5N1 transmission in UK poultry
Few detailed data on the precise time-course of viral shedding in poultry infected with
HPAI H5N1 are available (see section 2.3), so we make the simple default
assumptions of a fixed latent period (during which animals are not infectious) of 0.5
days, and a fixed infectious period (during which infectiousness is constant) of 2
days, after which animals are assumed to die. We then assume a high withinpremise R0 of 40 (though as Figure S5 below shows, sensitivity to the precise value
of R0 assumed is minor, so long as R0>20). We model the infection process
stochastically.
This simple model gives projections of the prevalence and incidence of infection and
the incidence of death as a function of time from when the infection enters a premise
(Figure S1). Detection of infection on a farm is likely to result from detection of
excess mortality, meaning the model can also be used to predict the likely time to
detection, given assumptions as to the likely trigger level of excess mortality (Figure
S1). Here we assume 5% mortality in a 2 day period for detection.
Figure S2 – Figure S6 show the effect of varying the default parameter assumptions
on within-farm epidemic dynamics. It is interesting to note that, with the exception of
premise size, the effect of varying most parameters on the time to detection is
relatively slight – with infection reliably being able to be detected (via excess
mortality) on a farm with 1000 birds within 48 hours. This figure increases by around
a day for a farm with 100,000. These results inform the between-farm transmission
models, which assume infection is typically detected in 2 days, reducing to 1.75 days
for a fast response.
100%
% of birds
infective
% of birds
dead
Probability
of detection
Percentage
80%
60%
40%
20%
0%
0
1
2
3
4
5
6
7
8
9 10
Day
Figure S1: Within-farm transmission model results for baseline parameters (0.5 day latent period, 2 day
infectious period, R0=40) on a1000 bird premise with 0.5% of birds initially infected. The average (based
on 1000 model runs) cumulative % mortality and prevalence of infective animals is shown, together with
the probability of detection of infection assuming 5% mortality over a 2 day period is needed for
detection.
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Modelling H5N1 transmission in UK poultry
b
200
1000
5000
25000
125000
Percentage
80%
60%
40%
20%
c
100%
80%
0%
100%
80%
Percentage
100%
Percentage
a
60%
40%
20%
0%
60%
40%
20%
0%
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Day
Day
Day
Figure S2: Effect of premise size (number of birds) on within-farm epidemic progression, for a fixed
number (5) of birds initially infected. a), b) and c) show % of birds infective, % of birds dead and
probability of the outbreak having been detected, respectively. All other parameters as Figure S1.
Results based on 1000 model runs. Varying premise size but keeping the initial proportion of birds
infected fixed gives results identical to Figure S1, except for increased rates of early outbreak extinction
for very small premise sizes.
b
0.10%
0.30%
1%
3%
10%
Percentage
80%
60%
40%
20%
c
100%
80%
0%
100%
80%
Percentage
100%
Percentage
a
60%
40%
20%
0%
60%
40%
20%
0%
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Day
Day
Day
Figure S3: As Figure S2, but showing effect of varying the proportion of birds initially infected between
0.1% and 10%.
b
1.5
2
2.5
3
3.5
Percentage
80%
60%
40%
20%
0%
c
100%
80%
100%
80%
Percentage
100%
Percentage
a
60%
40%
20%
0%
60%
40%
20%
0%
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Day
Day
Day
Figure S4: As Figure S2, but showing effect of varying the individual animal infectious period from 1.5 to
3.5 days.
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Modelling H5N1 transmission in UK poultry
b
10
20
30
40
50
Percentage
80%
60%
40%
20%
c
100%
100%
80%
80%
Percentage
100%
Percentage
a
60%
40%
20%
0%
60%
40%
20%
0%
0%
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Day
Day
Day
Figure S5: As Figure S2, but showing effect of varying R0 between 10 and 50.
100%
Percentage
80%
1%
3%
5%
7%
10%
60%
40%
20%
0%
0 1 2 3 4 5 6 7 8 9 10
Day
Figure S6: Effect of detection threshold (defined as cumulative mortality over a continuous 2 day period)
on timing of detection of a within-farm epidemic. All other parameters as Figure S1. Results based on
1000 model runs.
We do not use the infective prevalence profiles generated by the within-farm model
directly in the between farm transmission model. Instead they were used to motivate
the choices of the latent and infectious periods of infected farms, and the time to
detection. The generation time for between-farm transmission can be calculated from
the within-farm model as

Tg    I ( )d
0

 I ( )d
(1)
0
where I ( ) is the prevalence of infective animals on a single farm time  after that
farm was infected (Fraser et al., 2004).
The between-farm models used here assume a fixed latent period, L, and a fixed
infectious period, D, of constant infectiousness. For such models, Tg  L  D / 2 .
Assuming L=1.5 days, this enables D to be calculated from a knowledge of the
estimate of TG from the within-farm model. For the baseline parameters used for
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Modelling H5N1 transmission in UK poultry
Figure S1, TG  3.5 days, meaning D  4 days – as assumed for the between-farm
models.
It would of course be possible to embed the within-farm model directly within the
between-farm transmission model; we chose not to do this here for simplicity and due
to the many uncertainties surrounding within-farm transmission and how the
epidemic process on a farm varies as a function of the type of farm (layer/broiler,
intensive/free-range), number of birds, species mix and other variables. However,
future work will examine the impact of more realistic within-farm dynamics on
between-farm transmission.
Figure S7 shows how varying 2 parameters of the within-farm model affects the
between-farm generation time. In general, the impact of varying parameters is as
would be expected from Figure S2 – Figure S6, though in absolute terms even large
changes in basic parameters have a limited effect (Tg typically staying in the range 34).
50
Tg
5.5-6
40
5-5.5
30
20
R0
4.5-5
4-4.5
3.5-4
3-3.5
100
1000
10000
10
100000
2.5-3
Premise size
Figure S7: Effect of varying R0 and premise size on the between-farm generation time, Tg, shown as
isocline surface. All other parameters as Figure S1. Results based on 50 parameter combinations, and
1000 model runs per combination.
2.6. Interventions
The disease status for each premise is tracked in the models described in section 3
below. All premises are initially susceptible to infection and we assume that over the
period of the outbreak (typically less than 300 days) that IPs are not re-stocked once
the culled birds are removed and the premises disinfected. Fixed waiting times in
each disease state are used throughout; sensitivity analyses demonstrated that this
did not produce substantially different results to assuming exponentially-distributed
waiting times.
15
Modelling H5N1 transmission in UK poultry
The progress of epidemics on individual premises will clearly vary according to the
size of the premises, its type and the species of animals it contains. As an
uncontrolled baseline scenario we assume that, once infected, the premise has a
latent period of 1.5 days followed by an infectious period of 4 days in the absence of
any intervention. These parameters are informed by the within-farm model presented
earlier. While such a scenario is not considered to be plausible (as all outbreaks
would involve rapid interventions), it is used to calibrate the values of R0 assumed in
the models.
