Impact of spatial clustering on disease transmission and optimal control

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.

EPINEST, an agent-based model to simulate epidemic dynamics in large-scale poultry production and distribution networks

The rapid intensification of poultry production raises important concerns about the associated risks of zoonotic infections. Here, we introduce EPINEST (EPIdemic NEtwork Simulation in poultry Transportation systems): an agent-based modelling framework designed to simulate pathogen transmission within realistic poultry production and distribution networks. We provide example applications to broiler production in Bangladesh, but the modular structure of the model allows for easy parameterization to suit specific countries and system configurations. Moreover, the framework enables the replication of a wide range of eco-epidemiological scenarios by incorporating diverse pathogen life-history traits, modes of transmission and interactions between multiple strains and/or pathogens. EPINEST was developed in the context of an interdisciplinary multi-centre study conducted in Bangladesh, India, Vietnam and Sri Lanka, and will facilitate the investigation of the spreading patterns of various health hazards such as avian influenza, Campylobacter, Salmonella and antimicrobial resistance in these countries. Furthermore, this modelling framework holds potential for broader application in veterinary epidemiology and One Health research, extending its relevance beyond poultry to encompass other livestock species and disease systems.

Rational social distancing policy during epidemics with limited healthcare capacity

Epidemics of infectious diseases posing a serious risk to human health have occurred throughout history. During recent epidemics there has been much debate about policy, including how and when to impose restrictions on behaviour. Policymakers must balance a complex spectrum of objectives, suggesting a need for quantitative tools. Whether health services might be 'overwhelmed' has emerged as a key consideration. Here we show how costly interventions, such as taxes or subsidies on behaviour, can be used to exactly align individuals' decision making with government preferences even when these are not aligned. In order to achieve this, we develop a nested optimisation algorithm of both the government intervention strategy and the resulting equilibrium behaviour of individuals. We focus on a situation in which the capacity of the healthcare system to treat patients is limited and identify conditions under which the disease dynamics respect the capacity limit. We find an extremely sharp drop in peak infections at a critical maximum infection cost in the government's objective function. This is in marked contrast to the gradual reduction of infections if individuals make decisions without government intervention. We find optimal interventions vary less strongly in time when interventions are costly to the government and that the critical cost of the policy switch depends on how costly interventions are.

Rational social distancing in epidemics with uncertain vaccination timing

During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

Transition from susceptible-infected to susceptible-infected-recovered dynamics in a susceptible-cleric-zombie-recovered active matter model

The susceptible-infected (SI) and susceptible-infected-recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by whether or not the number of susceptibles always drops to zero at long times. Here we introduce a new active matter epidemic model, the "susceptible-cleric-zombie-recovered" (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability γ via interaction with a cleric. Upon colliding with a zombie, both susceptibles and clerics enter the zombie state with probability β and α, respectively. By changing the initial fraction of clerics or their healing ability rate γ, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which a finite number of clerics and susceptibles survive at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection.

Spatial aggregation choice in the era of digital and administrative surveillance data

Traditional disease surveillance is increasingly being complemented by data from non-traditional sources like medical claims, electronic health records, and participatory syndromic data platforms. As non-traditional data are often collected at the individual-level and are convenience samples from a population, choices must be made on the aggregation of these data for epidemiological inference. Our study seeks to understand the influence of spatial aggregation choice on our understanding of disease spread with a case study of influenza-like illness in the United States. Using U.S. medical claims data from 2002 to 2009, we examined the epidemic source location, onset and peak season timing, and epidemic duration of influenza seasons for data aggregated to the county and state scales. We also compared spatial autocorrelation and tested the relative magnitude of spatial aggregation differences between onset and peak measures of disease burden. We found discrepancies in the inferred epidemic source locations and estimated influenza season onsets and peaks when comparing county and state-level data. Spatial autocorrelation was detected across more expansive geographic ranges during the peak season as compared to the early flu season, and there were greater spatial aggregation differences in early season measures as well. Epidemiological inferences are more sensitive to spatial scale early on during U.S. influenza seasons, when there is greater heterogeneity in timing, intensity, and geographic spread of the epidemics. Users of non-traditional disease surveillance should carefully consider how to extract accurate disease signals from finer-scaled data for early use in disease outbreaks.

Delays in Epidemic Outbreak Control Cost Disproportionately Large Treatment Footprints to Offset

Epidemic outbreak control often involves a spatially explicit treatment area (quarantine, inoculation, ring cull) that covers the outbreak area and adjacent regions where hosts are thought to be latently infected. Emphasis on space however neglects the influence of treatment timing on outbreak control. We conducted field and in silico experiments with wheat stripe rust (WSR), a long-distance dispersed plant disease, to understand interactions between treatment timing and area interact to suppress an outbreak. Full-factorial field experiments with three different ring culls (outbreak area only to a 25-fold increase in treatment area) at three different disease control timings (1.125, 1.25, and 1.5 latent periods after initial disease expression) indicated that earlier treatment timing had a conspicuously greater suppressive effect than the area treated. Disease spread computer simulations over a broad range of influential epidemic parameter values (R0, outbreak disease prevalence, epidemic duration) suggested that potentially unrealistically large increases in treatment area would be required to compensate for even small delays in treatment timing. Although disease surveillance programs are costly, our results suggest that treatments early in an epidemic disease outbreak require smaller areas to be effective, which may ultimately compensate for the upfront costs of proactive disease surveillance programs.

Challenges for modelling interventions for future pandemics

Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.

