Epidemiological consequences of an incursion of highly pathogenic H5N1 avian influenza into the British poultry flock

A review of estimated transmission parameters for the spread of avian influenza viruses

Avian influenza poses an increasing problem in Europe and around the world. Simulation models are a useful tool to predict the spatiotemporal risk of avian influenza spread and evaluate appropriate control actions. To develop realistic simulation models, valid transmission parameters are critical. Here, we reviewed published estimates of the basic reproduction number (R₀ ), the latent period and the infectious period by virus type, pathogenicity, species, study type and poultry flock unit. We found a large variation in the parameter estimates, with highest R₀ estimates for H5N1 and H7N3 compared with other types; for low pathogenic avian influenza compared with high pathogenic avian influenza types; for ducks compared with other species; for estimates from field studies compared with experimental studies; and for within-flock estimates compared with between-flock estimates. Simulation models should reflect this observed variation so as to produce more reliable outputs and support decision-making. How to incorporate this information into simulation models remains a challenge.

Global dynamical analysis of H5 subtype avian influenza model

In order to study the comprehensive influence of factors such as contact between resident birds and poultry, poultry recruitment, environment and other factors on the transmission and control of H5 subtype avian influenza virus, a dynamic model of resident birds and poultry is developed. First, the basic reproduction number [Formula: see text] is obtained. When [Formula: see text], the dynamic model have a unique positive equilibrium and the disease persisted. Second, the Lyapunov functions is constructed to determine the global stability of the disease-free equilibrium and the endemic equilibrium. The results of numerical simulation show that regular disinfection and sterilization can increase the mortality of virus and effectively prevent the occurrence of epidemic situation. Although closing the live poultry trading market is not the main measure to control the epidemic, but it can control the epidemic to a lower level. Therefore, the regular closure of trading markets and sterilization can prevent and control the spread of the epidemic.

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions.

Knowledge and remaining gaps on the role of animal and human movements in the poultry production and trade networks in the global spread of avian influenza viruses - A scoping review

Poultry production has significantly increased worldwide, along with the number of avian influenza (AI) outbreaks and the potential threat for human pandemic emergence. The role of wild bird movements in this global spread has been extensively studied while the role of animal, human and fomite movement within commercial poultry production and trade networks remains poorly understood. The aim of this work is to better understand these roles in relation to the different routes of AI spread. A scoping literature review was conducted according to the PRISMA guidelines (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) using a search algorithm combining twelve domains linked to AI spread and animal/human movements within poultry production and trade networks. Only 28 out of 3,978 articles retrieved dealt especially with the role of animal, human and fomite movements in AI spread within the international trade network (4 articles), the national trade network (8 articles) and the production network (16 articles). While the role of animal movements in AI spread within national trade networks has been largely identified, human and fomite movements have been considered more at risk for AI spread within national production networks. However, the role of these movements has never been demonstrated with field data, and production networks have only been partially studied and never at international level. The complexity of poultry production networks and the limited access to production and trade data are important barriers to this knowledge. There is a need to study the role of animal and human movements within poultry production and trade networks in the global spread of AI in partnership with both public and private actors to fill this gap.

Optimal control of epidemic size and duration with limited resources

The total number of infections (epidemic size) and the time needed for the infection to go extinct (epidemic duration) represent two of the main indicators for the severity of infectious disease epidemics in human and livestock. However, few attempts have been made to address the problem of minimizing at the same time the epidemic size and duration from a theoretical point of view by using optimal control theory. Here, we investigate the multi-objective optimal control problem aiming to minimize, through either vaccination or isolation, a suitable combination of epidemic size and duration when both maximum control effort and total amount of resources available during the entire epidemic period are limited. Application of Pontryagin's Maximum Principle to a Susceptible-Infected-Removed epidemic model, shows that, when the resources are not sufficient to maintain the maximum control effort for the entire duration of the epidemic, the optimal vaccination control admits only bang-bang solutions with one or two switches, while the optimal isolation control admits only bang-bang solutions with one switch. We also find that, especially when the maximum control effort is low, there may exist a trade-off between the minimization of the two objectives. Consideration of this conflict among objectives can be crucial in successfully tackling real-world problems, where different stakeholders with potentially different objectives are involved. Finally, the particular case of the minimum time optimal control problem with limited resources is discussed.

