Transmission parameters of the 2001 foot and mouth epidemic in Great Britain

Spatial Transmission Characteristics of the Bluetongue Virus Serotype 3 Epidemic in The Netherlands, 2023

A devastating bluetongue (BT) epidemic caused by bluetongue virus serotype 3 (BTV-3) has spread throughout most of the Netherlands within two months since the first infection was officially confirmed in the beginning of September 2023. The epidemic comes with unusually strong suffering of infected cattle through severe lameness, often resulting in mortality or euthanisation for welfare reasons. In total, tens of thousands of sheep have died or had to be euthanised. By October 2023, more than 2200 locations with ruminant livestock were officially identified to be infected with BTV-3, and additionally, ruminants from 1300 locations were showing BTV-associated clinical symptoms (but not laboratory-confirmed BT). Here, we report on the spatial spread and dynamics of this BT epidemic. More specifically, we characterized the distance-dependent intensity of the between-holding transmission by estimating the spatial transmission kernel and by comparing it to transmission kernels estimated earlier for BTV-8 transmission in Northwestern Europe in 2006 and 2007. The 2023 BTV-3 kernel parameters are in line with those of the transmission kernel estimated previously for the between-holding spread of BTV-8 in Europe in 2007. The 2023 BTV-3 transmission kernel has a long-distance spatial range (across tens of kilometres), evidencing that in addition to short-distance dispersal of infected midges, other transmission routes such as livestock transports probably played an important role.

Ensemble learning methods of inference for spatially stratified infectious disease systems

Individual level models are a class of mechanistic models that are widely used to infer infectious disease transmission dynamics. These models incorporate individual level covariate information accounting for population heterogeneity and are generally fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. However, Bayesian MCMC methods of inference are computationally expensive for large data sets. This issue becomes more severe when applied to infectious disease data collected from spatially heterogeneous populations, as the number of covariates increases. In addition, summary statistics over the global population may not capture the true spatio-temporal dynamics of disease transmission. In this study we propose to use ensemble learning methods to predict epidemic generating models instead of time consuming Bayesian MCMC method. We apply these methods to infer disease transmission dynamics over spatially clustered populations, considering the clusters as natural strata instead of a global population. We compare the performance of two tree-based ensemble learning techniques: random forest and gradient boosting. These methods are applied to the 2001 foot-and-mouth disease epidemic in the U.K. and evaluated using simulated data from a clustered population. It is shown that the spatially clustered data can help to predict epidemic generating models more accurately than the global data.

Modeling target-density-based cull strategies to contain foot-and-mouth disease outbreaks

Total ring depopulation is sometimes used as a management strategy for emerging infectious diseases in livestock, which raises ethical concerns regarding the potential slaughter of large numbers of healthy animals. We evaluated a farm-density-based ring culling strategy to control foot-and-mouth disease (FMD) in the United Kingdom (UK), which may allow for some farms within rings around infected premises (IPs) to escape depopulation. We simulated this reduced farm density, or "target density", strategy using a spatially-explicit, stochastic, state-transition algorithm. We modeled FMD spread in four counties in the UK that have different farm demographics, using 740,000 simulations in a full-factorial analysis of epidemic impact measures (i.e., culled animals, culled farms, and epidemic length) and cull strategy parameters (i.e., target farm density, daily farm cull capacity, and cull radius). All of the cull strategy parameters listed above were drivers of epidemic impact. Our simulated target density strategy was usually more effective at combatting FMD compared with traditional total ring depopulation when considering mean culled animals and culled farms and was especially effective when daily farm cull capacity was low. The differences in epidemic impact measures among the counties are likely driven by farm demography, especially differences in cattle and farm density. To prevent over-culling and the associated economic, organizational, ethical, and psychological impacts, the target density strategy may be worth considering in decision-making processes for future control of FMD and other diseases.

Estimating the Transmission Kernel for Lumpy Skin Disease Virus from Data on Outbreaks in Thailand in 2021

Nationwide outbreaks of lumpy skin disease (LSD) were observed in Thailand in 2021. A better understanding of its disease transmission is crucial. This study utilized a kernel-based approach to characterize the transmission of LSD between cattle herds. Outbreak data from the Khon Kaen and Lamphun provinces in Thailand were used to estimate transmission kernels for each province. The results showed that the majority of herd-to-herd transmission occurs over short distances. For Khon Kaen, the median transmission distance from the donor herd was estimated to be between 0.3 and 0.8 km, while for Lamphun, it ranged from 0.2 to 0.6 km. The results imply the critical role that insects may play as vectors in the transmission of LSD within the two study areas. This is the first study to estimate transmission kernels from data on LSD outbreaks in Thailand. The findings from this study offer valuable insights into the spatial transmission of this disease, which will be useful in developing prevention and control strategies.

Impact of palmiped farm density on the resilience of the poultry sector to highly pathogenic avian influenza H5N8 in France

We analysed the interplay between palmiped farm density and the vulnerability of the poultry production system to highly pathogenic avian influenza (HPAI) H5N8. To do so, we used a spatially-explicit transmission model, which was calibrated to reproduce the observed spatio-temporal distribution of outbreaks in France during the 2016-2017 epidemic of HPAI. Six scenarios were investigated, in which the density of palmiped farms was decreased in the municipalities with the highest palmiped farm density. For each of the six scenarios, we first calculated the spatial distribution of the basic reproduction number (R0), i.e. the expected number of farms a particular farm would be likely to infect, should all other farms be susceptible. We also ran in silico simulations of the adjusted model for each scenario to estimate epidemic sizes and time-varying effective reproduction numbers. We showed that reducing palmiped farm density in the densest municipalities decreased substantially the size of the areas with high R0 values (> 1.5). In silico simulations suggested that reducing palmiped farm density, even slightly, in the densest municipalities was expected to decrease substantially the number of affected poultry farms and therefore provide benefits to the poultry sector as a whole. However, they also suggest that it would not have been sufficient, even in combination with the intervention measures implemented during the 2016-2017 epidemic, to completely prevent the virus from spreading. Therefore, the effectiveness of alternative structural preventive approaches now needs to be assessed, including flock size reduction and targeted vaccination.