Two-stage algorithms for visually exploring spatio-temporal clustering of avian influenza virus outbreaks in poultry farms

The development of visual tools for the timely identification of spatio-temporal clusters will assist in implementing control measures to prevent further damage. From January 2015 to June 2020, a total number of 1463 avian influenza outbreak farms were detected in Taiwan and further confirmed to be affected by highly pathogenic avian influenza subtype H5Nx. In this study, we adopted two common concepts of spatio-temporal clustering methods, the Knox test and scan statistics, with visual tools to explore the dynamic changes of clustering patterns. Since most (68.6%) of the outbreak farms were detected in 2015, only the data from 2015 was used in this study. The first two-stage algorithm performs the Knox test, which established a threshold of 7 days and identified 11 major clusters in the six counties of southwestern Taiwan, followed by the standard deviational ellipse (SDE) method implemented on each cluster to reveal the transmission direction. The second algorithm applies scan likelihood ratio statistics followed by AGC index to visualize the dynamic changes of the local aggregation pattern of disease clusters at the regional level. Compared to the one-stage aggregation approach, Knox-based and AGC mapping were more sensitive in small-scale spatio-temporal clustering.

Predictive Value of Time-Space Clusters for HIV Transmission in Washington State, 2017-2019

BACKGROUND

Pillar 4 of the United States' End the HIV Epidemic plan is to respond quickly to HIV outbreaks, but the utility of CDC's tool for identifying HIV outbreaks through time-space cluster detection has not been evaluated. The objective of this evaluation is to quantify the ability of the CDC time-space cluster criterion to predict future HIV diagnoses and to compare it to a space-time permutation statistic implemented in SaTScan software.

SETTING

Washington State from 2017 to 2019.

METHODS

We applied both cluster criteria to incident HIV cases in Washington State to identify clusters. Using a repeated-measures Poisson model, we calculated a rate ratio comparing the 6 months after cluster detection with a baseline rate from 24 to 12 months before the cluster was detected. We also compared the demographics of cases within clusters with all other incident cases.

RESULTS

The CDC criteria identified 17 clusters containing 192 cases in the 6 months after cluster detection, corresponding to a rate ratio of 1.25 (95% confidence interval: 0.95 to 1.65) relative to baseline. The time-space permutation statistic identified 5 clusters containing 25 cases with a rate ratio of 2.27 (95% confidence interval: 1.28 to 4.03). Individuals in clusters identified by the new criteria were more likely to be of Hispanic origin (61% vs 20%) and in rural areas (51% vs 12%).

CONCLUSIONS

The space-time permutation cluster analysis is a promising tool for identification of clusters with the largest growth potential for whom interruption may prove most beneficial.

The role of habitat configuration in shaping animal population processes: a framework to generate quantitative predictions

By shaping where individuals move, habitat configuration can fundamentally structure animal populations. Yet, we currently lack a framework for generating quantitative predictions about the role of habitat configuration in modulating population outcomes. To address this gap, we propose a modelling framework inspired by studies using networks to characterize habitat connectivity. We first define animal habitat networks, explain how they can integrate information about the different configurational features of animal habitats, and highlight the need for a bottom–up generative model that can depict realistic variations in habitat potential connectivity. Second, we describe a model for simulating animal habitat networks (available in the R package AnimalHabitatNetwork), and demonstrate its ability to generate alternative habitat configurations based on empirical data, which forms the basis for exploring the consequences of alternative habitat structures. Finally, we lay out three key research questions and demonstrate how our framework can address them. By simulating the spread of a pathogen within a population, we show how transmission properties can be impacted by both local potential connectivity and landscape-level characteristics of habitats. Our study highlights the importance of considering the underlying habitat configuration in studies linking social structure with population-level outcomes.

Causes of delayed outbreak responses and their impacts on epidemic spread

Livestock diseases have devastating consequences economically, socially and politically across the globe. In certain systems, pathogens remain viable after host death, which enables residual transmissions from infected carcasses. Rapid culling and carcass disposal are well-established strategies for stamping out an outbreak and limiting its impact; however, wait-times for these procedures, i.e. response delays, are typically farm-specific and time-varying due to logistical constraints. Failing to incorporate variable response delays in epidemiological models may understate outbreak projections and mislead management decisions. We revisited the 2001 foot-and-mouth epidemic in the United Kingdom and sought to understand how misrepresented response delays can influence model predictions. Survival analysis identified farm size and control demand as key factors that impeded timely culling and disposal activities on individual farms. Using these factors in the context of an existing policy to predict local variation in response times significantly affected predictions at the national scale. Models that assumed fixed, timely responses grossly underestimated epidemic severity and its long-term consequences. As a result, this study demonstrates how general inclusion of response dynamics and recognition of partial controllability of interventions can help inform management priorities during epidemics of livestock diseases.

Autocrine and paracrine interferon signalling as 'ring vaccination' and 'contact tracing' strategies to suppress virus infection in a host

The innate immune response, particularly the interferon response, represents a first line of defence against viral infections. The interferon molecules produced from infected cells act through autocrine and paracrine signalling to turn host cells into an antiviral state. Although the molecular mechanisms of IFN signalling have been well characterized, how the interferon response collectively contribute to the regulation of host cells to stop or suppress viral infection during early infection remain unclear. Here, we use mathematical models to delineate the roles of the autocrine and the paracrine signalling, and show that their impacts on viral spread are dependent on how infection proceeds. In particular, we found that when infection is well-mixed, the paracrine signalling is not as effective; by contrast, when infection spreads in a spatial manner, a likely scenario during initial infection in tissue, the paracrine signalling can impede the spread of infection by decreasing the number of susceptible cells close to the site of infection. Furthermore, we argue that the interferon response can be seen as a parallel to population-level epidemic prevention strategies such as ‘contact tracing’ or ‘ring vaccination’. Thus, our results here may have implications for the outbreak control at the population scale more broadly.