Modelling the impact of biosecurity practices on the risk of high pathogenic avian influenza outbreaks in Australian commercial chicken farms

As of 2018, Australia has experienced seven outbreaks of highly pathogenic avian influenza (HPAI) in poultry since 1976, all of which involved chickens. There is concern that increases in free-range farming could heighten HPAI outbreak risk due to the potential for greater contact between chickens and wild birds that are known to carry low pathogenic avian influenza (LPAI). We use mathematical models to assess the effect of a shift to free-range farming on the risk of HPAI outbreaks of H5 or H7 in the Australian commercial chicken industry, and the potential for intervention strategies to reduce this risk. We find that a shift of 25% of conventional indoor farms to free-range farming practices would result in a 6-7% increase in the risk of a HPAI outbreak. Current practices to treat water are highly effective, reducing the risk of outbreaks by 25-28% compared to no water treatment. Halving wild bird presence in feed storage areas could reduce risk by 16-19% while halving wild bird access of potential bridge-species to sheds could reduce outbreak risk by 23-25%, and relatively small improvements in biosecurity measures could entirely compensate for increased risks due to the increasing proportion of free-range farms in the industry. The short production cycle and cleaning practices for chicken meat sheds considerably reduce the risk that an introduced low pathogenic avian influenza virus is maintained in the flock until it is detected as HPAI through increased mortality of chickens. These findings help explain HPAI outbreak history in Australia and suggest practical changes in biosecurity practices that could reduce the risk of future outbreaks.

Dynamics of the 2004 avian influenza H5N1 outbreak in Thailand: The role of duck farming, sequential model fitting and control

The Highly Pathogenic Avian Influenza (HPAI) subtype H5N1 virus persists in many countries and has been circulating in poultry, wild birds. In addition, the virus has emerged in other species and frequent zoonotic spillover events indicate that there remains a significant risk to human health. It is crucial to understand the dynamics of the disease in the poultry industry to develop a more comprehensive knowledge of the risks of transmission and to establish a better distribution of resources when implementing control. In this paper, we develop a set of mathematical models that simulate the spread of HPAI H5N1 in the poultry industry in Thailand, utilising data from the 2004 epidemic. The model that incorporates the intensity of duck farming when assessing transmision risk provides the best fit to the spatiotemporal characteristics of the observed outbreak, implying that intensive duck farming drives transmission of HPAI in Thailand. We also extend our models using a sequential model fitting approach to explore the ability of the models to be used in “real time” during novel disease outbreaks. We conclude that, whilst predictions of epidemic size are estimated poorly in the early stages of disease outbreaks, the model can infer the preferred control policy that should be deployed to minimise the impact of the disease.

Modelling the outbreak of infectious disease following mutation from a non-transmissible strain

In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the past. We use simple mathematical models to describe this process with the aim to better understand the emergence of an epidemic resulting from such a mutation and the extent of measures that are needed to control it. The feared outbreak of a human–human transmissible form of avian influenza leading to a global epidemic is the paradigm for this study. We extend the SIR approach to derive a deterministic and a stochastic formulation to describe the evolution of two classes of susceptible and infected states and a removed state, leading to a system of ordinary differential equations and a stochastic equivalent based on a Markov process. For the deterministic model, the contrasting timescale of the mutation process and disease infectiousness is exploited in two limits using asymptotic analysis in order to determine, in terms of the model parameters, necessary conditions for an epidemic to take place and timescales for the onset of the epidemic, the size and duration of the epidemic and the maximum level of the infected individuals at one time. Furthermore, the basic reproduction number R0 is determined from asymptotic analysis of a distinguished limit. Comparisons between the deterministic and stochastic model demonstrate that stochasticity has little effect on most aspects of an epidemic, but does have significant impact on its onset particularly for smaller populations and lower mutation rates for representatively large populations. The deterministic model is extended to investigate a range of quarantine and vaccination programmes, whereby in the two asymptotic limits analysed, quantitative estimates on the outcomes and effectiveness of these control measures are established.

Assessment of China's H5N1 routine vaccination strategy

In this study, a simulation model was used to assess the epidemiological and economic impacts of the routine vaccination strategy for H5N1 in China at the national level. The results of the simulation show that a routine vaccination strategy at the national level could have a substantial impact on decreasing H5N1 outbreaks; it could therefore markedly reduce the severity and duration of an H5N1 epidemic at the national level in China. Under a routine vaccination programme, when a flock is infected, the number of depopulated birds could be reduced by approximately 91%, the outbreak duration could be reduced by one-fourth, and the probability of an H5N1 outbreak could be reduced to 51.5%. Although the use of vaccination has obvious benefits, if indirect costs were not considered, the mean direct cost of simulated disease control without vaccination was only 1.36% of the cost of the routine vaccination strategy, and this former approach would have saved 57 billion yuan for all poultry in China from 2004 to 2012. Traditional H5N1 control strategies with culling programmes at the national level represented a better choice for China.