We also consider three further possible natural histories within a premise to include
the control measures detailed in the main paper; standard response, fast response
and vaccinated flocks. For all controlled scenarios, we also consider the difference in
behaviour of premises within a restriction zone. The various stages and their
durations are listed in Table S5. The standard response scenario roughly matches
the speed of interventions achieved by Defra in the H5N1 outbreak in Suffolk in
February 2007, although we assume a slightly faster response than that observed in
this outbreak (Department for the Environment Food and Rural Affairs, 2007).
Table S5: Delay parameters for natural history of infection on a farm and detection/response.
Delay
Uncon-
Standard response
Fast response
Vaccinated
trolled
IP outside
IP inside
IP outside
IP inside
IP outside
IP inside
-
restriction
restriction
restriction
restriction
restriction
restriction
zone
zone
zone
zone
zone
zone
1.5
1.5
1.5
1.5
1.5
3.0
3.0
Infectiousness detection
-
0.5
0.5
0.5
0.25
1.0
1.0
detectionIsolation
-
1.0
0.0
0.5
0.0
1.0
0.0
detectionRestriction
-
1.5
0.5
1.0
0.25
1.5
0.5
detectionCulling
-
2.5
1.5
2.0
1.0
2.5
1.5
infectiousnessdeath
4.0
-
-
-
-
-
-
Latent period
[i.e. Infection  onset of
infectiousness]
3. Model Details
Premises are assigned to contact groups to match the quantitative and qualitative
data on the structure of the industry. Premises associated with a large company
(companies 10 to 140 in Table S1) are assumed to share a single supplier and
16
Modelling H5N1 transmission in UK poultry
abattoir. Of the remaining premises, we assume that those with capacities of less
than 500 birds (n=11967) do not use commercial slaughterhouses and suppliers and
are considered smallholdings. The remaining premises (n=10222) constitute the
independent commercial sector and are assigned to groups. For slaughterhouse
groups, data on the number and position of slaughterhouses were obtained from
DEFRA and the distribution of distances of premises from slaughterhouses were
calculated from the network data. For suppliers, data were available on the distance
distributions from bird suppliers to premises from the network data and this was
taken, in the absence of other data, as a proxy for the distance for all supplies.
However the locations and number of suppliers was unknown. We assumed 100
suppliers to match approximately the number of slaughterhouses. Positions of
suppliers were assigned randomly according to the density of birds in the country.
Each premise was then assigned randomly to a group according to a weighting
reflecting its distance from that group and the group’s remaining capacity. The
distance weighting-function was of the form
exp(  d ) / d
(2)
where d is the distance between the premise and the centre of the current group.
This is motivated by the apparent exponential distribution for distances for both
abattoirs and suppliers. We scale further by 1/d to account for the increasing area
contained in annuli of increasing radius.
The capacity of groups was taken into account by assuming that all group capacities
of a particular type were drawn from the same distribution. The fraction of the
capacity of any group taken by any member premise was taken to be proportional to
its population. The mean of the group capacity distribution could be calculated as the
total population of birds to be assigned to a group type (abattoir, supplier) divided by
the number of groups catering for the population. Evidence from a report on industry
structure (provided via Defra from Howard Hellig) indicates an average throughput of
9 million birds for abattoirs but with some taking more than 33 million birds per year.
We employed a log-normal distribution for abattoir distribution size with variance
informed by capacity data from this report. Supplier distributions were constructed in
a similar way.
The resulting distributions of distances from premises are compared to those
extracted from the network data (Figure S8).
17
Modelling H5N1 transmission in UK poultry
B
0.2
A 0.18
0.14
Fraction
Fraction
0.25
Simulation
Data
0.16
0.3
0.12
0.1
0.08
Simulation
Data
0.2
0.15
0.1
0.06
0.04
0.05
0.02
0
20
0
60 100 140 180 220 260 300 340 380
20
Distance (km)
60 100 140 180 220 260 300 340 380
Distance (km)
Figure S8: Distribution of distances from premises to A) abattoir B) supplier. Each chart shows the
distribution as generated by the group construction algorithm within the simulator and that derived from
the network data.
3.1. Spatial transmission
Spatial contact within the model represents a range of possible mechanisms. Contact
through people or machinery is probably best represented by a density-independent
description, implying some fixed rate of contact, while diffusive spread through airdispersal of fomites or wild bird movements is better described by a densitydependent approach. We therefore separately simulated epidemics under both
density-dependent and density-independent spatial spread as well as mixtures of
density-dependent and –independent spread. The infectious contact rate between
infectious premises i and susceptible premises j is given by
SI i f ( Ni ) SI j k (dij )
(3)
for density-dependent infection and
 SD i f ( Ni ) SD j
k (dij )
 k (d
k i
ik
)
(4)
for density-independent, where d is the distance between the premises and the
kernel is

 d
k (d )  1   .
 
(5)
Contact rate and susceptibility have been broken up into a number of independent
aspects. The function f ( N ) incorporates the effect of size dependence in contact
rate. For size independent scenarios, f  1, while for size dependent situations,
18
Modelling H5N1 transmission in UK poultry
f ( N )  1  exp( N / Nc ) . The parameters  SD ,  SD represent background unrestricted
contact rate and susceptibility (in this case for spatial contact (s) and density
dependent (D) interaction) and are determined through fitting R0 and proportion of
transmission through group structures (See Section 3.4). Other parameter values can
be found in Table S7 below.
 i ,  j represent modifications to contact rate or susceptibility in individual premises
through policy interventions as described in Table S6. The IP control is applied only
to detected IPs and is taken to be most effective within large companies, less so for
independent commercial premises and negligible for small-holdings. PZ/SZ
restrictions apply to all premises in the zone and effect both transmission and
susceptibility. Dangerous contact tracing is difficult to interpret in the absence of a
contact network and we approximate it here by assuming that all premises sharing a
feed supplier or abattoir with the IP are subject to a reduced contact rate.
Table S6: Adjustments to contact and susceptibility parameters under the intervention strategies
considered.
i
j
Group Independent Smallholding
Group Independent Smallholding
Policy
IP Control
PZ/PZ
Restriction
Dangerous
Contact
Vaccination
19
90%
75%
0%
-
-
-
50%
50%
50%
90%
90%
90%
75%
0%
0%
-
-
-
75%
75%
75%
75%
75%
75%
Modelling H5N1 transmission in UK poultry
Table S7: Parameters for the spatial simulation model.
Parameter name
Value
Source
kernel offset, 
1.2
(Chis-Ster and Ferguson,
2007)
kernel power, 
2.6
(Chis-Ster and Ferguson,
2007)
Slaughterhouse period, service time
40 days, 3 days
Table S2
Supplier period, service time
7 days, 1 day
Table S2
size-dependent contact rate parameter, Nc
1000
Section 3.4
3.2. Network transmission
Contact groups are structured to capture the episodic and periodic nature of
transmission between premises through the shared use of facilities such as
slaughterhouses. Within each contact group, holdings are assigned to randomly
p daily subgroups, where p is the period of the group. On a particular day, all
premises in that day’s subgroup are in contact with each other. When ‘active’, a
subgroup acts as a well-mixed subpopulation with a density-independent contact
process. Hence the force of infection, i experienced by a premise is
i 
 i GD , I
N
,
j inf .
j
(6)
where, as for spatial transmission, the parameter,  GD , I is the background contact
rate within the group and N is the number of premises in the subgroup. A premise
that is not a member of the active subgroup experiences no force of infection from it.