Modelling the domestic poultry population in the United States: A novel approach leveraging remote sensing and synthetic data methods

Comprehensive and spatially accurate poultry population demographic data do not currently exist in the United States; however, these data are critically needed to adequately prepare for, and efficiently respond to and manage disease outbreaks. In response to absence of these data, this study developed a national-level poultry population dataset by using a novel combination of remote sensing and probabilistic modelling methodologies. The Farm Location and Agricultural Production Simulator (FLAPS) (Burdett et al., 2015) was used to provide baseline national-scale data depicting the simulated locations and populations of individual poultry operations. Remote sensing methods (identification using aerial imagery) were used to identify actual locations of buildings having the characteristic size and shape of commercial poultry barns. This approach was applied to 594 U.S. counties with > 100,000 birds in 34 states based on the 2012 U.S. Department of Agriculture (USDA), National Agricultural Statistics Service (NASS), Census of Agriculture (CoA). The two methods were integrated in a hybrid approach to develop an automated machine learning process to locate commercial poultry operations and predict the number and type of poultry for each operation across the coterminous United States. Validation illustrated that the hybrid model had higher locational accuracy and more realistic distribution and density patterns when compared to purely simulated data. The resulting national poultry population dataset has significant potential for application in animal disease spread modelling, surveillance, emergency planning and response, economics, and other fields, providing a versatile asset for further agricultural research.

Challenges to the Application of Spatially Explicit Stochastic Simulation Models for Foot-and-Mouth Disease Control in Endemic Settings: A Systematic Review

Simulation modeling has become common for estimating the spread of highly contagious animal diseases. Several models have been developed to mimic the spread of foot-and-mouth disease (FMD) in specific regions or countries, conduct risk assessment, analyze outbreaks using historical data or hypothetical scenarios, assist in policy decisions during epidemics, formulate preparedness plans, and evaluate economic impacts. Majority of the available FMD simulation models were designed for and applied in disease-free countries, while there has been limited use of such models in FMD endemic countries. This paper's objective was to report the findings from a study conducted to review the existing published original research literature on spatially explicit stochastic simulation (SESS) models of FMD spread, focusing on assessing these models for their potential use in endemic settings. The goal was to identify the specific components of endemic FMD needed to adapt these SESS models for their potential application in FMD endemic settings. This systematic review followed the PRISMA guidelines, and three databases were searched, which resulted in 1176 citations. Eighty citations finally met the inclusion criteria and were included in the qualitative synthesis, identifying nine unique SESS models. These SESS models were assessed for their potential application in endemic settings. The assessed SESS models can be adapted for use in FMD endemic countries by modifying the underlying code to include multiple cocirculating serotypes, routine prophylactic vaccination (RPV), and livestock population dynamics to more realistically mimic the endemic characteristics of FMD. The application of SESS models in endemic settings will help evaluate strategies for FMD control, which will improve livestock health, provide economic gains for producers, help alleviate poverty and hunger, and will complement efforts to achieve the Sustainable Development Goals.

Poultry farm distribution models developed along a gradient of intensification

Efficient planning of measures limiting epidemic spread requires information on farm locations and sizes (number of animals per farm). However, such data are rarely available. The intensification process which is operating in most low- and middle-income countries (LMICs), comes together with a spatial clustering of farms, a characteristic epidemiological models are sensitive to. We developed farm distribution models predicting both the location and the number of animals per farm, while accounting for the spatial clustering of farms in data-poor countries, using poultry production as an example. We selected four countries, Nigeria, Thailand, Argentina and Belgium, along a gradient of intensification expressed by the per capita Gross Domestic Product (GDP). First, we investigated the distribution of chicken farms along the spectrum of intensification. Second, we built farm distribution models (FDM) based on censuses of commercial farms of each of the four countries, using point pattern and random forest models. As an external validation, we predicted farm locations and sizes in Bangladesh. The number of chicken per farm increased gradually in line with the gradient of GDP per capita in the following order: Nigeria, Thailand, Argentina and Belgium. Interestingly, we did not find such a gradient for farm clustering. Our modelling procedure could only partly reproduce the observed datasets in each of the four sample countries in internal validation. However, in the external validation, the clustering of farms could not be reproduced and the spatial predictors poorly explained the number and location of farms and farm sizes in Bangladesh. Further improvements of the methodology should explore other covariates of the intensity of farms and farm sizes, as well as improvements of the methodology. Structural transformation, economic development and environmental conditions are essential characteristics to consider for an extrapolation of our FDM procedure, as generalisation appeared challenging. We believe the FDM procedure could ultimately be used as a predictive tool in data-poor countries.

Challenges and opportunities for using national animal datasets to support foot-and-mouth disease control

National level databases of animal numbers, locations and movements provide the essential foundations for disease preparedness, outbreak investigations and control activities. These activities are particularly important for managing and mitigating the risks of high-impact transboundary animal disease outbreaks such as foot-and-mouth disease (FMD), which can significantly affect international trade access and domestic food security. In countries where livestock production systems are heavily subsidized by the government, producers are often required to provide detailed animal movement and demographic data as a condition of business. In the remaining countries, it can be difficult to maintain these types of databases and impossible to estimate the extent of missing or inaccurate information due to the absence of gold standard datasets for comparison. Consequently, competent authorities are often required to make decisions about disease preparedness and control based on available data, which may result in suboptimal outcomes for their livestock industries. It is important to understand the limitations of poor data quality as well as the range of methods that have been developed to compensate in both disease-free and endemic situations. Using FMD as a case example, this review first discusses the different activities that competent authorities use farm-level animal population data for to support (1) preparedness activities in disease-free countries, (2) response activities during an acute outbreak in a disease-free country, and (3) eradication and control activities in an endemic country. We then discuss (4) data requirements needed to support epidemiological investigations, surveillance, and disease spread modelling both in disease-free and endemic countries.

