The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions

Inferring transmission routes for foot-and-mouth disease virus within a cattle herd using approximate Bayesian computation

To control an outbreak of an infectious disease it is essential to understand the different routes of transmission and how they contribute to the overall spread of the pathogen. With this information, policy makers can choose the most efficient methods of detection and control during an outbreak. Here we assess the contributions of direct contact and environmental contamination to the transmission of foot-and-mouth disease virus (FMDV) in a cattle herd using an individual-based model that includes both routes. Model parameters are inferred using approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC) applied to data from transmission experiments and the 2007 epidemic in Great Britain. This demonstrates that the parameters derived from transmission experiments are applicable to outbreaks in the field, at least for closely related strains. Under the assumptions made in the model we show that environmental transmission likely contributes a majority of infections within a herd during an outbreak, although there is a lot of variation between simulated outbreaks. The accumulation of environmental contamination not only causes infections within a farm, but also has the potential to spread between farms via fomites. We also demonstrate the importance and effectiveness of rapid detection of infected farms in reducing transmission between farms, whether via direct contact or the environment.

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.

The aquaculture disease network model (AquaNet-Mod): A simulation model to evaluate disease spread and controls for the salmonid industry in England and Wales

Infectious disease causes significant mortality in wild and farmed systems, threatening biodiversity, conservation and animal welfare, as well as food security. To mitigate impacts and inform policy, tools such as mathematical models and computer simulations are valuable for predicting the potential spread and impact of disease. This paper describes the development of the Aquaculture Disease Network Model, AquaNet-Mod, and demonstrates its application to evaluating disease epidemics and the efficacy of control, using a Viral Haemorrhagic Septicaemia (VHS) case study. AquaNet-Mod is a data-driven, stochastic, state-transition model. Disease spread can occur via four different mechanisms, i) live fish movement, ii) river based, iii) short distance mechanical and iv) distance independent mechanical. Sites transit between three disease states: susceptible, clinically infected and subclinically infected. Disease spread can be interrupted by the application of disease mitigation measures and controls such as contact tracing, culling, fallowing and surveillance. Results from a VHS case study highlight the potential for VHS to spread to 96% of sites over a 10 year time horizon if no disease controls are applied. Epidemiological impact is significantly reduced when live fish movement restrictions are placed on the most connected sites and further still, when disease controls, representative of current disease control policy in England and Wales, are applied. The importance of specific disease control measures, particularly contact tracing and disease detection rate, are also highlighted. The merit of this model for evaluation of disease spread and the efficacy of controls, in the context of policy, along with potential for further application and development of the model, for example to include economic parameters, is discussed.

Should infectious disease modelling research be subject to ethics review?

Should research projects involving epidemiological modelling be subject to ethical scrutiny and peer review prior to publication? Mathematical modelling had considerable impacts during the COVID-19 pandemic, leading to social distancing and lockdowns. Imperial College conducted research leading to the website publication of a paper, Report 9, on non-pharmaceutical interventions (NPIs) and COVID-19 mortality demand dated 16th March 2020, arguing for a Government policy of non-pharmaceutical interventions (e.g. lockdowns, social distancing, mask wearing, working from home, furlough, school closures, reduced family interaction etc.) to counter COVID 19. Enquiries and Freedom of Information requests to the institution indicate that there was no formal ethical committee review of this specific research, nor was there any peer review prior to their online publication of Report 9. This paper considers the duties placed upon researchers, institutions and research funders under the UK 'Concordat to Support Research Integrity' (CSRI), across various bioethical domains, and whether ethical committee scrutiny should be required for this research.

Epicasting: An Ensemble Wavelet Neural Network for forecasting epidemics

Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The lack of specific drugs and ready-to-use vaccines to prevent most of these epidemics worsens the situation. These force public health officials and policymakers to rely on early warning systems generated by accurate and reliable epidemic forecasters. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyze various epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it Ensemble Wavelet Neural Network (EWNet) model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with twenty-two statistical, machine learning, and deep learning models for fifteen real-world epidemic datasets with three test horizons using four key performance indicators. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods.

Modelling the spread and mitigation of an emerging vector-borne pathogen: Citrus greening in the U.S

Predictive models, based upon epidemiological principles and fitted to surveillance data, play an increasingly important role in shaping regulatory and operational policies for emerging outbreaks. Data for parameterising these strategically important models are often scarce when rapid actions are required to change the course of an epidemic invading a new region. We introduce and test a flexible epidemiological framework for landscape-scale disease management of an emerging vector-borne pathogen for use with endemic and invading vector populations. We use the framework to analyse and predict the spread of Huanglongbing disease or citrus greening in the U.S. We estimate epidemiological parameters using survey data from one region (Texas) and show how to transfer and test parameters to construct predictive spatio-temporal models for another region (California). The models are used to screen effective coordinated and reactive management strategies for different regions.

Coproduction and modeling spatial contact networks prevent bias about infectious hematopoietic necrosis virus transmission for Snake River Basin salmonids

Much remains unknown about variation in pathogen transmission across the geographic range of a free-ranging fish or animal species and about the influence of movement (associated with husbandry practices or animal behavior) on pathogen transmission. Salmonid hatcheries are an ideal system in which to study these processes. Salmonid hatcheries are managed for endangered species recovery, supplementation of threatened or at-risk fish stocks, support of fisheries, and ecosystem stability. Infectious hematopoietic necrosis virus (IHNV) is a rhabdovirus of significant concern to salmon aquaculture. Landscape IHNV transmission dynamics previously had been estimated only for salmonid hatcheries in the Lower Columbia River Basin (LCRB). The objectives of this study were to estimate IHNV transmission dynamics in a unique geographic region, the Snake River Basin (SRB), and to quantitatively estimate the effect of model coproduction on inference because previous assessments of coproduction have been qualitative. In contrast to the LCRB, the SRB has hatchery complexes consisting of a main hatchery and ≥1 satellite facility. Knowledge about hatchery complexes was held by a subset of project researchers but would not have been available to project modelers without coproduction. Project modelers generated and tested multiple versions of Bayesian susceptible-exposedinfected models to realistically represent the SRB and estimate the effect of coproduction. Models estimated the frequency of transmission routes, route-specific infection probabilities, and infection probabilities for combinations of salmonid hosts and IHNV lineages. Model results indicated that in the SRB, avoiding exposure to IHNV-positive adult salmonids is the most important action to prevent juvenile infections. Migrating adult salmonids exposed juvenile cohort-sites most frequently, and the infection probability was greatest following exposure to migrating adults. Without coproduction, the frequency of exposure by migrating adults would have been overestimated by 70 cohort-sites, and the infection probability following exposure to migrating adults would have been underestimated by∼0.09. The coproduced model had less uncertainty in the infection probability if no transmission route could be identified (Bayesian credible interval (BCI) width = 0.12) compared to the model without coproduction (BCI width = 0.34). Evidence for virus lineage MD specialization on steelhead and rainbow trout (both Oncorhynchus mykiss) was apparent without model coproduction. In the SRB, we found a greater probability of virus lineage UC infection in Chinook salmon (Oncorhynchus tshawytscha) compared to in O. mykiss, whereas in the LCRB, UC more clearly exhibited a generalist approach. Coproduction influenced estimates that depended on transmission routes, which operated differently at main hatcheries and satellite sites within hatchery complexes. Hatchery complexes are found outside of the SRB and are not specific to salmonid hatcheries alone. There is great potential for coproduction and modeling spatial contact networks to advance understanding about infectious disease transmission in complex production systems and surrounding free-ranging animal populations.