Common features in spatial livestock disease transmission parameters

The risk of epidemic spread of diseases in livestock poses a threat to animal and often also human health. Important for the assessment of the effect of control measures is a statistical model quantification of between-farm transmission during epidemics. In particular, quantification of the between-farm transmission kernel has proven its importance for a range of different diseases in livestock. In this paper we explore if a comparison of the different transmission kernels yields further insight. Our comparison identifies common features that connect across the different pathogen-host combinations analyzed. We conjecture that these features are universal and thereby provide generic insights. Comparison of the shape of the spatial transmission kernel suggests that, in absence of animal movement bans, the distance dependence of transmission has a universal shape analogous to Lévy-walk model descriptions of human movement patterns. Also, our analysis suggests that interventions such as movement bans and zoning, through their impact on these movement patterns, change the shape of the kernel in a universal fashion. We discuss how the generic insights suggested can be of practical use for assessing risks of spread and optimizing control measures, in particular when outbreak data is scarce.

Effects of human mobility and behavior on disease transmission in a COVID-19 mathematical model

Human interactions and perceptions about health risk are essential to understand the evolution over the course of a pandemic. We present a Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Susceptible mathematical model with quarantine and social-distance-dependent transmission rates, to study COVID-19 dynamics. Human activities are split across different location settings: home, work, school, and elsewhere. Individuals move from home to the other locations at rates dependent on their epidemiological conditions and maintain a social distancing behavior, which varies with their location. We perform simulations and analyze how distinct social behaviors and restrictive measures affect the dynamic of the disease within a population. The model proposed in this study revealed that the main focus on the transmission of COVID-19 is attributed to the “home” location setting, which is understood as family gatherings including relatives and close friends. Limiting encounters at work, school and other locations will only be effective if COVID-19 restrictions occur simultaneously at all those locations and/or contact tracing or social distancing measures are effectively and strictly implemented, especially at the home setting.

Issues in Bayesian prospective surveillance of spatial health data

In this paper I review some of the major issues that arise when geo-referenced health data are to be the subject of prospective surveillance. The review focusses on modelbased approaches to this activity, and proposes the Bayesian paradigm as a convenient vehicle for modeling. Various posterior functional measures are discussed including the SCPO and SKL and a number of extensions to these are considered. Overall the value of Bayesian Hierarchical Modeling (BHM) with surveillance functionals is stressed in its relevance to early warning of adverse risk scenarios.

Pig farm vaccination against classical swine fever reduces the risk of transmission from wild boar

In 2018, classical swine fever (CSF) re-emerged in the Gifu Prefecture, central Japan, causing an on-going outbreak among wild boars and domestic pigs in the country. Consequently, oral vaccination for wild boar and compulsory vaccination for pig farms started in 2019. We have previously shown that, before vaccination in the Gifu Prefecture, the presence of CSF-infected wild boar near pig farms increased the risk of CSF transmission. This study aimed to re-evaluate the transmission risk from wild boars to pig farms under a vaccination program. The effectiveness of vaccination was evaluated by comparing the transmission risk estimated before and after the implementation of vaccinations. In this study, we focused on two affected areas, the Kanto (eastern Japan) and Kinki (west-central Japan) regions, in which eight of 11 infected farms were detected between the start of pig farm vaccinations and April 2021. Wild boar surveillance data from an area within a 50-km radius from the infected farms were used for analysis, consisting of 18,870 1-km grid cells (207 infected cells) in the Kanto region, and 15,677 cells (417 infected cells) in the Kinki region. The transmission rates in the post-vaccination period in the Kanto and Kinki regions were much lower than that in the pre-vaccination period in the Gifu Prefecture. The values of transmission kernels (h₀, transmission rate at 0 km) in the Kanto and Kinki regions decreased to 1% of the transmission kernel in the pre-vaccination period. In the pre-vaccination period, the risk of infection within 300 days was almost 95 % when one infected grid cell was detected within 1 km of a pig farm. Meanwhile, in the post-vaccination period, the risk of infection within 300 days was approximately 5% when several infected cells were detected within 1 km of a pig farm. Considering the limited effect of oral vaccination for wild boar due to distribution limitations in the Kanto and Kinki regions, vaccination on pig farms may seems to have mainly reduced the transmission risk from wild boar. However, despite the implementation of vaccination, the risk of infection on pig farms remains present due to the immunity gap of weaning pigs. Therefore, strict biosecurity measures on pig farms and an appropriate vaccination program are required to prevent and control CSF spread.

Regional Relative Risk, a Physics-Based Metric for Characterizing Airborne Infectious Disease Transmission

Airborne infectious disease transmission events occur over a wide range of spatial scales and can be an important means of disease transmission. Physics- and biology-based models can assist in predicting airborne transmission events, overall disease incidence, and disease control strategy efficacy. We describe a new theory that extends current approaches for the case in which an individual is infected by a single airborne particle, including the scenario in which numerous infectious particles are present in the air but only one causes infection. A single infectious particle can contain more than one pathogenic microorganism and be physically larger than the pathogen itself. This approach allows robust relative risk estimates even when there is wide variation in (i) individual exposures and (ii) the individual response to that exposure (the pathogen dose-response function can take any mathematical form and vary by individual). Based on this theory, we propose the regional relative risk-a new metric, distinct from the traditional relative risk metric, that compares the risk between two regions. In theory, these regions can range from individual rooms to large geographic areas. In this paper, we apply the regional relative risk metric to outdoor disease transmission events over spatial scales ranging from 50 m to 20 km, demonstrating that in many common cases minimal input information is required to use the metric. Also, we demonstrate that the model predictions are consistent with data from prior outbreaks. Future efforts could apply and validate this theory for other spatial scales, such as transmission within indoor environments. This work provides context for (i) the initial stages of an airborne disease outbreak and (ii) larger-scale disease spread, including unexpected low-probability disease "sparks" that potentially affect remote populations, a key practical issue in controlling airborne disease outbreaks. IMPORTANCE Airborne infectious disease transmission events occur over a wide range of spatial scales and can be important to disease outbreaks. We describe a new physics- and biology-based theory for the important case in which individuals are infected by a single airborne particle (even though numerous infectious particles can be emitted into the air and inhaled). Based on this theory, we propose a new epidemiological metric, regional relative risk, that compares the risk between two geographic regions (in theory, regions can range from individual rooms to large areas). Our modeling of transmission events predicts that for many scenarios of interest, minimal information is required to use this metric for locations 50 m to 20 km downwind. This prediction is consistent with data from prior disease outbreaks. Future efforts could apply and validate this theory for other spatial scales, such as indoor environments. Our results may be applicable to many airborne diseases a priori, as these results depend on the physics of airborne particulate dispersion.