FMD-VS: A virtual sensor to index FMD virus scattering

Foot-and-mouth disease (FMD) models—analytical models for tracking and analyzing FMD outbreaks—are known as dominant tools for examining the spread of the disease under various conditions and assessing the effectiveness of countermeasures. There has been some remarkable progress in modeling research since the UK epidemic in 2001. Several modeling methods have been introduced, developed, and are still growing. However, in 2010 when a FMD outbreak occurred in the Miyazaki prefecture, a crucial problem reported: Once a regional FMD outbreak occurs, municipal officials in the region must make various day-to-day decisions throughout this period of vulnerability. The deliverables of FMD modeling research in its current state appear insufficient to support the daily judgments required in such cases. FMD model can be an efficient support tool for prevention decisions. It requires being conversant with modeling and its preconditions. Therefore, most municipal officials with no knowledge or experience found full use of the model difficult. Given this limitation, the authors consider methods and systems to support users of FMD models who must make real-time epidemic-related judgments in the infected areas. We propose a virtual sensor, designated “FMD-VS,” to index FMD virus scattering in conditions where there is once a notion of FMD; and (2) shows how we apply the developed FMD-VS technique during an outbreak. In (1), we show our approach to constructing FMD-VS based on the existing FMD model and offer an analysis and evaluation method to assess its performance. We again present the results produced when the technique applied to 2010 infection data from the Miyazaki Prefecture. For (2), we outline the concept of a method that supports the prevention judgment of municipal officials and show how to use FMD-VS.

A systemic approach to assess the potential and risks of wildlife culling for infectious disease control

The maintenance of infectious diseases requires a sufficient number of susceptible hosts. Host culling is a potential control strategy for animal diseases. However, the reduction in biodiversity and increasing public concerns regarding the involved ethical issues have progressively challenged the use of wildlife culling. Here, we assess the potential of wildlife culling as an epidemiologically sound management tool, by examining the host ecology, pathogen characteristics, eco-sociological contexts, and field work constraints. We also discuss alternative solutions and make recommendations for the appropriate implementation of culling for disease control.

Trade-off between local transmission and long-range dispersal drives infectious disease outbreak size in spatially structured populations

Transmission of infectious diseases between immobile hosts (e.g., plants, farms) is strongly dependent on the spatial distribution of hosts and the distance-dependent probability of transmission. As the interplay between these factors is poorly understood, we use spatial process and transmission modelling to investigate how epidemic size is shaped by host clustering and spatial range of transmission. We find that for a given degree of clustering and individual-level infectivity, the probability that an epidemic occurs after an introduction is generally higher if transmission is predominantly local. However, local transmission also impedes transfer of the infection to new clusters. A consequence is that the total number of infections is maximal if the range of transmission is intermediate. In highly clustered populations, the infection dynamics is strongly determined by the probability of transmission between clusters of hosts, whereby local clusters act as multiplier of infection. We show that in such populations, a metapopulation model sometimes provides a good approximation of the total epidemic size, using probabilities of local extinction, the final size of infections in local clusters, and probabilities of cluster-to-cluster transmission. As a real-world example we analyse the case of avian influenza transmission between poultry farms in the Netherlands.

Transmission of infectious diseases between immobile hosts depends on the transmission characteristics of the infection and on the spatial distribution of hosts. Examples include infectious diseases of plants that are spread by wind or via vectors (e.g., Asiatic citrus canker spread between citrus trees), diseases that are transmitted between local host populations (e.g., sylvatic plague transmitted between rodents living in burrows), diseases of production animals that are spread between farms (e.g., avian influenza in poultry transmitted from farm to farm). We use spatial transmission modelling to investigate how the total number of infections over the course of an epidemic is determined by host clustering and spatial range of transmission. We find that for a given degree of clustering and infectivity of hosts, the number of infections is maximal if the spatial range of transmission is intermediate. In highly clustered populations we show that epidemic size can be approximated by a metapopulation model, illustrating that in such populations the transmission dynamics is dominated by transmission between clusters of hosts.

Preface to theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'

This preface forms part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R₀) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley’s K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R₀ was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R₀ and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches.

When modeling the spread of infectious livestock diseases such as foot-and-mouth disease (FMD), the distance between premises is an important aspect. In the U.S., locations of premises are not available, forcing modelers to make assumptions about their coordinates. Such assumptions can be more or less crude and will impact the conclusions drawn from the model. To investigate the impact of such assumptions, we modeled outbreaks of FMD within the cattle population of the U.S. under two assumptions about premises locations. Their position was either randomly distributed within counties or informed by a state-of-the-art method developed specifically to simulate realistic locations of agricultural operations. We found that the higher degree of spatial clustering of premises associated with more realistic assumptions about locations leads to a substantially higher risk of outbreaks. Our results also show that the amount with which the risk is under-estimated by randomizing locations is unevenly distributed across the landscape. Together, these findings show a clear support for using informed methods to determine the spatial locations of premises and highlight the importance of spatial clustering when modeling FMD-like diseases.

Network analyses to quantify effects of host movement in multilevel disease transmission models using foot and mouth disease in Cameroon as a case study

The dynamics of infectious diseases are greatly influenced by the movement of both susceptible and infected hosts. To accurately represent disease dynamics among a mobile host population, detailed movement models have been coupled with disease transmission models. However, a number of different host movement models have been proposed, each with their own set of assumptions and results that differ from the other models. Here, we compare two movement models coupled to the same disease transmission model using network analyses. This application of network analysis allows us to evaluate the fit and accuracy of the movement model in a multilevel modeling framework with more detail than established statistical modeling fitting methods. We used data that detailed mobile pastoralists’ movements as input for 100 stochastic simulations of a Spatio-Temporal Movement (STM) model and 100 stochastic simulations of an Individual Movement Model (IMM). Both models represent dynamic movement and subsequent contacts. We generated networks in which nodes represent camps and edges represent the distance between camps. We simulated pathogen transmission over these networks and tested five network metrics–strength, betweenness centrality, three-step reach, density, and transitivity–to determine which could predict disease simulation outcomes and thereby be used to correlate model simulation results with disease transmission simulations. We found that strength, network density, and three-step reach of movement model results correlated with the final epidemic size of outbreak simulations. Betweenness centrality only weakly correlated for the IMM model. Transitivity only weakly correlated for the STM model and time-varying IMM model metrics. We conclude that movement models coupled with disease transmission models can affect disease transmission results and should be carefully considered and vetted when modeling pathogen spread in mobile host populations. Strength, network density, and three-step reach can be used to evaluate movement models before disease simulations to predict final outbreak sizes. These findings can contribute to the analysis of multilevel models across systems.