Optimizing testing strategies for early detection of disease outbreaks in animal trade networks via MCMC

The animal trades between farms and other livestock holdings form a complex livestock trade network. The movement of animals between trade actors plays an important role in the spread of infectious diseases among premises. Particularly, the outbreak of silent diseases that have no clinically obvious symptoms in the animal trade system should be diagnosed by taking special tests. In practice, the authorities regularly conduct examinations on a random number of farms to make sure that there was no outbreak in the system. However, these actions, which aim to discover and block a disease cascade, are yet far from the effective and optimum solution and often fail to prevent epidemics. A testing strategy is defined as making decisions about distributing the fixed testing budget N between farms/nodes in the network. In this paper, first, we apply different heuristics for selecting sentinel farms on real and synthetic pig-trade networks and evaluate them by simulating disease spreading via the SI epidemic model. Later, we propose a Markov chain Monte Carlo (MCMC) based testing strategy with the aim of early detection of outbreaks. The experimental results show that the proposed method can reasonably well decrease the size of the outbreak on both the realistic synthetic and real trade data. A targeted selection of an N/52 fraction of nodes in the real pig-trade network based on the MCMC or simulated annealing can improve the performance of a baseline strategy by 89%. The best heuristic-based testing strategy results in a 75% reduction in the average size of the outbreak compared to that of the baseline testing strategy.

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.

An exploration of within-herd dynamics of a transboundary livestock disease: A foot and mouth disease case study

Transboundary livestock diseases are a high priority for policy makers because of the serious economic burdens associated with infection. In order to make well informed preparedness and response plans, policy makers often utilize mathematical models to understand possible outcomes of different control strategies and outbreak scenarios. Many of these models focus on the transmission between herds and the overall trajectory of the outbreak. While the course of infection within herds has not been the focus of the majority of models, a thorough understanding of within-herd dynamics can provide valuable insight into a disease system by providing information on herd-level biological properties of the infection, which can be used to inform decision making in both endemic and outbreak settings and to inform larger between-herd models. In this study, we develop three stochastic simulation models to study within-herd foot and mouth disease dynamics and the implications of different empirical data-based assumptions about the timing of the onset of infectiousness and clinical signs. We also study the influence of herd size and the proportion of the herd that is initially infected on the outcome of the infection. We find that increasing herd size increases the duration of infectiousness and that the size of the herd plays a more significant role in determining this duration than the number of initially infected cattle in that herd. We also find that the assumptions made regarding the onset of infectiousness and clinical signs, which are based on contradictory empirical findings, can result in the predictions about when infection would be detectable differing by several days. Therefore, the disease progression used to characterize the course of infection in a single bovine host could have significant implications for determining when herds can be detected and subsequently controlled; the timing of which could influence the overall predicted trajectory of outbreaks.

Analysis of suspensions and recoveries of official foot and mouth disease free status of WOAH Members between 1996 and 2020

Foot and mouth disease was the first disease for which, in 1996, the World Organisation for Animal Health (WOAH; founded as OIE) established an official list of disease-free territories, which has helped to facilitate the trade of animals and animal products from those territories. Since that year, there have been a number of suspensions of FMD-free status which have impacted the livestock industry of the territories affected. The objective of this study is to identify factors associated with the time taken to recover FMD-free status after suspension. Historical applications submitted (between 1996 and the first semester of 2020) by WOAH Members for recognition and recovery of FMD-free status were used as the main source of data. Only FMD-free status suspensions caused by outbreaks were considered. Data on the Member's socio-economic characteristics, livestock production systems, FMD outbreak characteristics, and control strategies were targeted for the analysis. The period of time taken to recover FMD-free status was estimated using Kaplan-Meier survival curves. A Cox proportional hazard model was used to identify factors associated with the time taken to recover FMD-free status after suspension. A total of 163 territories were granted official FMD-free status during the study period. The study sample consisted of 45 FMD-free status suspensions. Africa and the Americas accounted for over 50% of FMD-free status suspensions, while over 70% of these occurred in formerly FMD-free territories where vaccination was not practiced. The study noted that implementing a stamping-out or vaccination and remove policy shortened the time to recover FMD-free status, compared with a vaccination and retain policy. Other variables associated with the outcome were the income level of the Member, Veterinary Service capacity, time taken to implement control measures, time taken until the disposal of the last FMD case, whether the territory bordered FMD-infected territories, and time elapsed since FMD freedom. This analysis will contribute toward the understanding of the main determinants affecting the time to recover the FMD free status of WOAH Members and policy processes for FMD control and elimination.

The Importance of Livestock Demography and Infrastructure in Driving Foot and Mouth Disease Dynamics

Transboundary animal diseases, such as foot and mouth disease (FMD) pose a significant and ongoing threat to global food security. Such diseases can produce large, spatially complex outbreaks. Mathematical models are often used to understand the spatio-temporal dynamics and create response plans for possible disease introductions. Model assumptions regarding transmission behavior of premises and movement patterns of livestock directly impact our understanding of the ecological drivers of outbreaks and how to best control them. Here, we investigate the impact that these assumptions have on model predictions of FMD outbreaks in the U.S. using models of livestock shipment networks and disease spread. We explore the impact of changing assumptions about premises transmission behavior, both by including within-herd dynamics, and by accounting for premises type and increasing the accuracy of shipment predictions. We find that the impact these assumptions have on outbreak predictions is less than the impact of the underlying livestock demography, but that they are important for investigating some response objectives, such as the impact on trade. These results suggest that demography is a key ecological driver of outbreaks and is critical for making robust predictions but that understanding management objectives is also important when making choices about model assumptions.