Scientific Opinion on the assessment of the control measures for category A diseases of Animal Health Law: Foot and Mouth Disease

EFSA received a mandate from the European Commission to assess the effectiveness of some of the control measures against diseases included in the Category A list according to Regulation (EU) 2016/429 on transmissible animal diseases ('Animal Health Law'). This opinion belongs to a series of opinions where these control measures will be assessed, with this opinion covering the assessment of control measures for foot and mouth disease (FMD). In this opinion, EFSA and the AHAW Panel of experts review the effectiveness of: i) clinical and laboratory sampling procedures, ii) monitoring period and iii) the minimum radius of the protection and surveillance zones, and the minimum length of time the measures should be applied in these zones. The general methodology used for this series of opinions has been published elsewhere; nonetheless, the transmission kernels used for the assessment of the minimum radius of the protection zone of 3 km and of the surveillance zone of 10 km are shown. Several scenarios for which these control measures had to be assessed were designed and agreed prior to the start of the assessment. The monitoring period of 21 days was assessed as effective, and it was concluded that the protection and the surveillance zones comprise > 99% of the infections from an affected establishment if transmission occurred. Recommendations, provided for each of the scenarios assessed, aim to support the European Commission in the drafting of further pieces of legislation, as well as for plausible ad hoc requests in relation to FMD.

An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors

Modeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible-Infectious-Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

Spatial modeling of individual-level infectious disease transmission: Tuberculosis data in Manitoba, Canada

Geographically dependent individual level models (GD-ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete-time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD-ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD-ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.

Contact network uncertainty in individual level models of infectious disease transmission

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. This contact network can be spatial in nature, with connections between individuals closer in space being more likely. However, contact network data are often unobserved. Here, we consider the fit of an individual level model containing a spatially-based contact network that is either entirely, or partially, unobserved within a Bayesian framework, using data augmented Markov chain Monte Carlo (MCMC). We also incorporate the uncertainty about event history in the disease data. We also examine the performance of the data augmented MCMC analysis in the presence or absence of contact network observational models based upon either knowledge about the degree distribution or the total number of connections in the network. We find that the latter tend to provide better estimates of the model parameters and the underlying contact network.

Evaluation of strategies using simulation model to control a potential outbreak of highly pathogenic avian influenza among poultry farms in Central Luzon, Philippines

The Philippines confirmed its first epidemic of Highly Pathogenic Avian Influenza (HPAI) on August 11, 2017. It ended in November of 2017. Despite the successful management of the epidemic, reemergence is a continuous threat. The aim of this study was to conduct a mathematical model to assess the spatial transmission of HPAI among poultry farms in Central Luzon. Different control strategies and the current government protocol of 1 km radius pre-emptive culling (PEC) from infected farms were evaluated. The alternative strategies include 0.5km PEC, 1.5km PEC, 2 km PEC, 2.5 km PEC, and 3 km PEC, no pre-emptive culling (NPEC). The NPEC scenario was further modeled with a time of government notification set at 24hours, 48 hours, and 72 hours after the detection. Disease spread scenarios under each strategy were generated using an SEIR (susceptible-exposed-infectious-removed) stochastic model. A spatial transmission kernel was calculated and used to represent all potential routes of infection between farms. We assumed that the latent period occurs between 1–2 days, disease detection at 5–7 days post-infection, notification of authorities at 5–7 days post-detection and start of culling at 1–3 days post notification. The epidemic scenarios were compared based on the number of infected farms, the total number of culled farms, and the duration of the epidemic. Our results revealed that the current protocol is the most appropriate option compared with the other alternative interventions considered among farms with reproductive ratio (R_i) > 1. Shortening the culling radius to 0.5 km increased the duration of the epidemic. Further increase in the PEC zone decreased the duration of the epidemic but may not justify the increased number of farms to be culled. Nonetheless, the no-pre-emptive culling (NPEC) strategy can be an effective alternative to the current protocol if farm managers inform the government immediately within 24 hours of observation of the presence of HPAI in their farms. Moreover, if notification is made on days 1–3 after the detection, the scale and length of the outbreak have been significantly reduced. In conclusion, this study provided a comparison of various control measures for confronting the spread of HPAI infection using the simulation model. Policy makers can use this information to enhance the effectiveness of the current control strategy.

Latent likelihood ratio tests for assessing spatial kernels in epidemic models

One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically occur and estimation of this distance is very sensitive to the choice of kernel function, it is important that models used to inform control strategies can be scrutinised in the light of observation in order to elicit possible evidence against the selected kernel function. While a range of approaches to model criticism is in existence, the field remains one in which the need for further research is recognised. In this paper, building on earlier contributions by the authors, we introduce a new approach to assessing the validity of spatial kernels—the latent likelihood ratio tests—which use likelihood-based discrepancy variables that can be used to compare the fit of competing models, and compare the capacity of this approach to detect model mis-specification with that of tests based on the use of infection-link residuals. We demonstrate that the new approach can be used to formulate tests with greater power than infection-link residuals to detect kernel mis-specification particularly when the degree of mis-specification is modest. This new tests avoid the use of a fully Bayesian approach which may introduce undesirable complications related to computational complexity and prior sensitivity.