Assessment of Effectiveness of Control Strategies Against Simulated Outbreaks of Highly Pathogenic Avian Influenza in Ontario, Canada

The North American Animal Disease Spread Model (NAADSM) is a stochastic model framework developed to simulate the spread of highly contagious diseases of livestock and poultry, such as foot-and-mouth disease and highly pathogenic avian influenza (HPAI). The objective of this study was to make recommendations on the most effective HPAI control policy for Canada, specifically, on the effect of different speeds of detection, effectiveness of movement restrictions and stamping-out and ring-culling strategies on the magnitude of an HPAI outbreak. In addition, the effect of introduction of infection in a range of multiple farms simultaneously was also evaluated. A total of 21 060 scenarios, defined as different combinations of parameters for various epidemiological conditions and control measures, were created to simulate the number of poultry flocks that would become infected as a result of an incursion of HPAI. Each scenario was parameterized in NAADSM and replicated 1000 times, generating the median number of flocks infected at the end of the simulated outbreak for each scenario. Negative binomial regression analysis was used to model significant explanatory variables of the median number of flocks infected at the end of each simulated outbreak for each of the 21 060 scenarios. The final model included the following explanatory variables: number and type initially infected flock(s), density of flocks within the county where the initially infected flock(s) was located, probability of transmission through indirect contact, subclinical spread of the infection, speed of detection and a two-way interaction between intensity of bird destruction strategy and movement restriction effectiveness to reduce transmission through direct and indirect contacts. The modelling results suggested that stamping out of the detected infected flocks, without ring culling, in combination with effective movement restrictions on direct and indirect contacts, would be the most appropriate policy for Ontario.

Controlling highly pathogenic avian influenza outbreaks: An epidemiological and economic model analysis

Outbreaks of highly pathogenic avian influenza (HPAI) can cause large losses for the poultry sector and for animal disease controlling authorities, as well as risks for animal and human welfare. In the current simulation approach epidemiological and economic models are combined to compare different strategies to control highly pathogenic avian influenza in Dutch poultry flocks. Evaluated control strategies are the minimum EU strategy (i.e., culling of infected flocks, transport regulations, tracing and screening of contact flocks, establishment of protection and surveillance zones), and additional control strategies comprising pre-emptive culling of all susceptible poultry flocks in an area around infected flocks (1 km, 3 km and 10 km) and emergency vaccination of all flocks except broilers around infected flocks (3 km). Simulation results indicate that the EU strategy is not sufficient to eradicate an epidemic in high density poultry areas. From an epidemiological point of view, this strategy is the least effective, while pre-emptive culling in 10 km radius is the most effective of the studied strategies. But these two strategies incur the highest costs due to long duration (EU strategy) and large-scale culling (pre-emptive culling in 10 km radius). Other analysed pre-emptive culling strategies (i.e., in 1 km and 3 km radius) are more effective than the analysed emergency vaccination strategy (in 3 km radius) in terms of duration and size of the epidemics, despite the assumed optimistic vaccination capacity of 20 farms per day. However, the total costs of these strategies differ only marginally. Extending the capacity for culling substantially reduces the duration, size and costs of the epidemic. This study demonstrates the strength of combining epidemiological and economic model analysis to gain insight in a range of consequences and thus to serve as a decision support tool in the control of HPAI epidemics.

Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China

Brucellosis is one of the major infectious and contagious bacterial diseases in Hinggan League of Inner Mongolia, China. The number of newly infected human brucellosis data in this area has increased dramatically in the last 10 years. In this study, in order to explore effective control and prevention measures we propose a deterministic model to investigate the transmission dynamics of brucellosis in Hinggan League. The model describes the spread of brucellosis among sheep and from sheep to humans. The model simulations agree with newly infected human brucellosis data from 2001 to 2011, and the trend of newly infected human brucellosis cases is given. We estimate that the control reproduction number Rc is about 1.9789 for the brucellosis transmission in Hinggan League and compare the effect of existing mixed cross infection between basic ewes and other sheep or not for newly infected human brucellosis cases. Our study demonstrates that combination of prohibiting mixed feeding between basic ewes and other sheep, vaccination, detection and elimination are useful strategies in controlling human brucellosis in Hinggan League.

Intervention strategies to reduce the risk of zoonotic infection with avian influenza viruses: scientific basis, challenges and knowledge gaps

A range of measures has been recommended and used for the control and prevention of avian influenza. These measures are based on the assessment of local epidemiological situations, field observations and other scientific information. Other non-technical factors are (or in some cases should be) taken into account when developing and recommending control measures. The precise effects under field conditions of most individual interventions applied to control and prevent avian influenza have not been established or subjected to critical review, often because a number of measures are applied simultaneously without controls. In most cases, the combination of measures used results in control or elimination of the virus although there are some countries where this has not been the case. In others, especially those with low poultry density, it is not clear whether the link between the adoption of a set of measures and the subsequent control of the disease is causative. This article discusses the various measures recommended, with particular emphasis on stamping out and vaccination, examines how these measures assist in preventing zoonotic infections with avian influenza viruses and explores gaps in knowledge regarding their effectiveness.

Tracking socioeconomic vulnerability using network analysis: insights from an avian influenza outbreak in an ostrich production network

BACKGROUND

The focus of management in many complex systems is shifting towards facilitation, adaptation, building resilience, and reducing vulnerability. Resilience management requires the development and application of general heuristics and methods for tracking changes in both resilience and vulnerability. We explored the emergence of vulnerability in the South African domestic ostrich industry, an animal production system which typically involves 3-4 movements of each bird during its lifetime. This system has experienced several disease outbreaks, and the aim of this study was to investigate whether these movements have contributed to the vulnerability of this system to large disease outbreaks.