The African swine fever modelling challenge: Model comparison and lessons learnt

Robust epidemiological knowledge and predictive modelling tools are needed to address challenging objectives, such as: understanding epidemic drivers; forecasting epidemics; and prioritising control measures. Often, multiple modelling approaches can be used during an epidemic to support effective decision making in a timely manner. Modelling challenges contribute to understanding the pros and cons of different approaches and to fostering technical dialogue between modellers. In this paper, we present the results of the first modelling challenge in animal health - the ASF Challenge - which focused on a synthetic epidemic of African swine fever (ASF) on an island. The modelling approaches proposed by five independent international teams were compared. We assessed their ability to predict temporal and spatial epidemic expansion at the interface between domestic pigs and wild boar, and to prioritise a limited number of alternative interventions. We also compared their qualitative and quantitative spatio-temporal predictions over the first two one-month projection phases of the challenge. Top-performing models in predicting the ASF epidemic differed according to the challenge phase, host species, and in predicting spatial or temporal dynamics. Ensemble models built using all team-predictions outperformed any individual model in at least one phase. The ASF Challenge demonstrated that accounting for the interface between livestock and wildlife is key to increasing our effectiveness in controlling emerging animal diseases, and contributed to improving the readiness of the scientific community to face future ASF epidemics. Finally, we discuss the lessons learnt from model comparison to guide decision making.

Comparing the efficacy of control strategies for infectious disease outbreaks using field and simulation studies

Diseases characterized by long distance inoculum dispersal (LDD) are among the fastest spreading epidemics in both natural and managed landscapes. Management of such epidemics is extremely challenging because of asymptomatic infection extending at large spatial scales and frequent escape from the newly established disease sources. We compared the efficacy of area- and timing-based disease management strategies in artificially initiated field epidemics of wheat stripe rust and complemented with simulations from an updated version of the spatially explicit model EPIMUL, using model parameters relevant to field epidemics. The model was further used to expand the number of epidemic mitigations beyond that feasible to incorporate in the field. The field experiment was conducted for 2 years in two locations having different climatic conditions. Culling and protection treatments were applied at different times after epidemic initiation and to different spatial extents surrounding the outbreaks. In each experiment, treatments were replicated four times in plots 33.5 m long and 1.52 m wide with a 0.76 × 0.76 m inoculated focus centered within each plot. Disease gradients were assessed along the center lines of the plots at 1.52 m intervals both upwind and downwind from the focus. Both field and simulation results indicated that control measures applied over the entire population were highly effective in suppressing the epidemics by more than 99% but may not always be logistically and economically feasible at large spatial scales. Comparison between the variable sized treatment areas and application timings suggested that implementing contiguous premises (CP) cull at 1 day after first sporulation in the outbreak focus reduced rust by 52% and 60% in Corvallis and Madras, respectively. However, altering the cull size did not significantly affect the disease epidemic development, which suggested that early timing had a greater influence in suppressing the epidemics than did increased area of application. However, sufficiently large, treated areas may compensate for a delay in application timing to some extent. Results from these replicated treatments may help to devise appropriate management strategies for other LDD pathogens.

Phylodynamic analysis of the highly pathogenic avian influenza H5N8 epidemic in France, 2016-2017

In 2016-2017, France experienced a devastating epidemic of highly pathogenic avian influenza (HPAI) H5N8, with more than 400 outbreaks reported in poultry farms. We analyzed the spatiotemporal dynamics of the epidemic using a structured-coalescent-based phylodynamic approach that combined viral genomic data (n = 196; one viral genome per farm) and epidemiological data. In the process, we estimated viral migration rates between départements (French administrative regions) and the temporal dynamics of the effective viral population size (Ne) in each département. Viral migration rates quantify viral spread between départements and Ne is a population genetic measure of the epidemic size and, in turn, is indicative of the within-département transmission intensity. We extended the phylodynamic analysis with a generalized linear model to assess the impact of multiple factors-including large-scale preventive culling and live-duck movement bans-on viral migration rates and Ne. We showed that the large-scale culling of ducks that was initiated on 4 January 2017 significantly reduced the viral spread between départements. No relationship was found between the viral spread and duck movements between départements. The within-département transmission intensity was found to be weakly associated with the intensity of duck movements within départements. Together, these results indicated that the virus spread in short distances, either between adjacent départements or within départements. Results also suggested that the restrictions on duck transport within départements might not have stopped the viral spread completely. Overall, we demonstrated the usefulness of phylodynamics in characterizing the dynamics of a HPAI epidemic and assessing control measures. This method can be adapted to investigate other epidemics of fast-evolving livestock pathogens.

Time-Series Analysis for the Number of Foot and Mouth Disease Outbreak Episodes in Cattle Farms in Thailand Using Data from 2010-2020

Thailand is one of the countries where foot and mouth disease outbreaks have resulted in considerable economic losses. Forecasting is an important warning technique that can allow authorities to establish an FMD surveillance and control program. This study aimed to model and forecast the monthly number of FMD outbreak episodes (n-FMD episodes) in Thailand using the time-series methods, including seasonal autoregressive integrated moving average (SARIMA), error trend seasonality (ETS), neural network autoregression (NNAR), and Trigonometric Exponential smoothing state−space model with Box−Cox transformation, ARMA errors, Trend and Seasonal components (TBATS), and hybrid methods. These methods were applied to monthly n-FMD episodes (n = 1209) from January 2010 to December 2020. Results showed that the n-FMD episodes had a stable trend from 2010 to 2020, but they appeared to increase from 2014 to 2020. The outbreak episodes followed a seasonal pattern, with a predominant peak occurring from September to November annually. The single-technique methods yielded the best-fitting time-series models, including SARIMA(1,0,1)(0,1,1)12, NNAR(3,1,2)12,ETS(A,N,A), and TBATS(1,{0,0},0.8,{<12,5>}. Moreover, SARIMA-NNAR and NNAR-TBATS were the hybrid models that performed the best on the validation datasets. The models that incorporate seasonality and a non-linear trend performed better than others. The forecasts highlighted the rising trend of n-FMD episodes in Thailand, which shares borders with several FMD endemic countries in which cross-border trading of cattle is found common. Thus, control strategies and effective measures to prevent FMD outbreaks should be strengthened not only in Thailand but also in neighboring countries.

Dynamic survival analysis for non-Markovian epidemic models

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.