Identification of High-Risk Areas for the Spread of Highly Pathogenic Avian Influenza in Central Luzon, Philippines

Highly pathogenic avian influenza virus (HPAIV) is a major problem in the poultry industry. It is highly contagious and is associated with a high mortality rate. The Philippines experienced an outbreak of avian influenza (AI) in 2017. As there is always a risk of re-emergence, efforts to manage disease outbreaks should be optimal. Linked to this is the need for an effective surveillance procedure to capture disease outbreaks at their early stage. Risk-based surveillance is the most effective and economical approach to outbreak management. This study evaluated the potential of commercial poultry farms in Central Luzon to transmit HPAI by calculating their respective reproductive ratios (R0). The reproductive number for each farm is based on the spatial kernel and the infectious period. A risk map has been created based on the calculated R₀. There were 882 (76.63%) farms with R0 < 1. Farms with R0 ≥ 1 were all located in Pampanga Province. These farms were concentrated in the towns of San Luis (n = 12) and Candaba (n = 257). This study demonstrates the utility of mapping farm-level R0 estimates for informing HPAI risk management activities.

Multilevel model for airborne transmission of foot-and-mouth disease applied to Swedish livestock

The foot-and-mouth disease is an ever-present hazard to the livestock industry due to the huge economic consequences following an outbreak that necessitates culling of possibly infected animals in vast numbers. The disease is highly contagious and previous epizootics have shown that it spreads by many routes. One such route is airborne transmission, which has been investigated in this study by means of a detailed multilevel model that includes all scales of an outbreak. Local spread within an infected farm is described by a stochastic compartment model while the spread between farms is quantified by atmospheric dispersion simulations using a network representation of the set of farms. The model was applied to the Swedish livestock industry and the risk for an epizootic outbreak in Sweden was estimated using the basic reproduction number of each individual livestock-holding farm as the endpoint metric. The study was based on comprehensive official data sets for both the current livestock holdings and regional meteorological conditions. Three species of farm animals are susceptible to the disease and are present in large numbers: cattle, pigs and sheep. These species are all included in this study using their individual responses and consequences to the disease. It was concluded that some parts of southern Sweden are indeed preconditioned to harbor an airborne epizootic, while the sparse farm population of the north renders such events unlikely to occur there. The distribution of the basic reproduction number spans over several orders of magnitudes with low risk of disease spread from the majority of the farms while some farms may act as very strong disease transmitters. The results may serve as basic data in the planning of the national preparedness for this type of events.

Estimation of infection risk on pig farms in infected wild boar areas-Epidemiological analysis for the reemergence of classical swine fever in Japan in 2018

In September 2018, classical swine fever (CSF) reemerged in Japan after 26 years' absence. The first case was detected at a pig farm in Gifu Prefecture, in the center of Japan, and the disease spread to both domestic pigs and wild boar (Sus scrofa). The spread of CSF in wild boar is extremely difficult to control and is thus a great threat to domestic pig farms, and understanding the transmission risk from wild boar to domestic pigs is essential to implement effective control measures that will prevent domestic pig infection. Therefore, this study elucidates the transmission risk from wild boar to domestic pigs by introducing a transmission kernel that is dependent on the distance between infected wild boar and pig farms, and then estimating the risk area of infection from wild boar by describing the transmission probability. The study used epidemiological data from Gifu Prefecture in the period from September 2018 to March 2019, including a total of 171 1-km grid cells where an infected wild boar was detected and pig farm data from 13 infected and 34 uninfected farms. The estimated infection risk area within 28 days matched well with the observed data. The risk area widened gradually during the epidemic, and at the end of March, the risk area extended over a range of approximately 75 km from east to west and 40 km from north to south (almost 3000 km²). Ten out of the 13 infected farms and four out of the 34 uninfected farms were located within the high-risk area (>60 % infection probability). In contrast, one infected farm and 18 uninfected farms were located within the low-risk area (<5 % infection probability). When several infected grid cells were detected within 5 km of a pig farm, the risk of infection from wild boar within 28 days was more than 5 %. This analysis provides an estimate of the potential spatial range over which CSF virus can spread between wild boar and domestic pig farms, and can be used to inform the early detection of CSF-suspected pigs and the strengthening of biosecurity measures that will effectively prevent and control the disease based on the infection risk level.

Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.

Dispersal Kernels may be Scalable: Implications from a Plant Pathogen

AIM

Understanding how spatial scale of study affects observed dispersal patterns can provide insights into spatiotemporal population dynamics, particularly in systems with significant long-distance dispersal (LDD). We aimed to investigate the dispersal gradients of two rusts of wheat with spores of similar size, mass, and shape, over multiple spatial scales. We hypothesized that a single dispersal kernel could fit the dispersal from all spatial scales well, and that it would be possible to obtain similar results in spatiotemporal increase of disease when modeling based on differing scales.

LOCATION

Central Oregon and St. Croix Island.

TAXA

Puccinia striiformis f. sp. tritici, Puccinia graminis f. sp. tritici, Triticum aestivum.

METHODS

We compared empirically-derived primary disease gradients of cereal rust across three spatial scales: local (inoculum source and sampling unit = 0.0254 m, spatial extent = 1.52m) field-wide (inoculum source = 1.52 m, sampling unit = 0.305 m, and spatial extent = 91.44 m), and regional (inoculum source and sampling unit = 152 m, spatial extent = 10.7 km). We then examined whether disease spread in spatially explicit simulations depended upon the scale at which data were collected by constructing a compartmental time-step model.

RESULTS

The three data sets could be fit well by a single inverse-power law dispersal kernel. Simulating epidemic spread at different spatial resolutions resulted in similar patterns of spatiotemporal spread. Dispersal kernel data obtained at one spatial scale can be used to represent spatiotemporal disease spread at a larger spatial scale.