METHODOLOGY/PRINCIPAL FINDINGS

The ostrich production system requires numerous movements of birds between different farm types associated with growth (i.e. Hatchery to juvenile rearing farm to adult rearing farm). We used 5 years of movement records between 2005 and 2011 prior to an outbreak of Highly Pathogenic Avian Influenza (H5N2). These data were analyzed using a network analysis in which the farms were represented as nodes and the movements of birds as links. We tested the hypothesis that increasing economic efficiency in the domestic ostrich industry in South Africa made the system more vulnerable to outbreak of Highly Pathogenic Avian Influenza (H5N2). Our results indicated that as time progressed, the network became increasingly vulnerable to pathogen outbreaks. The farms that became infected during the outbreak displayed network qualities, such as significantly higher connectivity and centrality, which predisposed them to be more vulnerable to disease outbreak.

CONCLUSIONS/SIGNIFICANCE

Taken in the context of previous research, our results provide strong support for the application of network analysis to track vulnerability, while also providing useful practical implications for system monitoring and management.

A metapopulation model for highly pathogenic avian influenza: implications for compartmentalization as a control measure

Although the compartmentalization of poultry industry components has substantial economic implications, and is therefore a concept with huge significance to poultry industries worldwide, the current requirements for compartment status are generic to all OIE member countries. We examined the consequences for potential outbreaks of highly pathogenic avian influenza in the British poultry industry using a metapopulation modelling framework. This framework was used to assess the effectiveness of compartmentalization relative to zoning control, utilizing empirical data to inform the structure of potential epidemiological contacts within the British poultry industry via network links and spatial proximity. Conditions were identified where, despite the efficient isolation of poultry compartments through the removal of network-mediated links, spatially mediated airborne spread enabled spillover of infection with nearby premises making compartmentalization a more ‘risky’ option than zoning control. However, when zoning control did not effectively inhibit long-distance network links, compartmentalization became a relatively more effective control measure than zoning. With better knowledge of likely distance ranges for airborne spread, our approach could help define an appropriate minimum inter-farm distance to provide more specific guidelines for compartmentalization in Great Britain.

Using quantitative disease dynamics as a tool for guiding response to avian influenza in poultry in the United States of America

Wild birds are the primary source of genetic diversity for influenza A viruses that eventually emerge in poultry and humans. Much progress has been made in the descriptive ecology of avian influenza viruses (AIVs), but contributions are less evident from quantitative studies (e.g., those including disease dynamic models). Transmission between host species, individuals and flocks has not been measured with sufficient accuracy to allow robust quantitative evaluation of alternate control protocols. We focused on the United States of America (USA) as a case study for determining the state of our quantitative knowledge of potential AIV emergence processes from wild hosts to poultry. We identified priorities for quantitative research that would build on existing tools for responding to AIV in poultry and concluded that the following knowledge gaps can be addressed with current empirical data: (1) quantification of the spatio-temporal relationships between AIV prevalence in wild hosts and poultry populations, (2) understanding how the structure of different poultry sectors impacts within-flock transmission, (3) determining mechanisms and rates of between-farm spread, and (4) validating current policy-decision tools with data. The modeling studies we recommend will improve our mechanistic understanding of potential AIV transmission patterns in USA poultry, leading to improved measures of accuracy and reduced uncertainty when evaluating alternative control strategies.

Risk factors for the introduction of avian influenza virus in breeder duck flocks during the first 24 weeks of laying

A study was carried out in French breeder duck flocks in 2008 and 2009 to identify practices and events related to the introduction of avian influenza viruses (AIVs). The status of flocks was assessed using serological methods for all subtypes of AIV without typing. Flocks managed with both natural mating and artificial insemination were investigated every 4 weeks from the beginning of the laying period up to seroconversion or for a maximum of 6 months. A questionnaire was completed with the farmer during each visit and 20 female ducks were randomly sampled for blood testing. Only flocks that tested seronegative at the first visit were included in the study (n =151 flocks managed with natural mating or artificial insemination). Data were analysed using survival analysis to identify factors influencing the time to seroconversion. Three separate models were constructed: one for the whole sample, one for natural mating flocks, and one for artificial insemination flocks. Factors related to the time to introduction of AIV included the type of production system linked to artificial insemination practices, the neighbourhood, poor disinfection practices, liquid manure management, presence of wildlife, and vehicles entering the building. No clear relationship could be observed in the serological status of male and female ducks in farms keeping male ducks separately from female ducks for artificial insemination. By respecting carefully biosecurity measures, it should be possible to decrease AIV infection of breeder duck flocks.

An exact relationship between invasion probability and endemic prevalence for Markovian SIS dynamics on networks

Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation process and utilising the property of duality, we also provide a theoretical definition of invasion probability. We then show that, for undirected networks, the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual (we also provide a relationship for the directed case). The total (fractional) endemic prevalence in the population is thus equal to the average invasion probability (across all individuals). Consequently, for such systems, the regions or individuals already supporting a high level of infection are likely to be the source of a successful invasion by another infectious agent. This could be used to inform targeted interventions when there is a threat from an emerging infectious disease.