Dropping mortality by increasing connectivity in plant epidemics

Pathogen introduction in plant communities can cause serious impacts and biodiversity losses that may take a long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance because of its implications in conservation and potential economic losses. Understanding the mechanisms that hinder pathogen propagation is, therefore, crucial. Usual modelization approaches in epidemic spreading are based in compartmentalized models, without keeping track of pathogen concentrations during spreading. In this contribution we present and fully analyze a dynamical model for plant epidemic spreading based on pathogen abundances. The model, which is defined on top of network substrates, is amenable to a deep mathematical analysis in the absence of a limit in the amount of pathogen a plant can tolerate before dying. In the presence of such death threshold, we observe that the fraction of dead plants peaks at intermediate values of network connectivity, and mortality decreases for large average degrees. We discuss the implications of our results as mechanisms to halt infection propagation.

Forecasting for COVID-19 has failed

Epidemic forecasting has a dubious track-record, and its failures became more prominent with COVID-19. Poor data input, wrong modeling assumptions, high sensitivity of estimates, lack of incorporation of epidemiological features, poor past evidence on effects of available interventions, lack of transparency, errors, lack of determinacy, consideration of only one or a few dimensions of the problem at hand, lack of expertise in crucial disciplines, groupthink and bandwagon effects, and selective reporting are some of the causes of these failures. Nevertheless, epidemic forecasting is unlikely to be abandoned. Some (but not all) of these problems can be fixed. Careful modeling of predictive distributions rather than focusing on point estimates, considering multiple dimensions of impact, and continuously reappraising models based on their validated performance may help. If extreme values are considered, extremes should be considered for the consequences of multiple dimensions of impact so as to continuously calibrate predictive insights and decision-making. When major decisions (e.g. draconian lockdowns) are based on forecasts, the harms (in terms of health, economy, and society at large) and the asymmetry of risks need to be approached in a holistic fashion, considering the totality of the evidence.

Bayesian nonparametric inference for heterogeneously mixing infectious disease models

Mathematical models of infectious disease transmission continue to play a vital role in understanding, mitigating, and preventing outbreaks. The vast majority of epidemic models in the literature are parametric, meaning that they contain inherent assumptions about how transmission occurs in a population. However, such assumptions can be lacking in appropriate biological or epidemiological justification and in consequence lead to erroneous scientific conclusions and misleading predictions. We propose a flexible Bayesian nonparametric framework that avoids the need to make strict model assumptions about the infection process and enables a far more data-driven modeling approach for inferring the mechanisms governing transmission. We use our methods to enhance our understanding of the transmission mechanisms of the 2001 UK foot and mouth disease outbreak.

Infectious disease transmission models require assumptions about how the pathogen spreads between individuals. These assumptions may be somewhat arbitrary, particularly when it comes to describing how transmission varies between individuals of different types or in different locations, and may in turn lead to incorrect conclusions or policy decisions. We develop a general Bayesian nonparametric framework for transmission modeling that removes the need to make such specific assumptions with regard to the infection process. We use multioutput Gaussian process prior distributions to model different infection rates in populations containing multiple types of individuals. Further challenges arise because the transmission process itself is unobserved, and large outbreaks can be computationally demanding to analyze. We address these issues by data augmentation and a suitable efficient approximation method. Simulation studies using synthetic data demonstrate that our framework gives accurate results. We analyze an outbreak of foot and mouth disease in the United Kingdom, quantifying the spatial transmission mechanism between farms with different combinations of livestock.

Individual risk perception and empirical social structures shape the dynamics of infectious disease outbreaks

The dynamics of a spreading disease and individual behavioral changes are entangled processes that have to be addressed together in order to effectively manage an outbreak. Here, we relate individual risk perception to the adoption of a specific set of control measures, as obtained from an extensive large-scale survey performed via Facebook—involving more than 500,000 respondents from 64 countries—showing that there is a “one-to-one” relationship between perceived epidemic risk and compliance with a set of mitigation rules. We then develop a mathematical model for the spreading of a disease—sharing epidemiological features with COVID-19—that explicitly takes into account non-compliant individual behaviors and evaluates the impact of a population fraction of infectious risk-deniers on the epidemic dynamics. Our modeling study grounds on a wide set of structures, including both synthetic and more than 180 real-world contact patterns, to evaluate, in realistic scenarios, how network features typical of human interaction patterns impact the spread of a disease. In both synthetic and real contact patterns we find that epidemic spreading is hindered for decreasing population fractions of risk-denier individuals. From empirical contact patterns we demonstrate that connectivity heterogeneity and group structure significantly affect the peak of hospitalized population: higher modularity and heterogeneity of social contacts are linked to lower peaks at a fixed fraction of risk-denier individuals while, at the same time, such features increase the relative impact on hospitalizations with respect to the case where everyone correctly perceive the risks.

The spreading of a disease across a population is affected by the compliance with behavioral restrictions, enforced by governments to slow the diffusion of an epidemic. In this study, we use a large-scale survey to relate compliance with behavioral rules to individual level of disease risk perception. We asses that absence of risk awareness is associated with a set of harmful behaviors (namely, non-compliance with: social distancing, use of facial masks and adoption of any prevention measures) that can accelerate the diffusion of an epidemic. Through a mathematical model, we study how epidemic dynamics, and in particular hospitalization burden, is affected by the presence of different fractions of the total population who do not correctly perceive the disease risk and, accordingly, adopt harmful behaviors. Moreover, we study how different social contact structures among individuals modulate the effect on epidemic spreading of a fixed population fraction with null risk perception. Our findings highlight that a fixed percentage of people with null risk awareness has a lower impact on epidemic size in social structures characterized by communities and heterogeneity in contacts among individuals. The spreading of a disease across a population is affected by the compliance with behavioral restrictions, enforced by governments to slow the diffusion of an epidemic. In this study, we use a large-scale survey to relate compliance with behavioral rules to individual level of disease risk perception. We asses that absence of risk awareness is associated with a set of harmful behaviors (namely, non-compliance with: social distancing, use of facial masks and adoption of any prevention measures) that can accelerate the diffusion of an epidemic. Through a mathematical model, we study how epidemic dynamics, and in particular hospitalization burden, is affected by the presence of different fractions of the total population who do not correctly perceive the disease risk and, accordingly, adopt harmful behaviors. Moreover, we study how different social contact structures among individuals modulate the effect on epidemic spreading of a fixed population fraction with null risk perception. Our findings highlight that a fixed percentage of people with null risk awareness has a lower effectiveness on epidemic size in social structures characterized by communities and heterogeneity in contacts among individuals. However, in these same social structures, larger fractions of risk-denying population cause an enhanced effect on epidemic size.