MAIN CONCLUSIONS

Organisms spread by aerially dispersed small propagules that exhibit LDD may follow similar dispersal patterns over a several hundred- or thousand-fold expanse of spatial scale. Given that the primary mechanisms driving aerial dispersal remain constant, it may be possible to extrapolate across scales when empirical data are unavailable at a scale of interest.

Modeling the role of carrier and mobile herds on foot-and-mouth disease virus endemicity in the Far North Region of Cameroon

Foot and mouth disease virus (FMDV) is an RNA virus that infects cloven-hoofed animals, often produces either epidemic or endemic conditions, and negatively affects agricultural economies worldwide. FMDV epidemic dynamics have been extensively studied, but understanding of drivers of disease persistence in areas in which FMDV is endemic, such as most of sub-Saharan Africa, is lacking. We present a spatial stochastic model of disease dynamics that incorporates a spatial transmission kernel in a modified Gillespie algorithm, and use it to evaluate two hypothesized drivers of endemicity: asymptomatic carriers and the movement of mobile herds. The model is parameterized using data from the pastoral systems in the Far North Region of Cameroon. Our computational study provides evidence in support of the hypothesis that asymptomatic carriers, but not mobile herds, are a driver of endemicity.

Highly pathogenic avian influenza H5N8 in south-west France 2016-2017: A modeling study of control strategies

In the winter 2016-2017 the largest epidemic of highly pathogenic avian influenza (HPAI) ever recorded in the European Union spread to all 28 member states. France was hit particularly hard and reported a total of 484 infected premises (IPs) by March 2017. We developed a mathematical model to analyze the spatiotemporal evolution of the epidemic and evaluate the impact of control strategies. We estimated that farms rearing ducks were on average 2.5 times more infectious and 5.0 times more susceptible to HPAI than farms rearing other avian species. The implementation of surveillance zones around IPs reduced transmission by a factor of 1.8 on average. Compared to the strengthening of pre-emptive culling measures enforced by French authorities in February 2017, we found that a faster depopulation of diagnosed IPs would have had a larger impact on the total number of infections. For example, halving the time delay from detection to slaughter of infected animals would have reduced the total number of IPs by 52% and total cull numbers by 50% on average. This study showcases the possible contribution of modeling to inform and optimize control strategies during an outbreak.

A spatio-temporal individual-based network framework for West Nile virus in the USA: Spreading pattern of West Nile virus

West Nile virus (WNV)—a mosquito-borne arbovirus—entered the USA through New York City in 1999 and spread to the contiguous USA within three years while transitioning from epidemic outbreaks to endemic transmission. The virus is transmitted by vector competent mosquitoes and maintained in the avian populations. WNV spatial distribution is mainly determined by the movement of residential and migratory avian populations. We developed an individual-level heterogeneous network framework across the USA with the goal of understanding the long-range spatial distribution of WNV. To this end, we proposed three distance dispersal kernels model: 1) exponential—short-range dispersal, 2) power-law—long-range dispersal in all directions, and 3) power-law biased by flyway direction —long-range dispersal only along established migratory routes. To select the appropriate dispersal kernel we used the human case data and adopted a model selection framework based on approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC). From estimated parameters, we find that the power-law biased by flyway direction kernel is the best kernel to fit WNV human case data, supporting the hypothesis of long-range WNV transmission is mainly along the migratory bird flyways. Through extensive simulation from 2014 to 2016, we proposed and tested hypothetical mitigation strategies and found that mosquito population reduction in the infected states and neighboring states is potentially cost-effective.

The underlying pattern of West Nile virus (WNV) geographic spread across the United States is not completely clear, which is a necessary step for continental or state level mitigation strategies to reduce WNV transmission. We report a network model that explains the geographic spread of WNV in the United States. West Nile virus is a mosquito-borne pathogen that infects many avian species with different movement ranges. From our research, we found that migration patterns and routes play an essential role in the WNV spatial distribution. The virus spreads in all directions at short distances because of local birds and short-distance migratory birds. However, the virus also disperses long distances along the avian migratory routes. Our model is designed to be flexible and therefore can be used to explore spreading patterns of other infectious diseases in other geographic locations.

Consequences of Long-Distance Dispersal for Epidemic Spread: Patterns, Scaling, and Mitigation

Epidemics caused by long-distance dispersed pathogens result in some of the most explosive and difficult to control diseases of both plants and animals (including humans). Yet the factors influencing disease spread, especially in the early stages of the outbreak, are not well-understood. We present scaling relationships, of potentially widespread relevance, that were developed from more than 15 years of field and in silico single focus studies of wheat stripe rust spread. These relationships emerged as a consequence of accounting for a greater proportion of the fat-tailed disease gradient that may be frequently underestimated in disease spread studies. Leptokurtic dispersal gradients (highly peaked and fat-tailed) are relatively common in nature and they can be represented by power law functions. Power law scale invariance properties generate patterns that repeat over multiple spatial scales, suggesting important and predictable scaling relationships between disease levels during the first generation of disease outbreaks and subsequent epidemic spread. Experimental wheat stripe rust outbreaks and disease spread simulations support theoretical scaling relationships from power law properties and suggest that relatively straightforward scaling approximations may be useful for projecting the spread of disease caused by long-distance dispersed pathogens. Our results suggest that, when actual dispersal/disease data are lacking, an inverse power law with exponent = 2 may provide a reasonable approximation for modeling disease spread. Furthermore, our experiments and simulations strongly suggest that early control treatments with small spatial extent are likely to be more effective at suppressing an outbreak caused by a long-distance dispersed pathogen than would delayed treatment of a larger area. The scaling relationships we detail and the associated consequences for disease control may be broadly applicable to plant and animal pathogens characterized by non-exponentially bound, fat-tailed dispersal gradients.