Epidemics of infectious disease vary geographically and vary through time. A large part of this variation is caused by movement of individuals who are susceptible to the disease or infected with the disease. To study how movement affects epidemics, researchers often combine movement models with transmission models. However, multiple movement models have been proposed, and their effect on infectious disease model output is not well understood. Here, we combine two different movement models that we developed to represent mobile pastoralists in the Far North Region, Cameroon, with the same disease transmission model. We use network metrics to test how different movement models can affect the output of the disease transmission model. We found that three metrics could be applied to movement model output in order to predict epidemic model output. We conclude that movement models coupled with disease transmission models can affect disease transmission results and should be carefully considered and vetted when modeling epidemics.

Context matters: using reinforcement learning to develop human-readable, state-dependent outbreak response policies

The number of all possible epidemics of a given infectious disease that could occur on a given landscape is large for systems of real-world complexity. Furthermore, there is no guarantee that the control actions that are optimal, on average, over all possible epidemics are also best for each possible epidemic. Reinforcement learning (RL) and Monte Carlo control have been used to develop machine-readable context-dependent solutions for complex problems with many possible realizations ranging from video-games to the game of Go. RL could be a valuable tool to generate context-dependent policies for outbreak response, though translating the resulting policies into simple rules that can be read and interpreted by human decision-makers remains a challenge. Here we illustrate the application of RL to the development of context-dependent outbreak response policies to minimize outbreaks of foot-and-mouth disease. We show that control based on the resulting context-dependent policies, which adapt interventions to the specific outbreak, result in smaller outbreaks than static policies. We further illustrate two approaches for translating the complex machine-readable policies into simple heuristics that can be evaluated by human decision-makers. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Framework for Estimating Indirect Costs in Animal Health Using Time Series Analysis

Traditionally, cost-benefit analyses (CBAs) focus on the direct costs of animal disease, including animal mortality, morbidity, and associated response costs. However, such approaches often fail to capture the wider, dynamic market impacts that could arise. The duration of these market dislocations could last well after an initial disease outbreak. More generally, current approaches also muddle definitions of indirect costs, confusing debate on the scope of the totalities of disease-induced economic impacts. The aim of this work was to clarify definitions of indirect costs in the context of animal diseases and to apply this definition to a time series methodological framework to estimate the indirect costs of animal disease control strategies, using a foot and mouth disease (FMD) outbreak in Scotland as a case study. Time series analysis is an econometric method for analyzing statistical relationships between data series over time, thus allowing insights into how market dynamics may change following a disease outbreak. First an epidemiological model simulated FMD disease dynamics based on alternative control strategies. Output from the epidemiological model was used to quantify direct costs and applied in a multivariate vector error correction model to quantify the indirect costs of alternative vaccine stock strategies as a result of FMD. Indirect costs were defined as the economic losses incurred in markets after disease freedom is declared. As such, our definition of indirect costs captures the knock-on price and quantity effects in six agricultural markets after a disease outbreak. Our results suggest that controlling a FMD epidemic with vaccination is less costly in direct and indirect costs relative to a no vaccination (i.e., "cull only") strategy, when considering large FMD outbreaks in Scotland. Our research clarifies and provides a framework for estimating indirect costs, which is applicable to both exotic and endemic diseases. Standard accounting CBAs only capture activities in isolation, ignore linkages across sectors, and do not consider price effects. However, our framework not only delineates when indirect costs start, but also captures the wider knock-on price effects between sectors, which are often omitted from CBAs but are necessary to support decision-making in animal disease prevention and control strategies.

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.

Biological control of a predator–prey system through provision of an infected predator

Epidemic transmission has a substantial effect on the dynamics and stability of the predator–prey system, in which the transmission rate plays an important role. The probabilistic cellular automaton (PCA) approach is used to investigate the spatiotemporal dynamics of a predator–prey system with the infected predator. Remarkably, it is impossible to achieve a coexistence state of prey, susceptible predators, and infected predators in a spatial population. This is different from the analysis from a non-spatial population with the mean-field approximation, where Hopf bifurcation arises and the interior equilibrium becomes unstable, and a periodic solution appears with the increasing infection rate. The results show that the introduction of the infected predator with a high transmission rate is beneficial for the persistence of the prey population in space. However, a low transmission rate will promote the coexistence state of the prey and the susceptible predator populations. In summary, it is possible to develop management strategies to manipulate the transmission rate of the infected predator for the benefit of biological control.

Disease spreading in complex networks: A numerical study with Principal Component Analysis

Disease spreading models need a population model to organize how individuals are distributed over space and how they are connected. Usually, disease agent (bacteria, virus) passes between individuals through these connections and an epidemic outbreak may occur. Here, complex networks models, like Erdös-Rényi, Small-World, Scale-Free and Barábasi-Albert will be used for modeling a population, since they are used for social networks; and the disease will be modeled by a SIR (Susceptible-Infected-Recovered) model. The objective of this work is, regardless of the network/population model, analyze which topological parameters are more relevant for a disease success or failure. Therefore, the SIR model is simulated in a wide range of each network model and a first analysis is done. By using data from all simulations, an investigation with Principal Component Analysis (PCA) is done in order to find the most relevant topological and disease parameters.