A Temporal Network Model for Livestock Trade Systems

The movements of animals between farms and other livestock holdings for trading activities form a complex livestock trade network. These movements play an important role in the spread of infectious diseases among premises. For studying the disease spreading among animal holdings, it is of great importance to understand the structure and dynamics of the trade system. In this paper, we propose a temporal network model for animal trade systems. Furthermore, a novel measure of node centrality important for disease spreading is introduced. The experimental results show that the model can reasonably well describe these spreading-related properties of the network and it can generate crucial data for research in the field of the livestock trade system.

Unpacking the myth between increased government initiatives and reduced selling of dead live stocks in China: An approach towards exploring hidden danger of zoonotic diseases

Prohibiting the unsafe sale of livestock that have died in production and harmlessly disposing of them are key measures to control and prevent outbreaks of zoonotic diseases and exert a great significance for maintaining meat-derived food and public health safety. However, under the strict implementation of governmental initiatives, some farmers still choose to sell dead livestock unsafely in developing countries such as China, Brazil, Mexico, and Kenya, which have become an important hidden danger in preventing and controlling zoonotic diseases. Based on data from 496 pig farmers in Hebei, Henan, and Hubei, China, the Double Hurdle Model was employed to explore the impact of governmental initiatives on the willingness and proportion of dead pigs sold unsafely by farmers. Besides, based on the heterogeneity of organization participation and breeding scale, the impact of governmental initiatives on different scale farmers' unsafely selling behaviors is also discussed. The results showed that the harmless disposal subsidy significantly reduces farmers' willingness to unsafely sell dead pigs (SW, RC = −0.0666, and SE = 0.0261). Still, the impact on the proportion is weak (SP, RC = −0.0502, and SE = 0.0474). Though the effect of supervision punishment is greatly weakened (SW, RC =−0.0381, and SE = 0.0324; SP, RC = −0.0204 and SE = 0.0263), it can significantly enhance the effect of harmless disposal subsidy by creating a good law-abiding environment (SW, RC = −0.1370, and SE = 0.0374; SP, RC = −0.0820, and SE = 0.0431). Governmental initiatives have an undue impact on the unsafe sale of dead livestock by farmers participating in cooperatives. The effects of these measures on different scale farmers' unsafe sale of dead pigs are highly heterogeneous. In addition, the study also found that food and public health safety risk perceptions are important endogenous drivers for curbing farmers selling dead pigs. This research can also provide important inspiration for other countries. The government should raise farmers' risk perception level of food and public safety, optimize governmental initiatives, play the key role of cooperative organization, increase the proportion of dead pigs harmlessly disposed of, and finally eliminate new hidden dangers in the prevention and control of zoonotic diseases.

Modelling bluetongue risk in Kazakhstan

Background

Bluetongue is a serious disease of ruminants caused by the bluetongue virus (BTV). BTV is transmitted by biting midges (Culicoides spp.). Serological evidence from livestock and the presence of at least one competent vector species of Culicoides suggests that transmission of BTV is possible and may have occurred in Kazakhstan.

Methods

We estimated the risk of transmission using a mathematical model of the reproduction number R₀ for bluetongue. This model depends on livestock density and climatic factors which affect vector density. Data on climate and livestock numbers from the 2466 local communities were used. This, together with previously published model parameters, was used to estimate R₀ for each month of the year. We plotted the results on isopleth maps of Kazakhstan using interpolation to smooth the irregular data. We also mapped the estimated proportion of the population requiring vaccination to prevent outbreaks of bluetongue.

Results

The results suggest that transmission of bluetongue in Kazakhstan is not possible in the winter from October to March. Assuming there are vector-competent species of Culicoides endemic in Kazakhstan, then low levels of risk first appear in the south of Kazakhstan in April before spreading north and intensifying, reaching maximum levels in northern Kazakhstan in July. The risk declined in September and had disappeared by October.

Conclusion

These results should aid in surveillance efforts for the detection and control of bluetongue in Kazakhstan by indicating where and when outbreaks of bluetongue are most likely to occur. The results also indicate where vaccination efforts should be focussed to prevent outbreaks of disease.

Graphical abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s13071-021-04945-6.

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

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

Spatial model of foot-and-mouth disease outbreak in an endemic area of Thailand

Foot-and-mouth disease (FDM) is a disease of cloven-hoofed animals with high costs in animal welfare and animal production. Up to now, transmission between farms in FMD-endemic areas has been given little attention. Between farm transmission can be quantified by distance independent transmission parameters and a spatial transmission kernel indicating the rate of transmission of an infected farm to susceptible farms depending on the distance. The spatial transmission kernel and distance-independent transmission parameters were estimated from data of an FMD outbreak in Lamphaya Klang subdistrict in Thailand between 2016 and 2017. The spatial between-farm transmission rate in Lamphaya Klang subdistrict was higher compared with the spatial between-farm transmission rate from FMDV in epidemic areas. The result can be explained by the larger size of the within-farm outbreak in the endemic area due to no culling. The inclusion of distance-independent transmission parameters improved the model fit, which suggests the presence of transmission sources from outside the area and spread within the area independent of the distance between farms. The remaining distance-dependent transmission was mainly local and could be due to over-the-fence transmission or other forms of contact between nearby farms. Farm size on the kernel positively affects the transmission rate, by increasing both infectivity and susceptibility with increasing farm size. The results showed that both distance-dependent transmission and distance-independent transmission were contributed to FMDV transmission in Lamphaya Klang outbreak. These transmission parameters help to gain knowledge about FMD transmission dynamic in the endemic area.

The optimal controlling strategy on a dispersing population in a two-patch system: Experimental and theoretical perspectives

Invasive species, disease vectors, and pathogens are significant threats to biodiversity, ecosystem function and services, and human health. Understanding the optimal management strategy, which maximizes the effectiveness is crucial. Despite an abundance of theoretical work has conducted on projecting the optimal allocation strategy, almost no empirical work has been performed to validate the theory. We first used a consumer-resource model to simulate a series of allocation fractions of controlling treatment to determine the optimal controlling strategy. Further, we conducted rigorous laboratory experiments using spatially diffusing laboratory populations of yeast to verify our mathematical results. We found consistent results that: (1) When population growth is limited by the local resource, the controlling priority should be given to the areas with higher concentration of resource; (2) When population growth is not limited by the resource concentration, the best strategy is to allocate equal amount of controlling efforts among the regions; (3) With restricted budget, it is more efficient to prioritize the controlling effects to the areas with high population abundance, otherwise, it is better to control equally among the regions. The new theory, which was tested by laboratory experiments, will reveal new opportunities for future field interventions, thereby informing subsequent biological decision-making.

Development of a transboundary model of livestock disease in Europe

Epidemiological models of notifiable livestock disease are typically framed at a national level and targeted for specific diseases. There are inherent difficulties in extending models beyond national borders as details of the livestock population, production systems and marketing systems of neighbouring countries are not always readily available. It can also be a challenge to capture heterogeneities in production systems, control policies, and response resourcing across multiple countries, in a single transboundary model.