Equally, an infectious premise can exert no force of infection on other group
members outside its own active days.
3.3. Fixed network transmission
As an additional sensitivity analysis, we also considered the potential for
transmission if the commercial network contact is better represented by a small
number of fixed directional links instead of the larger group structures with periodic
contacts. For this aspect we constructed a pure network model for those premises
with more than 500 birds.
20
Modelling H5N1 transmission in UK poultry
Let X i , j ,l ,n denote a premise at location i (where i  {x, y} defines a location) of
species/husbandry purpose j which holds n birds and belongs to company l. Making
the reasonable assumption that there is only one premise at a given location,
i  {x, y} can be used to index the premises. Premise i is assigned an in-node degree
m1 (i ) where m1 (i ) ~ NegBin( 1 , k1 | j , l ) and an out-degree m2 (i ) where
m2 (i ) ~ NegBin( 2 , k2 | j , l ) which can depend on species/husbandry purpose and
company but is assumed independent of the number of birds or spatial location and
 s and k s are the mean and dispersion parameters of the Negative Binomial
distribution. Note that the dependence of the contact frequency on flock-size as
observed in the network data is accounted for by the fact that small premises with
less than 500 birds are excluded from the network transmission. Because of lack of
data, we set 1   2 and k1  k 2 and relax the dependence on j and l in our
specification (although in practice, to balance in- and out- links there is a slight
dependence on l).
Premises are then linked according to a specified mixing matrix
P(i, i ' | j, j ', l , l ', d ) which defines the probability that premise i will be linked to premise
i’. The matrix is dependent on the species/husbandry purpose of premises, company
status and the Euclidean distance d  ( x  x ')2  ( y  y ')2 between any two premises.
To enable construction of such a network we also need to ensure the matrix is
symmetric and so use the symmetrised version P  ( P  PT ) / 2 . The matrix is
summarised by the measure of assortativeness Q defined as Q 
Tr ( P)  1
, where C
C 1
is the number of classes and P is normalised such that the columns sum to 1.
We assume that premises are more likely to have contact with other premises in the
same sector than with premises in different sectors. Furthermore, if a premise
belongs to a company, it is more likely to use the resources of that company, and
therefore have most links to other premises in that company, less to other premises
outside that company but within the same sector, and the smallest number of links to
premises from a different sector. As the network data was not detailed enough to
give any information beyond the frequency and distance distributions, as a proxy to
understand the extent of overlap between companies and sectors, we calculated the
proportion of premises of species/husbandry purpose j that also kept
species/husbandry purpose j’ separately for the large companies and the
21
Modelling H5N1 transmission in UK poultry
independent sector. This is shown in Table S8 and was used as the basis for the
mixing matrix in the model. Note that in some of the rows in Table S8, the percentage
of premises keeping flocks of different types adds up to less than 100%. This is due
to premises that are not classified as commercial hatcheries, but only reporting flocks
with husbandry purpose hatching, which is not captured in the existing classification.
Table S8: The data show the number (%) of farms within classification/company j that report flocks of
type j’. CB=chicken broilers, CL=chicken layers, T=turkeys, Sh=reared for shooting, DG=ducks and
geese, O=other. For classification the company association was taken to be the primary quantity, and
companies were classified into species/husbandry purposes according the species/husbandry purpose
of the majority of their premises.
Class. Company Number of CB
CL
T
Sh
DG
O
premises
CB
10
286
274 (95.8) 4 (1.4)
1 (0.3)
9 (3.1)
1 (0.3)
5 (1.7)
30
119
111 (93.3) 6 (5.0)
0 (0)
0 (0)
0 (0)
2 (1.7)
40
138
122 (88.4) 4 (2.9)
1 (0.7)
2 (1.4)
0 (0)
5 (3.6)
50
64
49 (76.6)
2 (3.1)
0 (0)
3 (4.7)
0 (0)
7 (10.9)
140
207
196 (94.7) 9 (4.3)
0 (0)
2 (1.0)
0 (0)
4 (1.9)
indep.
985
985 (100)
68 (6.9)
81 (8.2)
28 (2.8)
73 (7.4)
58 (5.9)
70
101
0 (0)
85 (84.2)
1 (1.0)
1 (1.0)
5 (5.0)
3 (3.0)
80
20
0 (0)
13 (65.0)
0 (0)
0 (0)
0 (0)
0 (0)
90
14
0 (0)
11 (78.6)
0 (0)
0 (0)
0 (0)
0 (0)
130
223
3 (1.3)
191 (85.7) 3 (1.3)
17 (7.6)
10 (4.5)
8 (3.6)
indep.
1197
41 (3.4)
1197 (100) 66 (5.5)
24 (2.0)
159 (13.3) 82 (6.9)
110
45
1 (2.2)
0 (0)
indep.
636
108 (17.0) 79 (12.4)
Sh
indep.
6720
90 (1.3)
874 (13.0) 180 (2.7) 6720 (100) 412 (6.1) 842 (12.5)
DG
indep.
265
12 (4.5)
22 (8.3)
21 (7.9)
O
indep.
419
15 (3.6)
61 (14.6)
53 (12.6) 30 (7.2)
CL
T
44 (97.8) 1 (2.2)
1 (2.2)
636 (100) 25 (3.9)
101 (15.9) 53 (8.3)
9 (3.4)
0 (0)
265 (100) 46 (17.4)
97 (23.2) 219 (52.3)
Due to a lack of data, it was assumed that premises within companies have 80% of
their links within their sector to other premises within the same company. This
together with the number of premises per class determines the symmetrised mixing
matrix P . The assortativeness obtained with this mixing matrix is Q=0.472.
We parameterised the node degree to represent the expected number of contacts
that a premise would make over the time-course of an infection (mean number of
visits in the network data is 3.5 in 1 week and 15.4 in 1 month and hence we vary the
22
Modelling H5N1 transmission in UK poultry
node degree between 1.5 and 15). Note to obtain a specified R0 we require a mean
node degree at least as large as R0.
The transmission probability per link was derived from the parameter R0 by
1 / nin f
 R 
1  1  0 
 
 
f
(7)
where  is the mean node degree in the static network, ninf is the number of timesteps during which a premises is infectious, and f 
n
1
n
 1  f ( N ) is the mean
i
i 1
infectiousness of all n farms in the network, with f ( N i ) denoting the infectiousness
of premise i depending on the number of birds N it keeps.
For a given specified node degree distribution the network algorithm successfully
900
0.09
800
0.08
700
0.07
600
0.06
500
0.05
400
0.04
300
0.03
200
0.02
100
0.01
0
input distribution
frequency of nodes
matches this distribution (see example simulation in Figure S9)
0
0
5
10
15
20
25
30
35
40
45
50
number of links
desired in-links
desired out-links
actual in-links
actual out-links
input distribution
Figure S9: Comparison of the input distribution for the node degree with the desired and actual node
degree distribution for one network realisation.