Network analysis of swine shipments in Ontario, Canada, to support disease spread modelling and risk-based disease management

Understanding contact networks are important for modelling and managing the spread and control of communicable diseases in populations. This study characterizes the swine shipment network of a multi-site production system in southwestern Ontario, Canada. Data were extracted from a company's database listing swine shipments among 251 swine farms, including 20 sow, 69 nursery and 162 finishing farms, for the 2-year period of 2006 to 2007. Several network metrics were generated. The number of shipments per week between pairs of farms ranged from 1 to 6. The medians (and ranges) of out-degree were: sow 6 (1-21), nursery 8 (0-25), and finishing 0 (0-4), over the entire 2-year study period. Corresponding estimates for in-degree of nursery and finishing farms were 3 (0-9) and 3 (0-12) respectively. Outgoing and incoming infection chains (OIC and IIC), were also measured. The medians (ranges) of the monthly OIC and IIC were 0 (0-8) and 0 (0-6), respectively, with very similar measures observed for 2-week intervals. Nursery farms exhibited high measures of centrality. This indicates that they pose greater risks of disease spread in the network. Therefore, they should be given a high priority for disease prevention and control measures affecting all age groups alike. The network demonstrated scale-free and small-world topologies as observed in other livestock shipment studies. This heterogeneity in contacts among farm types and network topologies should be incorporated in simulation models to improve their validity. In conclusion, this study provided useful epidemiological information and parameters for the control and modelling of disease spread among swine farms, for the first time from Ontario, Canada.

Investigation into sampling strategies in response to potential outbreaks of low pathogenicity notifiable avian influenza initiated in commercial duck holdings in Great Britain

The aim of this study was to evaluate potential sampling strategies for detection of infected flocks that could be applied during an outbreak of low pathogenicity notifiable avian influenza (LPNAI) initiated in duck holdings, following initial detection. A simulation model of avian influenza virus transmission and spread within and between holdings, respectively, was used to predict the impact on the size and duration of an outbreak of (i) changing the tracing window within which premises that might be the source of infection or that may have been infected by the index premises were sampled and (ii) changing the number of birds sampled in the flock being tested. It has shown that there is potential benefit in increasing the tracing window in terms of reducing the likelihood of a large outbreak. It has also shown that there is comparatively little benefit from increasing the number of birds sampled per flock.

Implications of within-farm transmission for network dynamics: consequences for the spread of avian influenza

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Cross-scale dynamics were investigated for avian influenza in British poultry.

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Transmission risk is dependent on the assumed within-flock transmission mode.

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Transmission risk may not scale with transmissibility or flock size.

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Transmission risk corresponds with between-farm impact for 28% of farms.

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These results have implications for targeted disease control at the farm-level.

The importance of considering coupled interactions across multiple population scales has not previously been studied for highly pathogenic avian influenza (HPAI) in the British commercial poultry industry. By simulating the within-flock transmission of HPAI using a deterministic S-E-I-R model, and by incorporating an additional environmental class representing infectious faeces, we tracked the build-up of infectious faeces within a poultry house over time. A measure of the transmission risk (TR) was computed for each farm by linking the amount of infectious faeces present each day of an outbreak with data describing the daily on-farm visit schedules for a major British catching company. Larger flocks tended to have greater levels of these catching-team visits. However, where density-dependent contact was assumed, faster outbreak detection (according to an assumed mortality threshold) led to a decreased opportunity for catching-team visits to coincide with an outbreak. For this reason, maximum TR-levels were found for mid-range flock sizes (~25,000–35,000 birds). When assessing all factors simultaneously using multivariable linear regression on the simulated outputs, those related to the pattern of catching-team visits had the largest effect on TR, with the most important movement-related factor depending on the mode of transmission. Using social network analysis on a further database to inform a measure of between-farm connectivity, we identified a large fraction of farms (28%) that had both a high TR and a high potential impact at the between farm level. Our results have counter-intuitive implications for between-farm spread that could not be predicted based on flock size alone, and together with further knowledge of the relative importance of transmission risk and impact, could have implications for improved targeting of control measures.

An epidemiologic simulation model of the spread and control of highly pathogenic avian influenza (H5N1) among commercial and backyard poultry flocks in South Carolina, United States

Epidemiologic simulation modeling of highly pathogenic avian influenza (HPAI) outbreaks provides a useful conceptual framework with which to estimate the consequences of HPAI outbreaks and to evaluate disease control strategies. The purposes of this study were to establish detailed and informed input parameters for an epidemiologic simulation model of the H5N1 strain of HPAI among commercial and backyard poultry in the state of South Carolina in the United States using a highly realistic representation of this poultry population; to estimate the consequences of an outbreak of HPAI in this population with a model constructed from these parameters; and to briefly evaluate the sensitivity of model outcomes to several parameters. Parameters describing disease state durations; disease transmission via direct contact, indirect contact, and local-area spread; and disease detection, surveillance, and control were established through consultation with subject matter experts, a review of the current literature, and the use of several computational tools. The stochastic model constructed from these parameters produced simulated outbreaks ranging from 2 to 111 days in duration (median 25 days), during which 1 to 514 flocks were infected (median 28 flocks). Model results were particularly sensitive to the rate of indirect contact that occurs among flocks. The baseline model established in this study can be used in the future to evaluate various control strategies, as a tool for emergency preparedness and response planning, and to assess the costs associated with disease control and the economic consequences of a disease outbreak.