In this paper, we describe EuFMDiS, a continental‐scale modelling framework for transboundary animal disease, specifically designed to support emergency animal disease planning in Europe. EuFMDiS simulates the spread of livestock disease within and between countries and allows control policies to be enacted and resourced on a per‐country basis. It provides a sophisticated decision support tool that can be used to look at the risk of disease introduction, establishment and spread; control approaches in terms of effectiveness and costs; resource management; and post‐outbreak management issues.

Despite vaccination, China needs non-pharmaceutical interventions to prevent widespread outbreaks of COVID-19 in 2021

COVID-19 vaccination is being conducted in over 200 countries and regions to control SARS-CoV-2 transmission and return to a pre-pandemic lifestyle. However, understanding when non-pharmaceutical interventions (NPIs) can be lifted as immunity builds up remains a key question for policy makers. To address this, we built a data-driven model of SARS-CoV-2 transmission for China. We estimated that, to prevent the escalation of local outbreaks to widespread epidemics, stringent NPIs need to remain in place at least one year after the start of vaccination. Should NPIs alone be capable of keeping the reproduction number (R_t) around 1.3, the synergetic effect of NPIs and vaccination could reduce the COVID-19 burden by up to 99% and bring R_t below the epidemic threshold in about 9 months. Maintaining strict NPIs throughout 2021 is of paramount importance to reduce COVID-19 burden while vaccines are distributed to the population, especially in large populations with little natural immunity.

Using data-driven epidemiological modelling, Yu et al. estimate that, even with increasing vaccine availability, China will have to maintain stringent non-pharmaceutical interventions for at least a year to prevent new widespread outbreaks of COVID-19.

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.

Transient disease dynamics across ecological scales

Analyses of transient dynamics are critical to understanding infectious disease transmission and persistence. Identifying and predicting transients across scales, from within-host to community-level patterns, plays an important role in combating ongoing epidemics and mitigating the risk of future outbreaks. Moreover, greater emphases on non-asymptotic processes will enable timely evaluations of wildlife and human diseases and lead to improved surveillance efforts, preventive responses, and intervention strategies. Here, we explore the contributions of transient analyses in recent models spanning the fields of epidemiology, movement ecology, and parasitology. In addition to their roles in predicting epidemic patterns and endemic outbreaks, we explore transients in the contexts of pathogen transmission, resistance, and avoidance at various scales of the ecological hierarchy. Examples illustrate how (i) transient movement dynamics at the individual host level can modify opportunities for transmission events over time; (ii) within-host energetic processes often lead to transient dynamics in immunity, pathogen load, and transmission potential; (iii) transient connectivity between discrete populations in response to environmental factors and outbreak dynamics can affect disease spread across spatial networks; and (iv) increasing species richness in a community can provide transient protection to individuals against infection. Ultimately, we suggest that transient analyses offer deeper insights and raise new, interdisciplinary questions for disease research, consequently broadening the applications of dynamical models for outbreak preparedness and management.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12080-021-00514-w.

What can phylodynamics bring to animal health research?

Infectious diseases are a major burden to global economies, and public and animal health. To date, quantifying the spread of infectious diseases to inform policy making has traditionally relied on epidemiological data collected during epidemics. However, interest has grown in recent phylodynamic techniques to infer pathogen transmission dynamics from genetic data. Here, we provide examples of where this new discipline has enhanced disease management in public health and illustrate how it could be further applied in animal health. In particular, we describe how phylodynamics can address fundamental epidemiological questions, such as inferring key transmission parameters in animal populations and quantifying spillover events at the wildlife-livestock interface, and generate important insights for the design of more effective control strategies.

Temporal-spatial analysis of an age-space structured foot-and-mouth disease model with Dirichlet boundary condition

Foot-and-mouth disease is a highly contagious and economically devastating disease of cloven-hoofed animals. The historic occurrences of foot-and-mouth diseases led to huge economic losses and seriously threatened the livestock food security. In this paper, a novel age-space diffusive foot-and-mouth disease model with a Dirichlet boundary condition, coupling the virus-to-animals and animals-to-animals transmission routes, has been proposed. The basic reproduction number R₀ is defined as the spectral radius of a next generation operator K, which is calculated in an explicit form, and it serves as a vital value determining whether or not the disease persists. The existence of a unique trivial nonconstant steady state and at least one nonconstant endemic steady state of the system is established by a smart Lyapunov functional and the Kronoselskii fixed point theorem. An application to a foot-and-mouth outbreak in China is presented. The findings suggest that increasing the movements and disinfection of the environment for animals apparently reduce the risk of a foot-and-mouth infection.

Modeling epidemic spread in transportation networks: A review

The emergence of novel infectious diseases has become a serious global problem. Convenient transportation networks lead to rapid mobilization in the context of globalization, which is an important factor underlying the rapid spread of infectious diseases. Transportation systems can cause the transmission of viruses during the epidemic period, but they also support the reopening of economies after the epidemic. Understanding the mechanism of the impact of mobility on the spread of infectious diseases is thus important, as is establishing the risk model of the spread of infectious diseases in transportation networks. In this study, the basic structure and application of various epidemic spread models are reviewed, including mathematical models, statistical models, network-based models, and simulation models. The advantages and limitations of model applications within transportation systems are analyzed, including dynamic characteristics of epidemic transmission and decision supports for management and control. Lastly, research trends and prospects are discussed. It is suggested that there is a need for more in-depth research to examine the mutual feedback mechanism of epidemics and individual behavior, as well as the proposal and evaluation of intervention measures. The findings in this study can help evaluate disease intervention strategies, provide decision supports for transport policy during the epidemic period, and ameliorate the deficiencies of the existing system.

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Reviewed epidemic spread models and their applications in transportation networks.

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Analyzed the advantages and limitations of epidemic spread model applications in transportation systems.

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Summarized the emerging modeling requirements brought by the COVID-19 pandemic.

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Proposed research trends and prospects for epidemic spread modeling in transportation networks.