Assessing the Economic Impact of Vaccine Availability When Controlling Foot and Mouth Disease Outbreaks

Predictive models have been used extensively to assess the likely effectiveness of vaccination policies as part of control measures in the event of a foot and mouth disease (FMD) outbreak. However, the availability of vaccine stocks and the impact of vaccine availability on disease control strategies represent a key uncertainty when assessing potential control strategies. Using an epidemiological, spatially explicit, simulation model in combination with a direct cost calculator, we assessed how vaccine availability constraints may affect the economic benefit of a “vaccination-to-live” strategy during a FMD outbreak in Scotland, when implemented alongside culling of infected premises and dangerous contacts. We investigated the impact of vaccine stock size and restocking delays on epidemiological and economic outcomes. We also assessed delays in the initial decision to vaccinate, maximum daily vaccination capacity, and vaccine efficacy. For scenarios with conditions conducive to large outbreaks, all vaccination strategies perform better than the strategy where only culling is implemented. A stock of 200,000 doses, enough to vaccinate 12% of the Scottish cattle population, would be sufficient to maximize the relative benefits of vaccination, both epidemiologically and economically. However, this generates a wider variation in economic cost than if vaccination is not implemented, making outcomes harder to predict. The probability of direct costs exceeding £500 million is reduced when vaccination is used and is steadily reduced further as the size of initial vaccine stock increases. If only a suboptimal quantity of vaccine doses is initially available (100,000 doses), restocking delays of more than 2 weeks rapidly increase the cost of controlling outbreaks. Impacts of low vaccine availability or restocking delays are particularly aggravated by delays in the initial decision to vaccinate, or low vaccine efficacy. Our findings confirm that implementing an emergency vaccination-to-live strategy in addition to the conventional stamping out strategy is economically beneficial in scenarios with conditions conducive to large FMD outbreaks in Scotland. However, the size of the initial vaccine stock available at the start of the outbreak and the interplay with other factors, such as vaccine efficacy and delays in restocking or implementing vaccination, should be considered in making decisions about optimal control strategies for FMD outbreaks.

Forecasting Influenza Outbreaks in Boroughs and Neighborhoods of New York City

The ideal spatial scale, or granularity, at which infectious disease incidence should be monitored and forecast has been little explored. By identifying the optimal granularity for a given disease and host population, and matching surveillance and prediction efforts to this scale, response to emergent and recurrent outbreaks can be improved. Here we explore how granularity and representation of spatial structure affect influenza forecast accuracy within New York City. We develop network models at the borough and neighborhood levels, and use them in conjunction with surveillance data and a data assimilation method to forecast influenza activity. These forecasts are compared to an alternate system that predicts influenza for each borough or neighborhood in isolation. At the borough scale, influenza epidemics are highly synchronous despite substantial differences in intensity, and inclusion of network connectivity among boroughs generally improves forecast accuracy. At the neighborhood scale, we observe much greater spatial heterogeneity among influenza outbreaks including substantial differences in local outbreak timing and structure; however, inclusion of the network model structure generally degrades forecast accuracy. One notable exception is that local outbreak onset, particularly when signal is modest, is better predicted with the network model. These findings suggest that observation and forecast at sub-municipal scales within New York City provides richer, more discriminant information on influenza incidence, particularly at the neighborhood scale where greater heterogeneity exists, and that the spatial spread of influenza among localities can be forecast.

Influenza, or the flu, causes significant morbidity and mortality during both seasonal and pandemic outbreaks. Recently developed influenza forecast systems have the potential to aid public health planning for and mitigation of the burden of this disease. However, current forecasts are often generated at spatial scales (e.g. national level) that are coarser than the scales at which public health measures and interventions are implemented (e.g. community level). Here we build and test influenza forecast systems at county and community levels, which either include spatial connectivity among locations or are run in isolation. We test these four flu forecast systems (i.e. 2 models × 2 spatial scales) using data collected from 2008 to 2013, including the 2009 pandemic, for the five boroughs (corresponding to county level) and 42 neighborhoods (corresponding to community level) in New York City. We compare the performance of the four forecast systems in predicting the onset, duration, and intensity of flu outbreaks and found that the performance varied by spatial scale (borough vs. neighborhood), season (non-pandemic vs. pandemic) and metric (onset, duration, and intensity). In general, the inclusion of spatial network connectivity in the forecast model improves forecast accuracy at the borough scale but degrades accuracy at the neighborhood scale.

Preserving privacy whilst maintaining robust epidemiological predictions

Mathematical models are invaluable tools for quantifying potential epidemics and devising optimal control strategies in case of an outbreak. State-of-the-art models increasingly require detailed individual farm-based and sensitive data, which may not be available due to either lack of capacity for data collection or privacy concerns. However, in many situations, aggregated data are available for use. In this study, we systematically investigate the accuracy of predictions made by mathematical models initialised with varying data aggregations, using the UK 2001 Foot-and-Mouth Disease Epidemic as a case study. We consider the scenario when the only data available are aggregated into spatial grid cells, and develop a metapopulation model where individual farms in a single subpopulation are assumed to behave uniformly and transmit randomly. We also adapt this standard metapopulation model to capture heterogeneity in farm size and composition, using farm census data. Our results show that homogeneous models based on aggregated data overestimate final epidemic size but can perform well for predicting spatial spread. Recognising heterogeneity in farm sizes improves predictions of the final epidemic size, identifying risk areas, determining the likelihood of epidemic take-off and identifying the optimal control strategy. In conclusion, in cases where individual farm-based data are not available, models can still generate meaningful predictions, although care must be taken in their interpretation and use.

Spatial data aggregation for spatio-temporal individual-level models of infectious disease transmission

A class of complex statistical models, known as individual-level models, have been effectively used to model the spread of infectious diseases. These models are often fitted within a Bayesian Markov chain Monte Carlo framework, which can have a sig nificant computational expense due to the complex nature of the likelihood function associated with this class of models. Increases in population size or duration of the modeled epidemic can contribute to this computational burden. Here, we explore the effect of reducing this computational expense by aggregating the data into spatial clusters, and therefore reducing the overall population size. Individual-level models, reparameterized to account for this aggregation effect, may then be fitted to the spatially aggregated data. The ability of two reparameterized individual-level models, when fitted to this reduced data set, to identify a covariate effect is investigated through a simulation study.