Enhancing Bayesian risk prediction for epidemics using contact tracing

Contact-tracing data (CTD) collected from disease outbreaks has received relatively little attention in the epidemic modeling literature because it is thought to be unreliable: infection sources might be wrongly attributed, or data might be missing due to resource constraints in the questionnaire exercise. Nevertheless, these data might provide a rich source of information on the disease transmission rate. This paper presents a novel methodology for combining CTD with rate-based contact network data to improve posterior precision, and therefore predictive accuracy. We present an advancement in Bayesian inference for epidemics that assimilates these data and is robust to partial contact tracing. Using a simulation study based on the British poultry industry, we show how the presence of CTD improves posterior predictive accuracy and can directly inform a more effective control strategy.

Modeling the spread and control of foot-and-mouth disease in Pennsylvania following its discovery and options for control

In this paper, we simulate outbreaks of foot-and-mouth disease in the Commonwealth of Pennsylvania, USA - after the introduction of a state-wide movement ban - as they might unfold in the presence of mitigation strategies. We have adapted a model previously used to investigate FMD control policies in the UK to examine the potential for disease spread given an infection seeded in each county in Pennsylvania. The results are highly dependent upon the county of introduction and the spatial scale of transmission. Should the transmission kernel be identical to that for the UK, the epidemic impact is limited to fewer than 20 premises, regardless of the county of introduction. However, for wider kernels where infection can spread further, outbreaks seeded in or near the county with highest density of premises and animals result in large epidemics (>150 premises). Ring culling and vaccination reduce epidemic size, with the optimal radius of the rings being dependent upon the county of introduction. Should the kernel width exceed a given county-dependent threshold, ring culling is unable to control the epidemic. We find that a vaccinate-to-live policy is generally preferred to ring culling (in terms of reducing the overall number of premises culled), indicating that well-targeted control can dramatically reduce the risk of large scale outbreaks of foot-and-mouth disease occurring in Pennsylvania.

Generating social network data using partially described networks: an example informing avian influenza control in the British poultry industry

BACKGROUND

Targeted sampling can capture the characteristics of more vulnerable sectors of a population, but may bias the picture of population level disease risk. When sampling network data, an incomplete description of the population may arise leading to biased estimates of between-host connectivity. Avian influenza (AI) control planning in Great Britain (GB) provides one example where network data for the poultry industry (the Poultry Network Database or PND), targeted large premises and is consequently demographically biased. Exposing the effect of such biases on the geographical distribution of network properties could help target future poultry network data collection exercises. These data will be important for informing the control of potential future disease outbreaks.

RESULTS

The PND was used to compute between-farm association frequencies, assuming that farms sharing the same slaughterhouse or catching company, or through integration, are potentially epidemiologically linked. The fitted statistical models were extrapolated to the Great Britain Poultry Register (GBPR); this dataset is more representative of the poultry industry but lacks network information. This comparison showed how systematic biases in the demographic characterisation of a network, resulting from targeted sampling procedures, can bias the derived picture of between-host connectivity within the network.

CONCLUSIONS

With particular reference to the predictive modeling of AI in GB, we find significantly different connectivity patterns across GB when network estimates incorporate the more demographically representative information provided by the GBPR; this has not been accounted for by previous epidemiological analyses. We recommend ranking geographical regions, based on relative confidence in extrapolated estimates, for prioritising further data collection. Evaluating whether and how the between-farm association frequencies impact on the risk of between-farm transmission will be the focus of future work.

Uncertainties in the governance of animal disease: an interdisciplinary framework for analysis

Uncertainty is an inherent feature of strategies to contain animal disease. In this paper, an interdisciplinary framework for representing strategies of containment, and analysing how uncertainties are embedded and propagated through them, is developed and illustrated. Analysis centres on persistent, periodic and emerging disease threats, with a particular focus on cryptosporidiosis, foot and mouth disease and avian influenza. Uncertainty is shown to be produced at strategic, tactical and operational levels of containment, and across the different arenas of disease prevention, anticipation and alleviation. The paper argues for more critically reflexive assessments of uncertainty in containment policy and practice. An interdisciplinary approach has an important contribution to make, but is absent from current real-world containment policy.

