Optimal experimental designs for estimating genetic and non-genetic effects underlying infectious disease transmission.

BACKGROUND: The spread of infectious diseases in populations is controlled by the susceptibility (propensity to acquire infection), infectivity (propensity to transmit infection), and recoverability (propensity to recover/die) of individuals. Estimating genetic risk factors for these three underlying host epidemiological traits can help reduce disease spread through genetic control strategies. Previous studies have identified important 'disease resistance single nucleotide polymorphisms (SNPs)', but how these affect the underlying traits is an unresolved question. Recent advances in computational statistics make it now possible to estimate the effects of SNPs on host traits from epidemic data (e.g. infection and/or recovery times of individuals or diagnostic test results). However, little is known about how to effectively design disease transmission experiments or field studies to maximise the precision with which these effects can be estimated. RESULTS: In this paper, we develop and validate analytical expressions for the precision of the estimates of SNP effects on the three above host traits for a disease transmission experiment with one or more non-interacting contact groups. Maximising these expressions leads to three distinct 'experimental' designs, each specifying a different set of ideal SNP genotype compositions across groups: (a) appropriate for a single contact-group, (b) a multi-group design termed "pure", and (c) a multi-group design termed "mixed", where 'pure' and 'mixed' refer to groupings that consist of individuals with uniformly the same or different SNP genotypes, respectively. Precision estimates for susceptibility and recoverability were found to be less sensitive to the experimental design than estimates for infectivity. Whereas the analytical expressions suggest that the multi-group pure and mixed designs estimate SNP effects with similar precision, the mixed design is preferred because it uses information from naturally-occurring rather than artificial infections. The same design principles apply to estimates of the epidemiological impact of other categorical fixed effects, such as breed, line, family, sex, or vaccination status. Estimation of SNP effect precisions from a given experimental setup is implemented in an online software tool SIRE-PC. CONCLUSIONS: Methodology was developed to aid the design of disease transmission experiments for estimating the effect of individual SNPs and other categorical variables that underlie host susceptibility, infectivity and recoverability. Designs that maximize the precision of estimates were derived.

The challenges of data in future pandemics.

The use of data has been essential throughout the unfolding COVID-19 pandemic. We have needed it to populate our models, inform our understanding, and shape our responses to the disease. However, data has not always been easy to find and access, it has varied in quality and coverage, been difficult to reuse or repurpose. This paper reviews these and other challenges and recommends steps to develop a data ecosystem better able to deal with future pandemics by better supporting preparedness, prevention, detection and response.

Estimation of age-stratified contact rates during the COVID-19 pandemic using a novel inference algorithm.

Well parameterized epidemiological models including accurate representation of contacts are fundamental to controlling epidemics. However, age-stratified contacts are typically estimated from pre-pandemic/peace-time surveys, even though interventions and public response likely alter contacts. Here, we fit age-stratified models, including re-estimation of relative contact rates between age classes, to public data describing the 2020-2021 COVID-19 outbreak in England. This data includes age-stratified population size, cases, deaths, hospital admissions and results from the Coronavirus Infection Survey (almost 9000 observations in all). Fitting stochastic compartmental models to such detailed data is extremely challenging, especially considering the large number of model parameters being estimated (over 150). An efficient new inference algorithm ABC-MBP combining existing approximate Bayesian computation (ABC) methodology with model-based proposals (MBPs) is applied. Modified contact rates are inferred alongside time-varying reproduction numbers that quantify changes in overall transmission due to pandemic response, and age-stratified proportions of asymptomatic cases, hospitalization rates and deaths. These inferences are robust to a range of assumptions including the values of parameters that cannot be estimated from available data. ABC-MBP is shown to enable reliable joint analysis of complex epidemiological data yielding consistent parametrization of dynamic transmission models that can inform data-driven public health policy and interventions. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

FAIR data pipeline: provenance-driven data management for traceable scientific workflows.

Modern epidemiological analyses to understand and combat the spread of disease depend critically on access to, and use of, data. Rapidly evolving data, such as data streams changing during a disease outbreak, are particularly challenging. Data management is further complicated by data being imprecisely identified when used. Public trust in policy decisions resulting from such analyses is easily damaged and is often low, with cynicism arising where claims of 'following the science' are made without accompanying evidence. Tracing the provenance of such decisions back through open software to primary data would clarify this evidence, enhancing the transparency of the decision-making process. Here, we demonstrate a Findable, Accessible, Interoperable and Reusable (FAIR) data pipeline. Although developed during the COVID-19 pandemic, it allows easy annotation of any data as they are consumed by analyses, or conversely traces the provenance of scientific outputs back through the analytical or modelling source code to primary data. Such a tool provides a mechanism for the public, and fellow scientists, to better assess scientific evidence by inspecting its provenance, while allowing scientists to support policymakers in openly justifying their decisions. We believe that such tools should be promoted for use across all areas of policy-facing research. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Archetype models upscale understanding of natural pest control response to land-use change.