The pattern of mixing between premises was assumed to be assortative and
specified by the data given in Table S8. The distribution of achieved mixing patterns,
as measured by the degree of assortativeness obtained in the networks, is
reasonably matched by the algorithm (Figure S10).
23
Modelling H5N1 transmission in UK poultry
Figure S10: Distribution of assortativeness Q obtained from 1000 network realisations. Mean=0.459
(95% CI 0.421 – 0.476), whereas the assortativeness specified by the mixing matrix is Q=0.472.
To determine the distance distribution between two premises that are linked via these
routes, we first weighted the distributions of the distance between the premise and
slaughterhouse, premise and catching company HQ and premise and bird supplier
by the measured frequency of contact with these links. This overall distribution was
then convoluted with itself, taking into account the possible angles between premise
– resource – premise to obtain the distribution of distances between any two
premises connected via these three routes. This combined distribution, shown in
Figure S11, is close in shape to a Gamma distribution. In the same figure we also
show the distribution of distances between premises that are obtained when
premises were randomly linked. The figure shows that the distance between any two
premises connected via one of three resources (slaughterhouse, catching company
HQ or bird supplier) observed in the network data is smaller than that obtained if
premises are randomly linked, showing a degree of spatial clustering of links. Also
note that the majority of commercial premises are linked at distances of more than
20km with a substantial number of links between premises at distances of 100km or
more. This results in a national network of commercial premises. As before, the
algorithm results in simulated networks that closely match the desired distance
distribution.
24
Modelling H5N1 transmission in UK poultry
cumulative distribution function
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
80
10
0
12
0
14
0
16
0
18
0
20
0
22
0
24
0
26
0
28
0
30
0
32
0
34
0
36
0
38
0
40
0
50
0
70
10 0
00
0
60
0
20
40
0
distance in km
input distribution
unrestricted link length distribution
matched link length distribution
Figure S11: Comparison of the desired link length distribution with the “natural” link length distribution
where arbitrary link lengths were allowed and the actual link length distribution matched to the input
distribution. The distributions are obtained by averaging over 5 simulated networks.
3.4. Model calibration and risk calculation
In a full sensitivity analysis, the following were explored:

R0 values of 1.5, 3.0;

density-dependent and density–independent spatial transmission (with group
structures only);

contact rate independent of premise capacity or an increasing function of it;

proportion of disease transmission within groups of 0%, 25%, 50%, 75% and
100% (with group structures only);

fixed network structure versus periodic group structures.
Hence for each scenario, a total of forty-four separate parameter combinations were
investigated. For the proportion of transmission within groups, a distinction was made
in the parameterization of commercial premises and small premises. Small premises
are excluded from calculation of the proportion of transmission within groups. Without
this proviso, 100% group transmission would result in all smallholdings being
excluded from the epidemic, as they are not part of the group structure. Spatial
contact rates for all premises are fitted for the fully spatial scenario. For other
scenarios, smallholdings retain these values while spatial contact rates for
commercial premises are fitted to the desired R0 and group fractions.
25
Modelling H5N1 transmission in UK poultry
The model is calibrated with the uncontrolled disease episode parameters (Table
S5). Parameters  SD , I , GD , I were fitted to overall R0’s and group proportions outlined
above. R0 was defined as the mean number of secondary cases generated by one
infected premises in a susceptible population, averaged over all possible initial
premises. That is
R0i   (1  exp((hijg  hijs )) ,
(8)
j
where hijg is the hazard of group infection to j from i and hijs the hazard of spatial
infection. In practice, we find that the probability of being infected from both
processes is small compared to the probability of infection by one and hence the
effects are approximately additive. The spatial hazard for density-dependent
transmission is given by
hijs  T SI f ( Ni ) SI k (dij )
(9)
and for density-independent transmission,
hijs   SD f ( Ni ) SD
k (dij )
 k (d
k i
ik
)
.
(10)
For group transmission, most value of hijg will be zero except for the cases where the
two premises share a transmission group and also contact is made during the period
of infectiousness.
Figure S12 shows the breakdown of R0 into group, commercial spatial and small
premise components for the runs incorporating group structure. Small premises
make up approximately 50% of the premises in the data set and this is reflected in
the fraction of the size-independent R0 they account for. When size is taken into
account, the fraction is greatly reduced, reflecting the small populations of these
farms.
26
Modelling H5N1 transmission in UK poultry
7
Group
Com
S/H
6
R0 fraction
5
4
3
2
1
0
0%
25%
50%
75%
100%
Size-independent
0%
25%
50%
75%
100%
Size-dependent
Figure S12: Breakdown of R0 into group, commercial spatial and smallholding spatial components for
different fractions of group transmission and for both size-dependent and independent contact rate
within the simulation model.
To produce risk maps, the country was divided into a grid of 5 km squares and a risk
calculated for each. Our measure of risk was taken to be the mean number of
secondary infections generated, given a single index case within the grid square.
4. Sensitivity Analyses: Scenarios without controls
Prior to evaluating the impact of interventions, we explored the scenarios that would
occur in the absence of any intervention using the natural history parameters given in
the main text. The purpose of this analysis is to understand the impact of the different
model assumptions on the disease dynamics.
4.1. Incursion scenarios
In our baseline scenarios we assume a single incursion that is randomly picked from
the population of premises for each simulation. Here we consider the alternative
impact of four other potential incursions:
1. Single low-risk incursion: A single fixed premise in the Fife area (independent
pheasant premise with 600 birds)
27
Modelling H5N1 transmission in UK poultry
2. Single high-risk incursion: A single fixed premise in the Norfolk area
(independent chicken layer premise with 32,000 birds)
3. Monthly random incursions: A randomly chosen premise is infected under a
Poisson process with mean interval between infections of 30 days. This is
varied for each simulation run.
4. Multiple high risk incursions: Five fixed premises in Norfolk are
simultaneously infected at the beginning of the outbreak. These are 2 large
chicken broiler premises, one belonging to a large company, one medium
turkey premise and 2 small independent premises (birds reared for shooting
and other categories).
Tables S9 and S10 summarise the main outcomes for uncontrolled scenarios with R0
=1.5 and 3.0 respectively. The results for all five incursion scenarios are shown. For
the simulations in which a single incursion occurs and in which a large proportion of
transmission occurs via spatial spread, the extinction probability is highest for the low
risk premise (Fife) and lowest for the high risk premise (Norfolk), with results for a
single random incursion lying between these two extremes. This simply reflects the
reproductive capacity of the initial infected premise. A similar pattern is observed for
the final outbreak size, with larger epidemics occurring if the incursion occurs in a
high risk area, and this continues to hold even if the final outbreak size is conditioned
on the epidemic lasting for 14 or more days. This effect is a feature of the
geographical clustering of similar premises. Large premises tend to be clustered
densely with other large premises (e.g. Norfolk), enhancing density-dependent
spread if an incursion occurs in this high risk area. In contrast, smaller premises are
located in less densely populated regions and an incursion in these areas is more
likely to result in the extinction of infection chains. As the proportion of transmission
that occurs via the group structure increases, and in the pure network model, more
long-distance contacts are introduced, these ‘smooth out’ the spatial heterogeneity of
premises. As a result, there is less difference between final outbreak sizes for the
different incursion scenarios. Increasing the value of R0 from 1.5 to 3 has little effect
on the overall pattern. However, we find that outbreaks are now so large that
saturation of the entire poultry population occurs and hence large epidemics are only
limited by exhaustion of the pool of susceptible premises.