Spatial transmission of H5N2 highly pathogenic avian influenza between Minnesota poultry premises during the 2015 outbreak

The spatial spread of highly pathogenic avian influenza (HPAI) H5N2 during the 2015 outbreak in the U.S. state of Minnesota was analyzed through the estimation of a spatial transmission kernel, which quantifies the infection hazard an infectious premises poses to an uninfected premises some given distance away. Parameters were estimated using a maximum likelihood method for the entire outbreak as well as for two phases defined by the daily number of newly detected HPAI-positive premises. The results indicate both a strong dependence of the likelihood of transmission on distance and a significant distance-independent component of outbreak spread for the overall outbreak. The results further suggest that HPAI spread differed during the later phase of the outbreak. The estimated spatial transmission kernel was used to compare the Minnesota outbreak with previous HPAI outbreaks in the Netherlands and Italy to contextualize the Minnesota transmission kernel results and make additional inferences about HPAI transmission during the Minnesota outbreak. Lastly, the spatial transmission kernel was used to identify high risk areas for HPAI spread in Minnesota. Risk maps were also used to evaluate the potential impact of an early marketing strategy implemented by poultry producers in a county in Minnesota during the outbreak, with results providing evidence that the strategy was successful in reducing the potential for HPAI spread.

Forecasting the 2001 Foot-and-Mouth Disease Epidemic in the UK

Near real-time epidemic forecasting approaches are needed to respond to the increasing number of infectious disease outbreaks. In this paper, we retrospectively assess the performance of simple phenomenological models that incorporate early sub-exponential growth dynamics to generate short-term forecasts of the 2001 foot-and-mouth disease epidemic in the UK. For this purpose, we employed the generalized-growth model (GGM) for pre-peak predictions and the generalized-Richards model (GRM) for post-peak predictions. The epidemic exhibits a growth-decelerating pattern as the relative growth rate declines inversely with time. The uncertainty of the parameter estimates [Formula: see text] narrows down and becomes more precise using an increasing amount of data of the epidemic growth phase. Indeed, using only the first 10-15 days of the epidemic, the scaling of growth parameter (p) displays wide uncertainty with the confidence interval for p ranging from values ~ 0.5 to 1.0, indicating that less than 15 epidemic days of data are not sufficient to discriminate between sub-exponential (i.e., p < 1) and exponential growth dynamics (i.e., p = 1). By contrast, using 20, 25, or 30 days of epidemic data, it is possible to recover estimates of p around 0.6 and the confidence interval is substantially below the exponential growth regime. Local and national bans on the movement of livestock and a nationwide cull of infected and contiguous premises likely contributed to the decelerating trajectory of the epidemic. The GGM and GRM provided useful 10-day forecasts of the epidemic before and after the peak of the epidemic, respectively. Short-term forecasts improved as the model was calibrated with an increasing length of the epidemic growth phase. Phenomenological models incorporating generalized-growth dynamics are useful tools to generate short-term forecasts of epidemic growth in near real time, particularly in the context of limited epidemiological data as well as information about transmission mechanisms and the effects of control interventions.

Bayesian inference of epidemiological parameters from transmission experiments

Epidemiological parameters for livestock diseases are often inferred from transmission experiments. However, there are several limitations inherent to the design of such experiments that limits the precision of parameter estimates. In particular, infection times and latent periods cannot be directly observed and infectious periods may also be censored. We present a Bayesian framework accounting for these features directly and employ Markov chain Monte Carlo techniques to provide robust inferences and quantify the uncertainty in our estimates. We describe the transmission dynamics using a susceptible-exposed-infectious-removed compartmental model, with gamma-distributed transition times. We then fit the model to published data from transmission experiments for foot-and-mouth disease virus (FMDV) and African swine fever virus (ASFV). Where the previous analyses of these data made various assumptions on the unobserved processes in order to draw inferences, our Bayesian approach includes the unobserved infection times and latent periods and quantifies them along with all other model parameters. Drawing inferences about infection times helps identify who infected whom and can also provide insights into transmission mechanisms. Furthermore, we are able to use our models to measure the difference between the latent periods of inoculated and contact-challenged animals and to quantify the effect vaccination has on transmission.

Bayesian epidemic models for spatially aggregated count data

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time-varying factors. This paper addresses these issues via suitable Bayesian modelling. In doing so, we utilize a general class of stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework does incorporate serial correlation and time-varying covariates through an Ornstein-Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and variations of mixtures of g-priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process-based methods for testing scenarios for disease control, thus linking traditional epidemiological models with stochastic epidemic processes, useful in policy-focused decision making. The approach is illustrated with an application to a sheep pox dataset from the Evros region, Greece. Copyright © 2017 John Wiley & Sons, Ltd.

Collective effect of personal behavior induced preventive measures and differential rate of transmission on spread of epidemics

In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method. The network mean field approach is generalized to account for the effect of non-linear coupling between the aforementioned factors on the collective dynamics of nodes. The upper bound estimates of the disease outbreak threshold obtained from the mean field theory are found to be in good agreement with the corresponding non-linear stochastic model. From the results of parametric study, it is shown that the epidemic size has inverse dependence on the preventive measures (λ). It has also been shown that the increase in the average degree of the nodes lowers the time of spread and enhances the size of epidemics.

Spatiotemporal Variation in Distance Dependent Animal Movement Contacts: One Size Doesn't Fit All

The structure of contacts that mediate transmission has a pronounced effect on the outbreak dynamics of infectious disease and simulation models are powerful tools to inform policy decisions. Most simulation models of livestock disease spread rely to some degree on predictions of animal movement between holdings. Typically, movements are more common between nearby farms than between those located far away from each other. Here, we assessed spatiotemporal variation in such distance dependence of animal movement contacts from an epidemiological perspective. We evaluated and compared nine statistical models, applied to Swedish movement data from 2008. The models differed in at what level (if at all), they accounted for regional and/or seasonal heterogeneities in the distance dependence of the contacts. Using a kernel approach to describe how probability of contacts between farms changes with distance, we developed a hierarchical Bayesian framework and estimated parameters by using Markov Chain Monte Carlo techniques. We evaluated models by three different approaches of model selection. First, we used Deviance Information Criterion to evaluate their performance relative to each other. Secondly, we estimated the log predictive posterior distribution, this was also used to evaluate their relative performance. Thirdly, we performed posterior predictive checks by simulating movements with each of the parameterized models and evaluated their ability to recapture relevant summary statistics. Independent of selection criteria, we found that accounting for regional heterogeneity improved model accuracy. We also found that accounting for seasonal heterogeneity was beneficial, in terms of model accuracy, according to two of three methods used for model selection. Our results have important implications for livestock disease spread models where movement is an important risk factor for between farm transmission. We argue that modelers should refrain from using methods to simulate animal movements that assume the same pattern across all regions and seasons without explicitly testing for spatiotemporal variation.