How backyard poultry flocks influence the effort required to curtail avian influenza epidemics in commercial poultry flocks

This paper summarizes the evidence that the contribution of backyard poultry flocks to the on-going transmission dynamics of an avian influenza epidemic in commercial flocks is modest at best. Nevertheless, while disease control strategies need not involve the backyard flocks, an analysis of the contribution of each element of the next generation matrix to the basic reproduction number indicates that models which ignores the contribution of backyard flocks in estimating the effort required of strategies focused one host type (e.g. commercial flocks only) necessarily underestimate the level of effort to an extent that may matter to policy makers.

Impact of the implementation of rest days in live bird markets on the dynamics of H5N1 highly pathogenic avian influenza

Live bird markets (LBMs) act as a network 'hub' and potential reservoir of infection for domestic poultry. They may therefore be responsible for sustaining H5N1 highly pathogenic avian influenza (HPAI) virus circulation within the poultry sector, and thus a suitable target for implementing control strategies. We developed a stochastic transmission model to understand how market functioning impacts on the transmission dynamics. We then investigated the potential for rest days-periods during which markets are emptied and disinfected-to modulate the dynamics of H5N1 HPAI within the poultry sector using a stochastic meta-population model. Our results suggest that under plausible parameter scenarios, HPAI H5N1 could be sustained silently within LBMs with the time spent by poultry in markets and the frequency of introduction of new susceptible birds' dominant factors determining sustained silent spread. Compared with interventions applied in farms (i.e. stamping out, vaccination), our model shows that frequent rest days are an effective means to reduce HPAI transmission. Furthermore, our model predicts that full market closure would be only slightly more effective than rest days to reduce transmission. Strategies applied within markets could thus help to control transmission of the disease.

Epidemics and control strategies for diseases of farmed salmonids: a parameter study

The susceptibility of the English and Welsh fish farming and fisheries industry to emergent diseases is assessed using a stochastic simulation model. The model dynamics operate on a network comprising directed transport and river contacts, as well as undirected local and fomite transmissions. The directed connections cause outward transmission risk to be geographically more confined than inward risk. We consider reactive, proactive, and hybrid methods of control which correspond to a mixture of policy and the ease of disease detection. An explicit investigation of the impact of laboratory capacity is made. General quantified guidelines are derived to mitigate future epidemics.

Use of epidemiologic models in the control of highly pathogenic avian influenza

In the past decades, mathematical models have become more and more accepted as a tool to develop surveillance programs and to evaluate the efficacy of intervention measures for the control of infectious diseases such as highly pathogenic avian influenza. Predictive models are used to simulate the effect of various control measures on the course of an epidemic; analytical models are used to analyze data from outbreaks or from experiments. A key parameter in both types of models is the reproductive ratio, which indicates whether virus can be transmitted in the population, resulting in an epidemic, or not. Parameters obtained from real data using the analytical models can subsequently be used in predictive models to evaluate control strategies or surveillance programs. Examples of the use of these models are described here.

Stochastic model of the potential spread of highly pathogenic avian influenza from an infected commercial broiler operation in Georgia

The potential spread of highly pathogenic avian influenza among commercial broiler farms in Georgia, U. S. A., was mathematically modeled. The dynamics of the spread within the first infected flock were estimated using an SEIR (susceptible-exposed-infectious-recovered) deterministic model, and predicted that grower detection of flock infection is most likely 5 days after virus introduction. Off-farm spread of virus was estimated stochastically for this period, predicting a mean range of exposed farms from 0-5, depending on the density of farms in the area. Modeled off-farm spread was most frequently associated with feed trucks (highest daily probability and number of farm visits) and with company personnel or hired help (highest level of bird contact).

A quantitative assessment of the risk for highly pathogenic avian influenza introduction into Spain via legal trade of live poultry

Highly pathogenic avian influenza (HPAI) is considered one of the most important diseases of poultry. During the last 9 years, HPAI epidemics have been reported in Asia, the Americas, Africa, and in 18 countries of the European Union (EU). For that reason, it is possible that the risk for HPAI virus (HPAIV) introduction into Spain may have recently increased. Because of the EU free-trade policy and because legal trade of live poultry was considered an important route for HPAI spread in certain regions of the world, there are fears that Spain may become HPAIV-infected as a consequence of the legal introduction of live poultry. However, no quantitative assessment of the risk for HPAIV introduction into Spain or into any other EU member state via the trade of poultry has been published in the peer-reviewed literature. This article presents the results of the first quantitative assessment of the risk for HPAIV introduction into a free country via legal trade of live poultry, along with estimates of the geographical variation of the risk and of the relative contribution of exporting countries and susceptible poultry species to the risk. The annual mean risk for HPAI introduction into Spain was estimated to be as low as 1.36 x 10(-3), suggesting that under prevailing conditions, introduction of HPAIV into Spain through the trade of live poultry is unlikely to occur. Moreover, these results support the hypothesis that legal trade of live poultry does not impose a significant risk for the spread of HPAI into EU member states.