28
Modelling H5N1 transmission in UK poultry
Table S9: Summary of outbreak scenarios with no controls for R0=1.5. Shown are probability of early extinction and mean number of IPs and birds died conditioned on the
outbreak lasting 14 days or longer. Size-dependent contact rate and density dependent spatial transmission are assumed. Total premises in spatial model = 23407; network
model = 11439. Results from 1000 iterations.
R0=1.5
Pure Spatial Transmission
Spatial Transmission + 50% Group
Network Transmission Only
% extinct
Conditional
Conditional mean
% extinct
Conditional
Conditional mean
% extinct
Conditional
Conditional mean
within 14
mean number
number of birds
within 14
mean number
number of birds
within 14
mean number
number of birds
days
of IPs
died in millions
days
of IPs
died in millions
days
of IPs
died in millions
single
random
75
3,500
61
73
6,000
120
48
5,200
130
97
250
4.7
84
4,600
92
64
4,700
120
5
5,900
100
22
7,700
150
42
5,500
140
0.1
1,000
17.6
0.1
2,000
40
0
5,400
140
0
6,200
105
0.1
8,100
160
3.5
5,600
140
incursion
single lowrisk
incursion
single highrisk
incursion
monthly
incursions
multiple
high-risk
incursions
29
Modelling H5N1 transmission in UK poultry
Table S10: Summary of outbreak scenarios with no controls for R0=3.0. Shown are probability of early extinction and mean number of IPs and birds died conditioned on the
outbreak lasting 14 days or longer. Size-dependent contact rate and density dependent spatial transmission are assumed. Total premises in spatial model = 23407; network
model = 11439. Results from 1000 iterations.
R0=3.0
Pure Spatial Transmission
Spatial Transmission + 50% Group
Network Transmission Only
% extinct
Conditional
Conditional mean
% extinct
Conditional
Conditional mean
% extinct
Conditional
Conditional mean
within 14
mean number
number of birds
within 14
mean number
number of birds
within 14
mean number
number of birds
days
of IPs
died in millions
days
of IPs
died in millions
days
of IPs
died in millions
single
random
47
15,600
207
52
15,900
240
19
9,600
230
80
6,800
92
61
15,300
230
30
9,700
230
0
16,700
220
1.6
16,500
250
12
9,600
230
0
8,700
115
0.1
9,000
135
0
9,400
230
0
16,700
220
0
16, 600
247
1.2
9,500
230
incursion
single lowrisk
incursion
single highrisk
incursion
monthly
incursions
multiple
high-risk
incursions
30
Modelling H5N1 transmission in UK poultry
For the multiple incursion scenario, early extinction is extremely unlikely, as would be
expected given the very low probability of a single high-risk incursion undergoing
extinction. Final sizes are almost indistinguishable from those of the single high-risk
incursion at both low and high R0 values. A multiple high-risk incursion scenario is
effectively a single high-risk incursion identified at a slightly later point in the
epidemic.
4.2. Proportion of spatial and periodic group transmission
Table S11 shows the influence of the proportion of transmission within groups on
early extinction rates and the final outbreak size for R0=1.5, 3.0 and densitydependent spatial spread. Increasing the proportion of transmission amongst the
commercial sector that occurs via the group structure compared to spatially leads to
a larger proportion of early extinctions. This seems at first counter-intuitive, since
groups link premises over a much larger distance than purely spatial contact and
might be expected to overcome local saturation effects (there is some evidence of
this in the larger outbreaks for R0 =1.5, 25% group transmission). However the daily
substructure of the groups means that there is a high probability that a group
member will not be in infectious contact with other members, resulting in extinction in
the chains of transmission. More generally, we can say that for a given mean number
of secondary infections (R0) for an index case, the group transmission mechanism
has a high variance compared to spatial contact and this is known to increase the
probability of early extinction of an epidemic (Hagenaars et al., 2006). Similarly, the
short service times as a proportion of the group period results in poor transmission
between daily subgroups. These features of our group transmission model should be
kept in mind. In contrast, the network model, even without spatial spread, has much
lower rates of extinction. Although the frequency of contacts informs the node degree
in this model (i.e. the average number of premises each premise can have a potential
contact with), the extinction probability is lower because we assume that there is
always the potential for such a contact to occur. Thus transmission chains are much
less likely to go extinct.
The group and network models can be thought of as two extremes in terms of the
potential for transmission in the commercial sector. Some mechanisms of contact
(such as bird movements and feed deliveries) appear to be highly periodic favouring
the type of structure represented in the group model. Other contact mechanisms
31
Modelling H5N1 transmission in UK poultry
(such as cleaners, building maintenance, egg collections, veterinary staff and farm
workers) are likely to be more regular and less episodic, favouring the type of
structure represented in the network model. The potential scale of an outbreak
therefore requires further understanding both of the more detailed nature and
frequency of these contacts than it was possible to obtain from the current network
data. However, in addition we need to assess the relative likelihood of transmission
via these routes, which may additionally depend on the extent to which biosecurity is
adhered to, particularly for medium-sized commercial premises.
Table S11: Effect of group transmission on early extinction and final size, conditional on extinction later
than 2 weeks. Density-dependent spatial spread, size dependent contact rate for a single random seed.
Total premises in spatial model = 23407; network model = 11439. Results from 1000 iterations.
R0
Group
1.5
3.0
Mean final size
Mean final size
Percent extinct conditional on
Percent extinct conditional on
within 14 days lasting >14 days
within 14 days lasting >14 days
0%
75
3,600
47
15,700
25%
69
6,800
46
17,300
50%
74
6,100
52
16,000
75%
81
4,100
53
13,200
100%
91
420
80
6,600
Network
48
5,200
19
9,600
In Figure S13, we examine the influence of the proportion of group-mediated
transmission on the spatial distribution of infection. Maps A, B, C present an
increasing proportion of group transmission (0%, 50% and 100% respectively)
combined with density-dependent spatial spread and premise size-independent
transmission. The group structure introduces long-range connections, in contrast to
the local density-dependent contacts, and this blurs the regional clustering of highrisk premises. The time-dependence of within-group transmission also affects risk.
Premises only have infectious contact with other members of their group during the
time they are interacting with the group mechanism (‘service time’): at other times
they are effectively isolated within the group. Hence there is a high degree of
variability in R0 between individual premises that is independent of size or density
32
Modelling H5N1 transmission in UK poultry
effects. This adds to variability in the risk as the proportion of group transmission is
increased.