The Impact of Population, Contact, and Spatial Heterogeneity on Epidemic Model Predictions

Our objective was to evaluate the effect that complexity in the form of different levels of spatial, population, and contact heterogeneity has in the predictions of a mechanistic epidemic model. A model that simulates the spatiotemporal spread of infectious diseases between animal populations was developed. Sixteen scenarios of foot-and-mouth disease infection in cattle were analyzed, involving combinations of the following factors: multiple production-types (PT) with heterogeneous contact and population structure versus single PT, random versus actual spatial distribution of population units, high versus low infectivity, and no vaccination versus preemptive vaccination. The epidemic size and duration was larger for scenarios with multiple PT versus single PT. Ignoring the actual unit locations did not affect the epidemic size in scenarios with multiple PT/high infectivity, but resulted in smaller epidemic sizes in scenarios using multiple PT/low infectivity. In conclusion, when modeling fast-spreading epidemics, knowing the actual locations of population units may not be as relevant as collecting information on population and contact heterogeneity. In contrast, both population and spatial heterogeneity might be important to model slower spreading epidemic diseases. Our findings can be used to inform data collection and modeling efforts to inform health policy and planning.

Epidemic predictions in an imperfect world: modelling disease spread with partial data

‘Big-data’ epidemic models are being increasingly used to influence government policy to help with control and eradication of infectious diseases. In the case of livestock, detailed movement records have been used to parametrize realistic transmission models. While livestock movement data are readily available in the UK and other countries in the EU, in many countries around the world, such detailed data are not available. By using a comprehensive database of the UK cattle trade network, we implement various sampling strategies to determine the quantity of network data required to give accurate epidemiological predictions. It is found that by targeting nodes with the highest number of movements, accurate predictions on the size and spatial spread of epidemics can be made. This work has implications for countries such as the USA, where access to data is limited, and developing countries that may lack the resources to collect a full dataset on livestock movements.

Simulating the Distribution of Individual Livestock Farms and Their Populations in the United States: An Example Using Domestic Swine (Sus scrofa domesticus) Farms

Livestock distribution in the United States (U.S.) can only be mapped at a county-level or worse resolution. We developed a spatial microsimulation model called the Farm Location and Agricultural Production Simulator (FLAPS) that simulated the distribution and populations of individual livestock farms throughout the conterminous U.S. Using domestic pigs (Sus scrofa domesticus) as an example species, we customized iterative proportional-fitting algorithms for the hierarchical structure of the U.S. Census of Agriculture and imputed unpublished state- or county-level livestock population totals that were redacted to ensure confidentiality. We used a weighted sampling design to collect data on the presence and absence of farms and used them to develop a national-scale distribution model that predicted the distribution of individual farms at a 100 m resolution. We implemented microsimulation algorithms that simulated the populations and locations of individual farms using output from our imputed Census of Agriculture dataset and distribution model. Approximately 19% of county-level pig population totals were unpublished in the 2012 Census of Agriculture and needed to be imputed. Using aerial photography, we confirmed the presence or absence of livestock farms at 10,238 locations and found livestock farms were correlated with open areas, cropland, and roads, and also areas with cooler temperatures and gentler topography. The distribution of swine farms was highly variable, but cross-validation of our distribution model produced an area under the receiver-operating characteristics curve value of 0.78, which indicated good predictive performance. Verification analyses showed FLAPS accurately imputed and simulated Census of Agriculture data based on absolute percent difference values of < 0.01% at the state-to-national scale, 3.26% for the county-to-state scale, and 0.03% for the individual farm-to-county scale. Our output data have many applications for risk management of agricultural systems including epidemiological studies, food safety, biosecurity issues, emergency-response planning, and conflicts between livestock and other natural resources.

Hybrid epidemics--a case study on computer worm conficker

Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading: local, neighbourhood, and global, to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conficker epidemic. The model is then used to explore the tradeoff between spreading modes in determining the worm's effectiveness. Our results show that the Conficker epidemic is an example of a critically hybrid epidemic, in which the different modes of spreading in isolation do not lead to successful epidemics. Such hybrid spreading strategies may be used beneficially to provide the most effective strategies for promulgating information across a large population. When used maliciously, however, they can present a dangerous challenge to current internet security protocols.

Optimizing hybrid spreading in metapopulations

Epidemic spreading phenomena are ubiquitous in nature and society. Examples include the spreading of diseases, information, and computer viruses. Epidemics can spread by local spreading, where infected nodes can only infect a limited set of direct target nodes and global spreading, where an infected node can infect every other node. In reality, many epidemics spread using a hybrid mixture of both types of spreading. In this study we develop a theoretical framework for studying hybrid epidemics, and examine the optimum balance between spreading mechanisms in terms of achieving the maximum outbreak size. We show the existence of critically hybrid epidemics where neither spreading mechanism alone can cause a noticeable spread but a combination of the two spreading mechanisms would produce an enormous outbreak. Our results provide new strategies for maximising beneficial epidemics and estimating the worst outcome of damaging hybrid epidemics.

An approach for de-identification of point locations of livestock premises for further use in disease spread modeling

We describe a method for de-identifying point location data used for disease spread modeling to allow data custodians to share data with modeling experts without disclosing individual farm identities. The approach is implemented in an open-source software program that is described and evaluated here. The program allows a data custodian to select a level of de-identification based on the K-anonymity statistic. The program converts a file of true farm locations and attributes into a file appropriate for use in disease spread modeling with the locations randomly modified to prevent re-identification based on location. Important epidemiological relationships such as clustering are preserved to as much as possible to allow modeling similar to those using true identifiable data. The software implementation was verified by visual inspection and basic descriptive spatial analysis of the output. Performance is sufficient to allow de-identification of even large data sets on desktop computers available to any data custodian.

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics.