A modeling framework to describe the transmission of bluetongue virus within and between farms in Great Britain

BACKGROUND

Recently much attention has been given to developing national-scale micro-simulation models for livestock diseases that can be used to predict spread and assess the impact of control measures. The focus of these models has been on directly transmitted infections with little attention given to vector-borne diseases such as bluetongue, a viral disease of ruminants transmitted by Culicoides biting midges. Yet BT has emerged over the past decade as one of the most important diseases of livestock.

METHODOLOGY/PRINCIPAL FINDINGS

We developed a stochastic, spatially-explicit, farm-level model to describe the spread of bluetongue virus (BTV) within and between farms. Transmission between farms was modeled by a generic kernel, which includes both animal and vector movements. Once a farm acquired infection, the within-farm dynamics were simulated based on the number of cattle and sheep kept on the farm and on local temperatures. Parameter estimates were derived from the published literature and using data from the outbreak of bluetongue in northern Europe in 2006. The model was validated using data on the spread of BTV in Great Britain during 2007. The sensitivity of model predictions to the shape of the transmission kernel was assessed.

CONCLUSIONS/SIGNIFICANCE

The model is able to replicate the dynamics of BTV in Great Britain. Although uncertainty remains over the precise shape of the transmission kernel and certain aspects of the vector, the modeling approach we develop constitutes an ideal framework in which to incorporate these aspects as more and better data become available. Moreover, the model provides a tool with which to examine scenarios for the spread and control of BTV in Great Britain.

Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales

Epidemics are frequently simulated on redundantly wired contact networks, which have many more links between sites than are minimally required to connect all. Consequently, the modelled pathogen can travel numerous alternative routes, complicating effective containment strategies. These networks have moreover been found to exhibit 'scale-free' properties and percolation, suggesting resilience to damage. However, realistic H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales. These system-preferred scales constitute small areas within an observed power law distribution that exhibit a lesser slope than the power law itself, indicating a slightly increased relative likelihood. These characteristic scales are here produced by a network-pervading intranet of so-called hotspot sites that propagate large epidemics below the percolation threshold. This intranet is, however, extremely vulnerable; targeted inoculation of a mere 3-6% (depending on incorporated biosecurity measures) of the British poultry industry network prevents large and moderate H5N1 outbreaks completely, offering an order of magnitude improvement over previously advocated strategies affecting the most highly connected 'hub' sites. In other words, hotspots and hubs are separate functional entities that do not necessarily coincide, and hotspots can make more effective inoculation targets. Given the ubiquity and relevance of networks (epidemics, Internet, power grids, protein interaction), recognition of this spreading regime elsewhere would suggest a similar disproportionate sensitivity to such surgical interventions.

Contact structures in the poultry industry in Great Britain: exploring transmission routes for a potential avian influenza virus epidemic

Background

The commercial poultry industry in United Kingdom (UK) is worth an estimated £3.4 billion at retail value, producing over 174 million birds for consumption per year. An epidemic of any poultry disease with high mortality or which is zoonotic, such as avian influenza virus (AIV), would result in the culling of significant numbers of birds, as seen in the Netherlands in 2003 and Italy in 2000. Such an epidemic would cost the UK government millions of pounds in compensation costs, with further economic losses through reduction of international and UK consumption of British poultry. In order to better inform policy advisers and makers on the potential for a large epidemic in GB, we investigate the role that interactions amongst premises within the British commercial poultry industry could play in promoting an AIV epidemic, given an introduction of the virus in a specific part of poultry industry in Great Britain (GB).

Results

Poultry premises using multiple slaughterhouses lead to a large number of premises being potentially connected, with the resultant potential for large and sometimes widespread epidemics. Catching companies can also potentially link a large proportion of the poultry population. Critical to this is the maximum distance traveled by catching companies between premises and whether or not between-species transmission could occur within individual premises. Premises closely linked by proximity may result in connections being formed between different species and or sectors within the industry.

Conclusion

Even quite well-contained epidemics have the potential for geographically widespread dissemination, potentially resulting in severe logistical problems for epidemic control, and with economic impact on a large part of the country. Premises sending birds to multiple slaughterhouses or housing multiple species may act as a bridge between otherwise separate sectors of the industry, resulting in the potential for large epidemics. Investment into further data collection and analyses on the importance of industry structure as a determinant for spread of AIV would enable us to use the results from this study to contribute to policy on disease control.

Deterministic epidemiological models at the individual level

In many fields of science including population dynamics, the vast state spaces inhabited by all but the very simplest of systems can preclude a deterministic analysis. Here, a class of approximate deterministic models is introduced into the field of epidemiology that reduces this state space to one that is numerically feasible. However, these reduced state space master equations do not in general form a closed set. To resolve this, the equations are approximated using closure approximations. This process results in a method for constructing deterministic differential equation models with a potentially large scope of application including dynamic directed contact networks and heterogeneous systems using time dependent parameters. The method is exemplified in the case of an SIR (susceptible-infectious-removed) epidemiological model and is numerically evaluated on a range of networks from spatially local to random. In the context of epidemics propagated on contact networks, this work assists in clarifying the link between stochastic simulation and traditional population level deterministic models.