Figure S13: Risk maps for R0=3.0 with density-dependent spread and size-independent contact rate A)
0% within-group transmission, B) 50% C) 100%.
4.3. Scaling of infectiousness with number of birds at a premise
The size distribution of premises is highly skewed with 50% of the bird population
contained in 2.5% of the premises. We compared constant infectiousness across
premises with a scaling of infectiousness with premises size (Figure S14), given by
f ( N )  1  exp(  N / N c ) ,
(11)
with the number of birds kept at a premise, N, and Nc=1000. This function assumes
that infectiousness increases with the number of birds but saturates to a fixed level
for premises with approximately 2000 or more birds. Clearly there is no unique way
to specify such a function, and it is likely that infectivity will also decrease for larger
premises because of increased biosecurity. However, in the absence of data with
which to specify a function, we limited our present sensitivity analyses to the above
function.
This scaling had little effect in the network model because this model only considers
premises with 500 or more birds which already have a reasonably high
infectiousness whilst the scaling strongly suppresses the infectiousness of premises
with <100 birds. We therefore only present results for the spatial and group
structures.
33
Infectiousness
Modelling H5N1 transmission in UK poultry
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1000
2000
3000
4000
5000
Number of birds
Figure S14: Assumed scaling of infectiousness with the number of birds kept at a premise.
Allowing the infectiousness of a premise to increase with the size of the premise
gives rise to additional heterogeneity in R0 between premises. Two consequences of
this can be seen in the results in Table S12. Firstly, such a scaling will impact
differently on the extinction probabilities for different incursion scenarios. If
transmission is independent of the density of premises in a local area and the size of
premises, single seeding scenarios in Fife and Norfolk have comparable extinction
probabilities (see Table S11). However, if infectiousness increases for larger
premises, the smaller Fife farm (600 birds) now has a much increased chance of
rapid extinction whereas the large Norfolk farm (32,000 birds) has a greatly reduced
extinction probability. Second, conditional on early establishment of the epidemic,
assuming that infectiousness increases with the size of premises results in larger
final outbreak sizes for small values of R0. The same effect can be seen when
density dependent spatial transmission is introduced. This behaviour reflects the
heterogeneity of premises with the UK. Certain regions have particularly high
densities of farms (and more large farms) giving a high local transmission rate and
hence larger outbreaks.
34
Modelling H5N1 transmission in UK poultry
Table S12: Effect of size and density-dependence for the spatial simulation model with 100% spatial
transmission on early extinction and mean final size conditional on extinction later than 2 weeks. Results
from 1000 iterations.
R0
1.5
3
Conditional
Density Size
Seeding
Dep.
Single IP
in Fife
Yes
(low-risk
area)
No
Single IP
in Norfolk
Yes
(high risk
area)
No
Multiple
IPs in
Yes
Norfolk
Fraction extinct
Conditional
Fraction extinct
mean final
Dep.
within 14 days
mean final size
within 14 days
size
Yes
0.97
254
0.796
6870
No
0.69
98
0.273
11600
Yes
0.89
125
0.649
16800
No
0.63
32
0.123
18600
Yes
0.05
5920
0
16700
No
0.21
3990
0.017
17400
Yes
0.22
1340
0.009
18800
No
0.57
108
0.123
19400
Yes
0
6180
0
16700
No
0
4600
0
17400
Yes
0.01
1840
0
18800
No
0.08
195
0
19500
(high risk
multiple
incursions)
No
4.4. Density-dependent spatial transmission
Table S12 highlights two main aspects of the difference between density-dependent
and density-independent transmission. For low R0, density-dependent transmission
leads to larger outbreak final sizes than density-independent transmission. Under
density dependence, highly clustered regions, if infected, have large outbreaks,
although transmission between dense areas is unlikely. With density-independent
transmission, R0 is uniformly low and large outbreaks are unlikely. For higher values
of R0, transmission is high for all flocks and the epidemic is able to spread through
almost the entire population under density-independent transmission, while for
density-dependent transmission, sparse regions with low R0 still contribute to the
isolation of dense regions. Hence density-independent transmission leads to larger
final outbreak sizes. This effect is amplified by local restriction interventions as
illustrated in Figure 3 of the main text.
35
Modelling H5N1 transmission in UK poultry
5. Additional Results & Sensitivity Analyses: Impact of
interventions
5.1. Single incursions
For the fixed network simulations of transmission in the commercial poultry sector,
rapid isolation of infected premises is a relatively effective intervention (Tables S13
and S14). The protection and surveillance zones have little impact because most
network links are formed at more than 10km distances. However, tracing of
dangerous contacts is effective because of the assumed fixed network structure and
hence with this additional intervention the majority of outbreaks are controlled. The
remaining small number of uncontrolled outbreaks reflects a worst-case scenario in
which infection enters the highly connected commercial sector (including the large
integrated companies) and onward transmission occurs predominantly to premises
outside the protection and surveillance zones of the IP. Whilst the dangerous contact
tracing is therefore potentially effective, our simulations assume that only direct
contacts in the network (which represent those that have been in recent contact and
hence could potentially have acquired infection) are included in the policy. In reality,
more complete isolation of, for example, an affected company is likely to have an
even greater impact.
For the spatial and group simulations, more stringent measures are needed to control
outbreaks at higher R0 values. For R0 = 1.5, IP isolation is highly effective (Table
S13). The number of extended outbreaks (longer than 14 days) is reduced by only
30% compared to scenarios with no interventions, but these outbreaks are on
average 10 times smaller than with no interventions. With the addition of local area
restrictions (PZ/SZ), only 1-2% of outbreaks last longer than 14 days. The fraction of
group transmission present in a scenario makes little difference to the effectiveness
of the interventions at low R0 values.
When R0 is increased to 3 (Table S14), IP isolation alone has very little power to
bring about the early extinction of the epidemic and only limits the growth of
established outbreaks by a factor of 2. However if the PZ/SZ are added to this the
intervention is highly successfully. Although almost 20% of epidemics are more than
14 days long, a mean of only 10 IP are generated with a mean of 260 premises
36
Modelling H5N1 transmission in UK poultry
placed under restriction. At this higher R0, significant differences can be seen
between purely spatially spread scenarios and those with a greater proportion of
transmission occurring in the group structures. The additional group-mediated
transmission makes control through local area restrictions considerably less effective.
This is a result of the longer premise-to-premise connections occurring in the group
structure. The addition of dangerous contact tracing to the interventions restores the
effectiveness of the overall intervention. Dangerous contact tracing is restricted to the
commercial sector interactions in our model and hence focuses on those contacts
that are not affected by the IP/PZ/SZ restrictions.
37
Modelling H5N1 transmission in UK poultry
Table S13: Impact of isolation of infected premise (IP isolation), isolation of infected premise plus implementation of protection and surveillance zones (IP/PZ/SZ) and
additional tracing of dangerous contacts (IP/PZ/SZ/DC) on the percentage of simulation runs which are extinct within 14 days for R0=1.5. The table also shows the mean
number of infected premises and restricted premises for each scenario and the mean number of birds culled, conditional on the epidemic lasting 14 days or longer. Size
dependent contact rate and density dependent spatial transmission are assumed. Total premises in spatial model = 23407; network model = 11439. Single random
seeding. Results from 1000 iterations.