Estimating infectious disease transmission distances using the overall distribution of cases

The average spatial distance between transmission-linked cases is a fundamental property of infectious disease dispersal. However, the distance between a case and their infector is rarely measurable. Contact-tracing investigations are resource intensive or even impossible, particularly when only a subset of cases are detected. Here, we developed an approach that uses onset dates, the generation time distribution and location information to estimate the mean transmission distance. We tested our method using outbreak simulations. We then applied it to the 2001 foot-and-mouth outbreak in Cumbria, UK, and compared our results to contact-tracing activities. In simulations with a true mean distance of 106m, the average mean distance estimated was 109m when cases were fully observed (95% range of 71-142). Estimates remained consistent with the true mean distance when only five percent of cases were observed, (average estimate of 128m, 95% range 87-165). Estimates were robust to spatial heterogeneity in the underlying population. We estimated that both the mean and the standard deviation of the transmission distance during the 2001 foot-and-mouth outbreak was 8.9km (95% CI: 8.4km-9.7km). Contact-tracing activities found similar values of 6.3km (5.2km-7.4km) and 11.2km (9.5km-12.8km), respectively. We were also able to capture the drop in mean transmission distance over the course of the outbreak. Our approach is applicable across diseases, robust to under-reporting and can inform interventions and surveillance.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation

Likelihood-based inference for disease outbreak data can be very challenging due to the inherent dependence of the data and the fact that they are usually incomplete. In this paper we review recent Approximate Bayesian Computation (ABC) methods for the analysis of such data by fitting to them stochastic epidemic models without having to calculate the likelihood of the observed data. We consider both non-temporal and temporal-data and illustrate the methods with a number of examples featuring different models and datasets. In addition, we present extensions to existing algorithms which are easy to implement and provide an improvement to the existing methodology. Finally, R code to implement the algorithms presented in the paper is available on https://github.com/kypraios/epiABC.

Parameterizing Spatial Models of Infectious Disease Transmission that Incorporate Infection Time Uncertainty Using Sampling-Based Likelihood Approximations

A class of discrete-time models of infectious disease spread, referred to as individual-level models (ILMs), are typically fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. These models quantify probabilistic outcomes regarding the risk of infection of susceptible individuals due to various susceptibility and transmissibility factors, including their spatial distance from infectious individuals. The infectious pressure from infected individuals exerted on susceptible individuals is intrinsic to these ILMs. Unfortunately, quantifying this infectious pressure for data sets containing many individuals can be computationally burdensome, leading to a time-consuming likelihood calculation and, thus, computationally prohibitive MCMC-based analysis. This problem worsens when using data augmentation to allow for uncertainty in infection times. In this paper, we develop sampling methods that can be used to calculate a fast, approximate likelihood when fitting such disease models. A simple random sampling approach is initially considered followed by various spatially-stratified schemes. We test and compare the performance of our methods with both simulated data and data from the 2001 foot-and-mouth disease (FMD) epidemic in the U.K. Our results indicate that substantial computation savings can be obtained--albeit, of course, with some information loss--suggesting that such techniques may be of use in the analysis of very large epidemic data sets.

Data-Driven Models of Foot-and-Mouth Disease Dynamics: A Review

Foot-and-mouth disease virus (FMDV) threatens animal health and leads to considerable economic losses worldwide. Progress towards minimizing both veterinary and financial impact of the disease will be made with targeted disease control policies. To move towards targeted control, specific targets and detailed control strategies must be defined. One approach for identifying targets is to use mathematical and simulation models quantified with accurate and fine-scale data to design and evaluate alternative control policies. Nevertheless, published models of FMDV vary in modelling techniques and resolution of data incorporated. In order to determine which models and data sources contain enough detail to represent realistic control policy alternatives, we performed a systematic literature review of all FMDV dynamical models that use host data, disease data or both data types. For the purpose of evaluating modelling methodology, we classified models by control strategy represented, resolution of models and data, and location modelled. We found that modelling methodology has been well developed to the point where multiple methods are available to represent detailed and contact-specific transmission and targeted control. However, detailed host and disease data needed to quantify these models are only available from a few outbreaks. To address existing challenges in data collection, novel data sources should be considered and integrated into models of FMDV transmission and control. We suggest modelling multiple endemic areas to advance local control and global control and better understand FMDV transmission dynamics. With incorporation of additional data, models can assist with both the design of targeted control and identification of transmission drivers across geographic boundaries.

An empirically adjusted approach to reproductive number estimation for stochastic compartmental models: A case study of two Ebola outbreaks

The various thresholding quantities grouped under the "Basic Reproductive Number" umbrella are often confused, but represent distinct approaches to estimating epidemic spread potential, and address different modeling needs. Here, we contrast several common reproduction measures applied to stochastic compartmental models, and introduce a new quantity dubbed the "empirically adjusted reproductive number" with several advantages. These include: more complete use of the underlying compartmental dynamics than common alternatives, use as a potential diagnostic tool to detect the presence and causes of intensity process underfitting, and the ability to provide timely feedback on disease spread. Conceptual connections between traditional reproduction measures and our approach are explored, and the behavior of our method is examined under simulation. Two illustrative examples are developed: First, the single location applications of our method are established using data from the 1995 Ebola outbreak in the Democratic Republic of the Congo and a traditional stochastic SEIR model. Second, a spatial formulation of this technique is explored in the context of the ongoing Ebola outbreak in West Africa with particular emphasis on potential use in model selection, diagnosis, and the resulting applications to estimation and prediction. Both analyses are placed in the context of a newly developed spatial analogue of the traditional SEIR modeling approach.