Space-time cluster analysis of sea lice infestation (Caligus clemensi and Lepeophtheirus salmonis) on wild juvenile Pacific salmon in the Broughton Archipelago of Canada

Sea lice infestation levels on wild chum and pink salmon in the Broughton Archipelago region are known to vary spatially and temporally; however, the locations of areas associated with a high infestation level had not been investigated yet. In the present study, the multivariate spatial scan statistic based on a Poisson model was used to assess spatial clustering of elevated sea lice (Caligus clemensi and Lepeophtheirus salmonis) infestation levels on wild chum and pink salmon sampled between March and July of 2004 to 2012 in the Broughton Archipelago and Knight Inlet regions of British Columbia, Canada. Three covariates, seine type (beach and purse seining), fish size, and year effect, were used to provide adjustment within the analyses. The analyses were carried out across the five months/datasets and between two fish species to assess the consistency of the identified clusters. Sea lice stages were explored separately for the early life stages (non-motile) and the late life stages of sea lice (motile). Spatial patterns in fish migration were also explored using monthly plots showing the average number of each fish species captured per sampling site. The results revealed three clusters for non-motile C. clemensi, two clusters for non-motile L. salmonis, and one cluster for the motile stage in each of the sea lice species. In general, the location and timing of clusters detected for both fish species were similar. Early in the season, the clusters of elevated sea lice infestation levels on wild fish are detected in areas closer to the rivers, with decreasing relative risks as the season progresses. Clusters were detected further from the estuaries later in the season, accompanied by increasing relative risks. In addition, the plots for fish migration exhibit similar patterns for both fish species in that, as expected, the juveniles move from the rivers toward the open ocean as the season progresses The identification of space-time clustering of infestation on wild fish from this study can help in targeting investigations of factors associated with these infestations and thereby support the development of more effective sea lice control measures.

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.

Optimal sampling strategies for detecting zoonotic disease epidemics

The early detection of disease epidemics reduces the chance of successful introductions into new locales, minimizes the number of infections, and reduces the financial impact. We develop a framework to determine the optimal sampling strategy for disease detection in zoonotic host-vector epidemiological systems when a disease goes from below detectable levels to an epidemic. We find that if the time of disease introduction is known then the optimal sampling strategy can switch abruptly between sampling only from the vector population to sampling only from the host population. We also construct time-independent optimal sampling strategies when conducting periodic sampling that can involve sampling both the host and the vector populations simultaneously. Both time-dependent and -independent solutions can be useful for sampling design, depending on whether the time of introduction of the disease is known or not. We illustrate the approach with West Nile virus, a globally-spreading zoonotic arbovirus. Though our analytical results are based on a linearization of the dynamical systems, the sampling rules appear robust over a wide range of parameter space when compared to nonlinear simulation models. Our results suggest some simple rules that can be used by practitioners when developing surveillance programs. These rules require knowledge of transition rates between epidemiological compartments, which population was initially infected, and of the cost per sample for serological tests.

Outbreaks of zoonoses can have large costs to society through public health and agricultural impacts. Because many zoonoses co-occur in multiple animal populations simultaneously, detection of zoonotic outbreaks can be especially difficult. We evaluated how to design sampling strategies for the early detection of disease outbreaks of vector-borne diseases. We built a framework to integrate epidemiological dynamical models with a sampling process that accounts for budgetary constraints, such as those faced by many management agencies. We illustrate our approach using West Nile virus, a globally-spreading zoonotic arbovirus that has significantly affected North American bird populations. Our results suggest that simple formulas can often make robust predictions about the proper sampling procedure, though we also illustrate how computational methods can be used to extend our framework to more realistic modeling scenarios when these simple predictions break down.

Publishing data from electronic health records while preserving privacy: a survey of algorithms

The dissemination of Electronic Health Records (EHRs) can be highly beneficial for a range of medical studies, spanning from clinical trials to epidemic control studies, but it must be performed in a way that preserves patients' privacy. This is not straightforward, because the disseminated data need to be protected against several privacy threats, while remaining useful for subsequent analysis tasks. In this work, we present a survey of algorithms that have been proposed for publishing structured patient data, in a privacy-preserving way. We review more than 45 algorithms, derive insights on their operation, and highlight their advantages and disadvantages. We also provide a discussion of some promising directions for future research in this area.

Dynamics of infectious diseases

Modern infectious disease epidemiology has a strong history of using mathematics both for prediction and to gain a deeper understanding. However the study of infectious diseases is a highly interdisciplinary subject requiring insights from multiple disciplines, in particular a biological knowledge of the pathogen, a statistical description of the available data and a mathematical framework for prediction. Here we begin with the basic building blocks of infectious disease epidemiology--the SIS and SIR type models--before considering the progress that has been made over the recent decades and the challenges that lie ahead. Throughout we focus on the understanding that can be developed from relatively simple models, although accurate prediction will inevitably require far greater complexity beyond the scope of this review. In particular, we focus on three critical aspects of infectious disease models that we feel fundamentally shape their dynamics: heterogeneously structured populations, stochasticity and spatial structure. Throughout we relate the mathematical models and their results to a variety of real-world problems.

Coupling Vector-host Dynamics with Weather Geography and Mitigation Measures to Model Rift Valley Fever in Africa

We present and characterize a multi-host epidemic model of Rift Valley fever (RVF) virus in East Africa with geographic spread on a network, rule-based mitigation measures, and mosquito infection and population dynamics. Susceptible populations are depleted by disease and vaccination and are replenished with the birth of new animals. We observe that the severity of the epidemics is strongly correlated with the duration of the rainy season and that even severe epidemics are abruptly terminated when the rain stops. Because naturally acquired herd immunity is established, total mortality across 25 years is relatively insensitive to many mitigation approaches. Strong reductions in cattle mortality are expected, however, with sufficient reduction in population densities of either vectors or susceptible (ie. unvaccinated) hosts. A better understanding of RVF epidemiology would result from serology surveys to quantify the importance of herd immunity in epidemic control, and sequencing of virus from representative animals to quantify the realative importance of transportation and local reservoirs in nucleating yearly epidemics. Our results suggest that an effective multi-layered mitigation strategy would include vector control, movement control, and vaccination of young animals yearly, even in the absence of expected rainfall.