R0=1.5
Pure Spatial Transmission
Spatial Transmission + 50% Group
Network Transmission Only
% extinct
Conditional
Conditional
% extinct
Conditional
Conditional
% extinct
Conditional
Conditional
within 14
mean IPs +
mean number
within 14
mean IPs +
mean number
within 14
mean IPs +
mean number
days
restricted
of birds culled
days
restricted
of birds culled
days
restricted
of birds culled
premises
in millions
premises
in millions
premises
in millions
73
4,700 + 0
77
74
7,000 + 0
137
48
5,200 + 0
130
IP isolation
83
320 + 0
6.6
88
420 + 0
11
90
66 + 0
1.6
IP+PZ+SZ
96
15 + 440
0.5
94
24 + 810
0.7
91
20 + 530
0.4
IP+PZ+SZ+DC
96
14 + 390
0.5
97
15 + 480
0.4
99.9
8 + 380
0.4
No controls
(baseline)
38
Modelling H5N1 transmission in UK poultry
Table S14: Impact of isolation of infected premise (IP isolation), isolation of infected premise plus implementation of protection and surveillance zones (IP/PZ/SZ) and
additional tracing of dangerous contacts (IP/PZ/SZ/DC) on the percentage of simulation runs which are extinct within 14 days for R0=3.0. The table also shows the mean
number of infected premises and restricted premises for each scenario and the mean number of birds culled, conditional on the epidemic lasting 14 days or longer. Size
dependent contact rate and density dependent spatial transmission are assumed. Total premises in spatial model = 23407; network model = 11439. Single random
seeding. Results from 1000 iterations.
R0=3.0
Pure Spatial Transmission
Spatial Transmission + 50% Group
Network Transmission Only
% extinct
Conditional
Conditional
% extinct
Conditional
Conditional
% extinct
Conditional
Conditional
within 14
mean IPs +
mean number
within 14
mean IPs +
mean number
within 14
mean IPs +
mean number
days
restricted
of birds culled
days
restricted
of birds culled
days
restricted
of birds culled
premises
in millions
premises
in millions
premises
in millions
47
15,700 + 0
200
50
15,600 + 0
240
19
9,600 + 0
232
IP isolation
58
11,400 + 0
160
62
10,800 + 0
180
58
4,400 + 0
113
IP+PZ+SZ
80
54 + 1,100
1.0
77
340 + 7,600
7.8
58
430 + 6,000
11
IP+PZ+SZ+DC
81
58 + 1,200
1.2
82
38 + 1,100
0.9
98
78 + 1600
1.6
No controls
(baseline)
39
Modelling H5N1 transmission in UK poultry
5.2. Proportion of spatial and periodic group transmission
The proportion of transmission that occurs via the group structure only has a
significant effect on the final outbreak size (conditional on infection persisting for
more than 14 days) if it is increased to very high levels (close to 100%). Under the
range of control strategies listed in Table S15, the effect of increasing the proportion
of group transmission from none to 100% is a 40% to 85% reduction in the mean
final outbreak size. This is the result of the transmission between daily subgroups
within each group that makes transmission inefficient and hence makes control
easier. Recalling the breakdown of R0 by mode of transmission (Figure S12), it might
be assumed that, under 100% group transmission, all transmission is confined to
spatial transmission amongst smallholdings. However, if infectiousness is assumed
to increase with increasing number of birds, the small premises make up a very small
fraction of the overall population R0 and therefore a substantial part of the
transmission does occur via the group structure. Thus, for example, the proportion of
total transmission that occurs spatially (via the small premises) when R0 = 3.0 and
100% of transmission amongst larger premises occurs via the group structure is
actually very low (and much less than for an R0 = 1.5 purely spatial transmission
scenario).
We also note that final outbreak sizes conditional on infection persisting for more
than 14 days are largest for 25%-75% group transmission, and this remains the case
if the IP/PZ/SZ restrictions are in place. The longer distance links associated with the
group structure allow chains of infection to stretch beyond localised controls. This
effect is eliminated if dangerous contact tracing is incorporated into the intervention
as this specifically targets the longer distance links in the commercial group sector.
40
Modelling H5N1 transmission in UK poultry
Table S15: Sensitivity of fraction of runs resulting in early extinction and mean final outbreak size
conditional on infection persisting for >14 days to the proportion of R0 within groups. R0=3, densitydependent spatial spread premise size-dependent infectiousness and random initial incursion are
assumed. Results from 1000 iterations.
Group fraction
0%
25%
50%
75%
100%
% extinct
47
46
52
54
80
15700
17300
15900
13200
6650
58
59
63
68
89
11200
12400
11000
8340
3600
% extinct
82
77
77
83
91
mean final Size
48
191
286
251
146
% extinct
82
80
84
88
97
mean final Size
48
47
34
32
28
Uncontrolled
mean final Size
% extinct
IP
mean final Size
IP+PZ/SZ
IP+PZ/SZ+DC
Table S16: Sensitivity of the percentage of runs suffering early extinction and conditional mean final
outbreak size to size dependency in contact rate. R0= 3, density-dependent transmission, 100% spatial
transmission and random seeding are assumed. Results from 1000 iterations of the simulation model.
Size
% extinct
mean outbreak size
Size-dependent
47
15700
Size-independent
22
16700
Size-dependent
58
11200
Size-independent
31
14500
Size-dependent
82
48
Size-independent
69
38
Uncontrolled
IP
IP+PZ/SZ
5.3. Density-dependent spatial transmission and size-dependent contact
rate
Density- and size- dependence are closely related in their effect on outbreak size.
They both increase the variability in R0 among premises and, because dense regions
are usually commercial and have large premises sizes, premises with high R0’s are
clustered together spatially. Due to the high correlation between size and density, we
can talk about density-dependent and density-independent behaviour (the effect of
size dependence is less marked than density dependence due to the saturating
function describing the size-transmissibility relationship (Equation 11). As discussed
in Section 3.3 of the main text, the effect of density dependent spread is generally to
give a reduced outbreak size for R0 = 3. Sparse regions with low R0 act as a barrier
to epidemics. These barrier effects are not present when density-dependence is
41
Modelling H5N1 transmission in UK poultry
relaxed and hence outbreaks are larger. Controls generally have a greater effect in
regions with already low R0 and hence have a more pronounced effect under densitydependent regimes (Tables S16 and S17).
Conversely, for low R0, the average R0 is low enough to limit epidemics in the
homogeneous density-independent case, while density-dependence leads to regions
of higher transmissibility in which epidemics can be supported, leading to larger
epidemics in this case. Again, interventions exacerbate this effect.
Table S17: Sensitivity of the percentage of runs suffering early extinction and conditional mean final size
to density dependence in transmission. Size-dependent contact rate, 100% spatial transmission and
random seeding are assumed. Results from 1000 iterations of the simulation model.