Potential impact of species and livestock density on the epidemic size and effectiveness of control measures for foot-and-mouth disease in Japan

The characteristics of a livestock area, including farm density and animal species, influence the spread of foot-and-mouth disease (FMD). In this study, the impact of livestock area on FMD epidemics was examined using an FMD transmission model. For this simulation, three major livestock areas were selected: the 2010 FMD epidemic area in Japan as the baseline area (BS), a cattle and pig mixed production area (CP) and a cattle production area (C). Simulation results demonstrated that under the 24-hr culling policy, only 12% of epidemics among 1,000 simulations were abated within 100 days in the CP area, whereas 90% of the epidemics ceased in the BS area. In the C area, all epidemics were successfully contained within 100 days. Evaluation of additional control measures in the CP area showed that the 0.5-km pre-emptive culling, even when only targeting pig farms, raised the potential for successful containment to 94%. A 10-km vaccination on day 7 or 14 after initial detection was also effective in halting the epidemics (80%), but accompanied a large number of culled or vaccinated farms. The combined strategy of 10-km vaccination and 0.5-km pre-emptive culling targeting pig farms succeeded in containing all epidemics within 100 days. The present study suggests the importance of preparedness for the 24-hr culling policy and additional control measures when an FMD outbreak occurs in a densely populated area. Considering the characteristics of the livestock area is important in planning FMD control strategies.

Evaluation of the transmission risk of foot-and-mouth disease in Japan

The transmission risk of foot-and-mouth disease (FMD) in Japan was evaluated using a mathematical FMD transmission model. The distance-based transmission rate between farms, which was parameterized using the FMD epidemic data in 2010 in Japan, was used to calculate the local-level reproduction numbers-expected numbers of secondary infections caused by one infected farm-for all cattle and pig farms in the country, which were then visualized as a risk map. The risk map demonstrated the spatial heterogeneity of transmission risk in the country and identified risk areas with higher possibility of disease spread. This result suggests that, particularly in high-risk areas, it is important to prepare for the smooth and efficient implementation of control measures against FMD outbreaks.

Rapid simulation of spatial epidemics: a spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel.

Supervised learning and prediction of spatial epidemics

Parameter estimation for mechanistic models of infectious disease can be computationally intensive. Nsoesie et al. (2011) introduced an approach for inference on infectious disease data based on the idea of supervised learning. Their method involves simulating epidemics from various infectious disease models, and using classifiers built from the epidemic curve data to predict which model were most likely to have generated observed epidemic curves. They showed that the classification approach could fairly identify underlying characteristics of the disease system, without fitting various transmission models via, say, Bayesian Markov chain Monte Carlo. We extend this work to the case where the underlying infectious disease model is inherently spatial. Our goal is to compare the use of global epidemic curves for building the classifier, with the use of spatially stratified epidemic curves. We demonstrate these methods on simulated data and apply the method to analyze a tomato spotted wilt virus epidemic dataset.

OutbreakTools: a new platform for disease outbreak analysis using the R software

The investigation of infectious disease outbreaks relies on the analysis of increasingly complex and diverse data, which offer new prospects for gaining insights into disease transmission processes and informing public health policies. However, the potential of such data can only be harnessed using a number of different, complementary approaches and tools, and a unified platform for the analysis of disease outbreaks is still lacking. In this paper, we present the new R package OutbreakTools, which aims to provide a basis for outbreak data management and analysis in R. OutbreakTools is developed by a community of epidemiologists, statisticians, modellers and bioinformaticians, and implements classes and methods for storing, handling and visualizing outbreak data. It includes real and simulated outbreak datasets. Together with a number of tools for infectious disease epidemiology recently made available in R, OutbreakTools contributes to the emergence of a new, free and open-source platform for the analysis of disease outbreaks.

The impact of movements and animal density on continental scale cattle disease outbreaks in the United States

Globalization has increased the potential for the introduction and spread of novel pathogens over large spatial scales necessitating continental-scale disease models to guide emergency preparedness. Livestock disease spread models, such as those for the 2001 foot-and-mouth disease (FMD) epidemic in the United Kingdom, represent some of the best case studies of large-scale disease spread. However, generalization of these models to explore disease outcomes in other systems, such as the United States's cattle industry, has been hampered by differences in system size and complexity and the absence of suitable livestock movement data. Here, a unique database of US cattle shipments allows estimation of synthetic movement networks that inform a near-continental scale disease model of a potential FMD-like (i.e., rapidly spreading) epidemic in US cattle. The largest epidemics may affect over one-third of the US and 120,000 cattle premises, but cattle movement restrictions from infected counties, as opposed to national movement moratoriums, are found to effectively contain outbreaks. Slow detection or weak compliance may necessitate more severe state-level bans for similar control. Such results highlight the role of large-scale disease models in emergency preparedness, particularly for systems lacking comprehensive movement and outbreak data, and the need to rapidly implement multi-scale contingency plans during a potential US outbreak.

Modelling the continental-scale spread of Schmallenberg virus in Europe: approaches and challenges

Following its emergence in northern Europe in 2011 Schmallenberg virus (SBV), a vector-borne disease transmitted by the bites of Culicoides midges, has spread across much of the continent. Here we develop simple models to describe the spread of SBV at a continental scale and, more specifically, within and between NUTS2 regions in Europe. The model for the transmission of SBV between regions suggests that vector dispersal is the principle mechanism for transmission, even at the continental scale. The within-region model indicates that there is substantial heterogeneity amongst regions in the force of infection for cattle and sheep farms. Moreover, there is considerable under-ascertainment of SBV-affected holdings, though the level of under-ascertainment varies between regions. We contrast the relatively simple approach adopted in this study with the more complex continental-scale micro-simulation models which have been developed for pandemic influenza and discuss the strengths, weaknesses and data requirements of both approaches.