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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 1 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. 3 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. 4 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. 5 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 6 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 7 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, 8 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 9 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 10 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. 11 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. 12 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. 13 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 14 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 detectionIsolation - 1.0 0.0 0.5 0.0 1.0 0.0 detectionRestriction - 1.5 0.5 1.0 0.25 1.5 0.5 detectionCulling - 2.5 1.5 2.0 1.0 2.5 1.5 infectiousnessdeath 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). 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