Control of crop pests by shifting host plant availability and natural enemy activity at landscape scales has great potential to enhance the sustainability of agriculture. However, mainstreaming natural pest control requires improved understanding of how its benefits can be realized across a variety of agroecological contexts. Empirical studies suggest significant but highly variable responses of natural pest control to land-use change. Current ecological models are either too specific to provide insight across agroecosystems or too generic to guide management with actionable predictions. We suggest obtaining the full benefit of available empirical, theoretical, and methodological knowledge by combining trait-mediated understanding from correlative studies with the explicit representation of causal relationships achieved by mechanistic modeling. To link these frameworks, we adapt the concept of archetypes, or context-specific generalizations, from sustainability science. Similar responses of natural pest control to land-use gradients across cases that share key attributes, such as functional traits of focal organisms, indicate general processes that drive system behavior in a context-sensitive manner. Based on such observations of natural pest control, a systematic definition of archetypes can provide the basis for mechanistic models of intermediate generality that cover all major agroecosystems worldwide. Example applications demonstrate the potential for upscaling understanding and improving predictions of natural pest control, based on knowledge transfer and scientific synthesis. A broader application of this mechanistic archetype approach promises to enhance ecology's contribution to natural resource management across diverse regions and social-ecological contexts.

Modelling: Understanding pandemics and how to control them.

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Exact Bayesian inference of epidemiological parameters from mortality data: application to African swine fever virus.

Pathogens such as African swine fever virus (ASFV) are an increasing threat to global livestock production with implications for economic well-being and food security. Quantification of epidemiological parameters, such as transmission rates and latent and infectious periods, is critical to inform efficient disease control. Parameter estimation for livestock disease systems is often reliant upon transmission experiments, which provide valuable insights in the epidemiology of disease but which may also be unrepresentative of at-risk populations and incur economic and animal welfare costs. Routinely collected mortality data are a potential source of readily available and representative information regarding disease transmission early in outbreaks. We develop methodology to conduct exact Bayesian parameter inference from mortality data using reversible jump Markov chain Monte Carlo incorporating multiple routes of transmission (e.g. within-farm secondary and background transmission from external sources). We use this methodology to infer epidemiological parameters for ASFV using data from outbreaks on nine farms in the Russian Federation. This approach improves inference on transmission rates in comparison with previous methods based on approximate Bayesian computation, allows better estimation of time of introduction and could readily be applied to other outbreaks or pathogens.

A mechanistic model captures livestock trading, disease dynamics, and compensatory behaviour in response to control measures.

Trade is a complex, multi-faceted process that can contribute to the spread and persistence of disease. We here develop novel mechanistic models of supply. Our model is framed within a livestock trading system, where farms form and end trade partnerships with rates dependent on current demand, with these trade partnerships facilitating trade between partners. With these time-varying, stock dependent partnership and trade dynamics, our trading model goes beyond current state of the art modelling approaches. By studying instantaneous shocks to farm-level supply and demand we show that behavioural responses of farms lead to trading systems that are highly resistant to shocks with only temporary disturbances to trade observed. Individual adaptation in response to permanent alterations to trading propensities, such that animal flows are maintained, illustrates the ability for farms to find new avenues of trade, minimising disruptions imposed by such alterations to trade that common modelling approaches cannot adequately capture. In the context of endemic disease control, we show that these adaptations hinder the potential beneficial reductions in prevalence such changes to trading propensities have previously been shown to confer. Assessing the impact of a common disease control measure, post-movement batch testing, highlights the ability for our model to measure the stress on multiple components of trade imposed by such control measures and also highlights the temporary and, in some cases, the permanent disturbances to trade that post-movement testing has on the trading system.

Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling.

The estimation of parameters and model structure for informing infectious disease response has become a focal point of the recent pandemic. However, it has also highlighted a plethora of challenges remaining in the fast and robust extraction of information using data and models to help inform policy. In this paper, we identify and discuss four broad challenges in the estimation paradigm relating to infectious disease modelling, namely the Uncertainty Quantification framework, data challenges in estimation, model-based inference and prediction, and expert judgement. We also postulate priorities in estimation methodology to facilitate preparation for future pandemics.

When and why direct transmission models can be used for environmentally persistent pathogens.

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen's characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models' mean outputs diverge, with distinct predictions of outbreak size and duration.

Generative models of network dynamics provide insight into the effects of trade on endemic livestock disease.