The model crisis, or how to have critical promiscuity in the time of Covid-19

During the past forty years, statistical modelling and simulation have come to frame perceptions of epidemic disease and to determine public health interventions that might limit or suppress the transmission of the causative agent. The influence of such formulaic disease modelling has pervaded public health policy and practice during the Covid-19 pandemic. The critical vocabulary of epidemiology, and now popular debate, thus includes R₀, the basic reproduction number of the virus, 'flattening the curve', and epidemic 'waves'. How did this happen? What are the consequences of framing and foreseeing the pandemic in these modes? Focusing on historical and contemporary disease responses, primarily in Britain, I explore the emergence of statistical modelling as a 'crisis technology', a reductive mechanism for making rapid decisions or judgments under uncertain biological constraint. I consider how Covid-19 might be configured or assembled otherwise, constituted as a more heterogeneous object of knowledge, a different and more encompassing moment of truth - not simply as a measured telos directing us to a new normal. Drawing on earlier critical engagements with the AIDS pandemic, inquiries into how to have 'theory' and 'promiscuity' in a crisis, I seek to open up a space for greater ecological, sociological, and cultural complexity in the biopolitics of modelling, thereby attempting to validate a role for critique in the Covid-19 crisis.

SARS-CoV-2: Cross-scale Insights from Ecology and Evolution

Ecological and evolutionary processes govern the fitness, propagation, and interactions of organisms through space and time, and viruses are no exception. While coronavirus disease 2019 (COVID-19) research has primarily emphasized virological, clinical, and epidemiological perspectives, crucial aspects of the pandemic are fundamentally ecological or evolutionary. Here, we highlight five conceptual domains of ecology and evolution – invasion, consumer-resource interactions, spatial ecology, diversity, and adaptation – that illuminate (sometimes unexpectedly) the emergence and spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We describe the applications of these concepts across levels of biological organization and spatial scales, including within individual hosts, host populations, and multispecies communities. Together, these perspectives illustrate the integrative power of ecological and evolutionary ideas and highlight the benefits of interdisciplinary thinking for understanding emerging viruses.

Role of Live-Duck Movement Networks in Transmission of Avian Influenza, France, 2016-2017

The relative roles that movement and proximity networks play in the spread of highly pathogenic avian influenza (HPAI) viruses are often unknown during an epidemic, preventing effective control. We used network analysis to explore the devastating epidemic of HPAI A(H5N8) among poultry, in particular ducks, in France during 2016–2017 and to estimate the likely contribution of live-duck movements. Approximately 0.2% of live-duck movements could have been responsible for between-farm transmission events, mostly early during the epidemic. Results also suggest a transmission risk of 35.5% when an infected holding moves flocks to another holding within 14 days before detection. Finally, we found that densely connected groups of holdings with sparse connections between groups overlapped farmer organizations, which represents important knowledge for surveillance design. This study highlights the importance of movement bans in zones affected by HPAI and of understanding transmission routes to develop appropriate HPAI control strategies.

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.

Modeling Intervention Scenarios During Potential Foot-and-Mouth Disease Outbreaks Within U.S. Beef Feedlots

Foot-and-mouth disease (FMD) is a highly contagious disease of livestock and has severely affected livestock industries during the past two decades in previously FMD-free countries. The disease was eliminated in North America in 1953 but remains a threat for re-introduction. Approximately 44% of the on-feed beef cattle in the U.S. are concentrated in feedlots <32,000 heads, but little information is available on dynamics of FMD in large feedlots. Therefore, there is a need to explore possible management and intervention strategies that might be implemented during potential FMD outbreaks on feedlots. We used a within home-pen stochastic susceptible-latent-infectious-recovered (SLIR) FMD dynamics model nested in a meta-population model of home-pens in a feedlot. The combinatory model was previously developed to simulate foot-and-mouth disease virus (FMDv) transmission within U.S. beef feedlots. We evaluated three intervention strategies initiated on the day of FMD detection: stopping movements of cattle between home-pens and hospital-pen(s) (NH), barrier depopulation combined with NH (NH-BD), and targeted depopulation of at-risk home-pens combined with NH (NH-TD). Depopulation rates investigated ranged from 500 to 4,000 cattle per day. We evaluated the projected effectiveness of interventions by comparing them with the no-intervention FMD dynamics in the feedlot. We modeled a small-size (4,000 cattle), medium-size (12,000 cattle), and large-size (24,000 cattle) feedlots. Implementation of NH delayed the outbreak progression, but it did not prevent infection of the entire feedlot. Implementation of NH-BD resulted in depopulation of 50% of cattle in small- and medium-size feedlots, and 25% in large-size feedlots, but the intervention prevented infection of the entire feedlot in 40% of simulated outbreaks in medium-size feedlots, and in 8% in large-size feedlots. Implementation of NH-TD resulted in depopulation of up to 50% of cattle in small-size feedlots, 75% in medium-size feedlots, and 25% in large-size feedlots, but rarely prevented infection of the entire feedlot. Number of hospital-pens in the feedlot was shown to weakly impact the success of NH-TD. Overall, the results suggest that stopping cattle movements between the home-pens and hospital-pens, without or with barrier or targeted cattle depopulation, would not be highly effective to interrupt FMDv transmission within a feedlot.

A Practical Introduction to Mechanistic Modeling of Disease Transmission in Veterinary Science

Computer-based disease spread models are frequently used in veterinary science to simulate disease spread. They are used to predict the impacts of the disease, plan and assess surveillance, or control strategies, and provide insights about disease causation by comparing model outputs with real life data. There are many types of disease spread models, and here we present and describe the implementation of a particular type: individual-based models. Our aim is to provide a practical introduction to building individual-based disease spread models. We also introduce code examples with the goal to make these techniques more accessible to those who are new to the field. We describe the important steps in building such models before, during and after the programming stage, including model verification (to ensure that the model does what was intended), validation (to investigate whether the model results reflect the modeled system), and convergence analysis (to ensure models of endemic diseases are stable before outputs are collected). We also describe how sensitivity analysis can be used to assess the potential impact of uncertainty about model parameters. Finally, we provide an overview of some interesting recent developments in the field of disease spread models.

Social structure defines spatial transmission of African swine fever in wild boar

The spatial spread of infectious disease is determined by spatial and social processes such as animal space use and family group structure. Yet, the impacts of social processes on spatial spread remain poorly understood and estimates of spatial transmission kernels (STKs) often exclude social structure. Understanding the impacts of social structure on STKs is important for obtaining robust inferences for policy decisions and optimizing response plans. We fit spatially explicit transmission models with different assumptions about contact structure to African swine fever virus surveillance data from eastern Poland from 2014 to 2015 and evaluated how social structure affected inference of STKs and spatial spread. The model with social structure provided better inference of spatial spread, predicted that approximately 80% of transmission events occurred within family groups, and that transmission was weakly female-biased (other models predicted weakly male-biased transmission). In all models, most transmission events were within 1.5 km, with some rare events at longer distances. Effective reproductive numbers were between 1.1 and 2.5 (maximum values between 4 and 8). Social structure can modify spatial transmission dynamics. Accounting for this additional contact heterogeneity in spatial transmission models could provide more robust inferences of STKs for policy decisions, identify best control targets and improve transparency in model uncertainty.