R0
1.5
3
Conditional mean
Policy
Density dependence % extinct
outbreak size
Conditional mean
% extinct
outbreak size
Dependent
75
3560
47
15700
Independent
71
532
43
18500
Dependent
84
277
58
11200
Independent
87
21
51
11100
Dependent
98
14
82
48
Independent
93
13
62
492
Uncontrolled
IP
IP+PZ/SZ
5.4. Shortening the infectious period through faster implementation of
interventions
In this section, we consider the additional impact of the planned intervention policies
if isolation of infected premises occurs on a more rapid timescale. Timing is critically
important for HPAI infections in which the infectious period is approximately 4 days.
For example, if on average an infected premise is isolated within 2 days of becoming
infected, the reproduction number is effectively halved. Here, we compare the shorter
timescale as detailed as fast response in Table S5 with the standard response used
for the baseline scenarios.
42
Modelling H5N1 transmission in UK poultry
Figure S15: Impact of faster implementation of control measures on proportion of IPs at extinction time
for R0=3 for current HPAI contingency plans. Standard Box-Whisker plots are presented where the black
dot represents the median proportion of IPs, the blue bars the inter-quartile range, the thin lines the
range and the crosses the outliers from the 1000 simulations. 1 = no controls, 2 = isolation of IP, 3 =
isolation of IP and implementation of PZ/SZ, 4 = isolation of IP, implementation of PZ/SZ and tracing of
dangerous contacts. Results shown are for a single random seed with size dependent contact rate and
density dependent spatial spread.
Figure S15 shows the effect of this faster response on a range of scenarios with
R0=3. Under the spatial and group transmission scenarios, the effect is most
noticeable if IP isolation only is initiated. Here the final outbreak size is reduced by
almost 50% compared to the same interventions under the default timings. This is
similar to the reduction in R0 for individual premises. Isolation means that most
transmission events occur in the period between the onset of infectiousness and
isolation. For the faster response, this period is reduced by a third. However, this
increase in effectiveness is much less than that achieved by the PZ/SZ restrictions
under standard response times. Under a 50% group transmission scenario, a faster
43
Modelling H5N1 transmission in UK poultry
response is highly effective. For the network model, a faster response has a more
limited impact by reducing the size of the ‘outlier’ epidemics.
5.5. Sensitivity to intervention parameters
Given that HPAI control interventions have not, to date, been implemented in GB, the
parameters governing their efficiency are hard to estimate. To examine their
effectiveness we have so far assumed that they have been put into practice relatively
efficiently. Here we examine the sensitivity of our results to these assumptions. We
use the probability of an outbreak that exceeds 20 IPs as a measure of the
effectiveness of the intervention. To test the effectiveness of IP isolation alone as an
intervention, we vary the percentage reduction in infectiousness for group and spatial
contact between 10 and 90%. To test PZ/SZ restriction, we vary the percentage
reduction in infectiousness and susceptibility together over the same range while
keeping IP isolation in place at the default assumed value.
Figure S16: Probability of outbreak exceeding 20 IPs under A) 0%, B) 50%, C) 90% group transmission
and D) static network model. Figures a) and c) show varying efficiency of IP isolation for R0=1.5 and 3
respectively. Figures b) and d) illustrate variation in efficiency of PZ/SZ restriction for R0=1.5 and 3
respectively. Results shown are for a single random seed with size dependent infectiousness and
density-dependent spatial transmission. Percentages along the x-axis show efficiency of the IP and
PZ/SZ controls.
44
Modelling H5N1 transmission in UK poultry
Figure S16 a) and c) show that the effectiveness of IP isolation alone at the
population level, as measured by the probability of a large outbreak, increases fairly
linearly with increasing IP isolation effectiveness in all scenarios. This linear
relationship suggests that there is no characteristic or critical value of efficiency to be
aimed for. The fixed network structure shows greater sensitivity to IP efficiency than
the spatial or group transmission scenarios as expected from the greater
effectiveness of IP control under pure network transmission (Section 5.1).
In contrast, there is a clear interaction between PZ/SZ intervention efficiency, group
transmission and R0. For low R0 and spatial transmission only (Figure S16b, graph
A), there is a strong, apparently quadratic, effect of efficiency on the effectiveness of
the intervention as measured by the probability of a large outbreak. This reflects the
high frequency of short transmission events. Most transmission events are between
infected and susceptible farms both within restriction zones. As such, reducing
infectiousness and susceptibility compound each other, and hence intervention
efficiencies higher than 50% give rise to little further gain in the overall effectiveness
of the intervention. For higher proportions of group transmission, the longer distance
transmission events mean that contacts are made outside the PZ/SZ and these
dominate the outbreak. As a result, the quadratic effect is lost, as is the effectiveness
of the policy (as noted in Section 5.2). A similar effect can be seen as R0 is
increased, for similar reasons. We conclude that for low R0, in scenarios in which the
PZ/SZ restriction is effective, there is little to be gained by pursuing efficiency above
50%. For higher R0, efficiency has a linear return where it is effective at all.
5.6. Sensitivity to vaccine parameters
The effectiveness of vaccine in protecting flocks and the logistical problems of
distribution through the poultry industry are difficult to parameterise. Simulations
indicate that the strategy is generally not very successful, but that the most effective
vaccination policy (while possibly remaining practical) is global coverage triggered
when 20 IPs are reached. For R0=1.5, this can achieve a reduction in the conditional
mean final outbreak size of about 30% compared to the unvaccinated scenario. Here
we test the sensitivity of this strategy by varying vaccinated-flock susceptibility and
infectiousness together from 100% to 0% of their unvaccinated levels.
45
Modelling H5N1 transmission in UK poultry
Figure S17: Final size of epidemic under global vaccination triggered by 20 IPs with various levels of
efficiency. Results show final sizes conditional on at least 20 IPs under A) 0%, B) 50%, C) 90% group
transmission and D) static network model for a) R0=1.5 b), R0=3. Percentages represent efficiency of
vaccination. 5000 iterations with random seeding, density-dependent spatial transmission and size
dependent contact rate. Total premises in spatial model = 23407; network model = 11439.
For R0=1.5, the variation of efficiency between 0 and 100% causes a halving of the
conditional mean final outbreak size of the epidemic with the exception of the 10%
spatial transmission scenario, which rarely reaches the trigger point (Figure S17). As
for the other interventions the dependence is quadratic in nature; for efficiencies
greater then 50% very little is gained in control. Both infectious contact rate and
susceptibility vary together and compound each other in any individual transmission
event between vaccinated premises.
For R0=3, the intervention is much less effective as the outbreak is able to
adequately maintain itself through the unvaccinated farms. In this regime, vaccinated
premises merely reduce the number of effective transmissions from unvaccinated
farms (i.e. local R0) and the dependence on efficiency is linear.
46
Modelling H5N1 transmission in UK poultry
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Chis-Ster, I. and Ferguson, N. M. 2007 Estimating key epidemiological parameters
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Department for the Environment Food and Rural Affairs 2007 Avian influenza (bird
flu): News archive.
Ellis, T. M., Leung, C., Chow, M. K. W., Bissett, L. A., Wong, W., Guan, Y. and Peiris,
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