Development and dissemination of infectious disease dynamic transmission models during the COVID-19 pandemic: what can we learn from other pathogens and how can we move forward?

The current COVID-19 pandemic has resulted in the unprecedented development and integration of infectious disease dynamic transmission models into policy making and public health practice. Models offer a systematic way to investigate transmission dynamics and produce short-term and long-term predictions that explicitly integrate assumptions about biological, behavioural, and epidemiological processes that affect disease transmission, burden, and surveillance. Models have been valuable tools during the COVID-19 pandemic and other infectious disease outbreaks, able to generate possible trajectories of disease burden, evaluate the effectiveness of intervention strategies, and estimate key transmission variables. Particularly given the rapid pace of model development, evaluation, and integration with decision making in emergency situations, it is necessary to understand the benefits and pitfalls of transmission models. We review and highlight key aspects of the history of infectious disease dynamic models, the role of rigorous testing and evaluation, the integration with data, and the successful application of models to guide public health. Rather than being an expansive history of infectious disease models, this Review focuses on how the integration of modelling can continue to be advanced through policy and practice in appropriate and conscientious ways to support the current pandemic response.

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic

Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.

Estimating the basic reproduction number for the 2015 bubonic plague outbreak in Nyimba district of Eastern Zambia

BACKGROUND

Plague is a re-emerging flea-borne infectious disease of global importance and in recent years, Zambia has periodically experienced increased incidence of outbreaks of this disease. However, there are currently no studies in the country that provide a quantitative assessment of the ability of the disease to spread during these outbreaks. This limits our understanding of the epidemiology of the disease especially for planning and implementing quantifiable and cost-effective control measures. To fill this gap, the basic reproduction number, R0, for bubonic plague was estimated in this study, using data from the 2015 Nyimba district outbreak, in the Eastern province of Zambia. R0 is the average number of secondary infections arising from a single infectious individual during their infectious period in an entirely susceptible population.

METHODOLOGY/PRINCIPAL FINDINGS

Secondary epidemic data for the most recent 2015 Nyimba district bubonic plague outbreak in Zambia was analyzed. R0 was estimated as a function of the average epidemic doubling time based on the initial exponential growth rate of the outbreak and the average infectious period for bubonic plague. R0 was estimated to range between 1.5599 [95% CI: 1.382-1.7378] and 1.9332 [95% CI: 1.6366-2.2297], with average of 1.7465 [95% CI: 1.5093-1.9838]. Further, an SIR deterministic mathematical model was derived for this infection and this estimated R0 to be between 1.4 to 1.5, which was within the range estimated above.

CONCLUSIONS/SIGNIFICANCE

This estimated R0 for bubonic plague is an indication that each bubonic plague case can typically give rise to almost two new cases during these outbreaks. This R0 estimate can now be used to quantitatively analyze and plan measurable interventions against future plague outbreaks in Zambia.

Real-Time Standard Analysis of Disease Investigation (SADI)-A Toolbox Approach to Inform Disease Outbreak Response

An incursion of an important exotic transboundary animal disease requires a prompt and intensive response. The routine analysis of up-to-date data, as near to real time as possible, is essential for the objective assessment of the patterns of disease spread or effectiveness of control measures and the formulation of alternative control strategies. In this paper, we describe the Standard Analysis of Disease Investigation (SADI), a toolbox for informing disease outbreak response, which was developed as part of New Zealand's biosecurity preparedness. SADI was generically designed on a web-based software platform, Integrated Real-time Information System (IRIS). We demonstrated the use of SADI for a hypothetical foot-and-mouth disease (FMD) outbreak scenario in New Zealand. The data standards were set within SADI, accommodating a single relational database that integrated the national livestock population data, outbreak data, and tracing data. We collected a well-researched, standardised set of 16 epidemiologically relevant analyses for informing the FMD outbreak response, including farm response timelines, interactive outbreak/network maps, stratified epidemic curves, estimated dissemination rates, estimated reproduction numbers, and areal attack rates. The analyses were programmed within SADI to automate the process to generate the reports at a regular interval (daily) using the most up-to-date data. Having SADI prepared in advance and the process streamlined for data collection, analysis and reporting would free a wider group of epidemiologists during an actual disease outbreak from solving data inconsistency among response teams, daily “number crunching,” or providing largely retrospective analyses. Instead, the focus could be directed into enhancing data collection strategies, improving data quality, understanding the limitations of the data available, interpreting the set of analyses, and communicating their meaning with response teams, decision makers and public in the context of the epidemic.

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.

Modelling infectious viral diseases in swine populations: a state of the art

Mathematical modelling is nowadays a pivotal tool for infectious diseases studies, completing regular biological investigations. The rapid growth of computer technology allowed for development of computational tools to address biological issues that could not be unravelled in the past. The global understanding of viral disease dynamics requires to account for all interactions at all levels, from within-host to between-herd, to have all the keys for development of control measures. A literature review was performed to disentangle modelling frameworks according to their major objectives and methodologies. One hundred and seventeen articles published between 1994 and 2020 were found to meet our inclusion criteria, which were defined to target papers representative of studies dealing with models of viral infection dynamics in pigs. A first descriptive analysis, using bibliometric indexes, permitted to identify keywords strongly related to the study scopes. Modelling studies were focused on particular infectious agents, with a shared objective: to better understand the viral dynamics for appropriate control measure adaptation. In a second step, selected papers were analysed to disentangle the modelling structures according to the objectives of the studies. The system representation was highly dependent on the nature of the pathogens. Enzootic viruses, such as swine influenza or porcine reproductive and respiratory syndrome, were generally investigated at the herd scale to analyse the impact of husbandry practices and prophylactic measures on infection dynamics. Epizootic agents (classical swine fever, foot-and-mouth disease or African swine fever viruses) were mostly studied using spatio-temporal simulation tools, to investigate the efficiency of surveillance and control protocols, which are predetermined for regulated diseases. A huge effort was made on model parameterization through the development of specific studies and methodologies insuring the robustness of parameter values to feed simulation tools. Integrative modelling frameworks, from within-host to spatio-temporal models, is clearly on the way. This would allow to capture the complexity of individual biological variabilities and to assess their consequences on the whole system at the population level. This would offer the opportunity to test and evaluate in silico the efficiency of possible control measures targeting specific epidemiological units, from hosts to herds, either individually or through their contact networks. Such decision support tools represent a strength for stakeholders to help mitigating infectious diseases dynamics and limiting economic consequences.