We develop and apply analytically tractable generative models of livestock movements at national scale. These go beyond current models through mechanistic modelling of heterogeneous trade partnership network dynamics and the trade events that occur on them. Linking resulting animal movements to disease transmission between farms yields analytical expressions for the basic reproduction number R 0. We show how these novel modelling tools enable systems approaches to disease control, using R 0 to explore impacts of changes in trading practices on between-farm prevalence levels. Using the Scottish cattle trade network as a case study, we show our approach captures critical complexities of real-world trade networks at the national scale for a broad range of endemic diseases. Changes in trading patterns that minimize disruption to business by maintaining in-flow of animals for each individual farm reduce R 0, with the largest reductions for diseases that are most challenging to eradicate. Incentivizing high-risk farms to adopt such changes exploits 'scale-free' properties of the system and is likely to be particularly effective in reducing national livestock disease burden and incursion risk. Encouragingly, gains made by such targeted modification of trade practices scale much more favourably than comparably targeted improvements to more commonly adopted farm-level biosecurity.

Estimating individuals' genetic and non-genetic effects underlying infectious disease transmission from temporal epidemic data.

Individuals differ widely in their contribution to the spread of infection within and across populations. Three key epidemiological host traits affect infectious disease spread: susceptibility (propensity to acquire infection), infectivity (propensity to transmit infection to others) and recoverability (propensity to recover quickly). Interventions aiming to reduce disease spread may target improvement in any one of these traits, but the necessary statistical methods for obtaining risk estimates are lacking. In this paper we introduce a novel software tool called SIRE (standing for "Susceptibility, Infectivity and Recoverability Estimation"), which allows for the first time simultaneous estimation of the genetic effect of a single nucleotide polymorphism (SNP), as well as non-genetic influences on these three unobservable host traits. SIRE implements a flexible Bayesian algorithm which accommodates a wide range of disease surveillance data comprising any combination of recorded individual infection and/or recovery times, or disease diagnostic test results. Different genetic and non-genetic regulations and data scenarios (representing realistic recording schemes) were simulated to validate SIRE and to assess their impact on the precision, accuracy and bias of parameter estimates. This analysis revealed that with few exceptions, SIRE provides unbiased, accurate parameter estimates associated with all three host traits. For most scenarios, SNP effects associated with recoverability can be estimated with highest precision, followed by susceptibility. For infectivity, many epidemics with few individuals give substantially more statistical power to identify SNP effects than the reverse. Importantly, precise estimates of SNP and other effects could be obtained even in the case of incomplete, censored and relatively infrequent measurements of individuals' infection or survival status, albeit requiring more individuals to yield equivalent precision. SIRE represents a new tool for analysing a wide range of experimental and field disease data with the aim of discovering and validating SNPs and other factors controlling infectious disease transmission.

Learning-induced switching costs in a parasitoid can maintain diversity of host aphid phenotypes although biocontrol is destabilized under abiotic stress.

Aphid populations frequently include phenotypes that are resistant to parasitism by hymenopterous parasitoid wasps, which is often attributed to the presence of 'protective' facultative endosymbionts residing in aphid tissues, particularly Hamiltonella defensa. In field conditions, under parasitoid pressure, the observed coexistence of aphids with and without protective symbionts cannot be explained by their difference in fitness alone. Using the cereal aphid Rhopalosiphum padi as a model, we propose an alternative mechanism whereby parasitoids are more efficient at finding common phenotypes of aphid and experience a fitness cost when switching to the less common phenotype. We construct a model based on delay differential equations and parameterize and validate the model with values within the ranges obtained from experimental studies. We then use it to explore the possible effects on system dynamics under conditions of environmental stress, using our existing data on the effects of drought stress in crops as an example. We show the 'switching penalty' incurred by parasitoids leads to stable coexistence of aphids with and without H. defensa and provides a potential mechanism for maintaining phenotypic diversity among host organisms. We show that drought-induced reduction in aphid development time has little impact. However, greater reduction in fecundity on droughted plants of symbiont-protected aphids can cause insect population cycles when the system would be stable in the absence of drought stress. The stabilizing effect of the increased efficiency in dealing with more commonly encountered host phenotypes is applicable to a broad range of consumer-resource systems and could explain stable coexistence in competitive environments. The loss of stable coexistence when drought has different effects on the competing aphid phenotypes highlights the importance of scenario testing when considering biocontrol for pest management.

When to kill a cull: factors affecting the success of culling wildlife for disease control.

Culling wildlife to control disease can lead to both decreases and increases in disease levels, with apparently conflicting responses observed, even for the same wildlife-disease system. There is therefore a pressing need to understand how culling design and implementation influence culling's potential to achieve disease control. We address this gap in understanding using a spatial metapopulation model representing wildlife living in distinct groups with density-dependent dispersal and framed on the badger-bovine tuberculosis (bTB) system. We show that if population reduction is too low, or too few groups are targeted, a 'perturbation effect' is observed, whereby culling leads to increased movement and disease spread. We also demonstrate the importance of culling across appropriate time scales, with otherwise successful control strategies leading to increased disease if they are not implemented for long enough. These results potentially explain a number of observations of the dynamics of both successful and unsuccessful attempts to control TB in badgers including the Randomized Badger Culling Trial in the UK, and we highlight their policy implications. Additionally, for parametrizations reflecting a broad range of wildlife-disease systems, we characterize 'Goldilocks zones', where, for a restricted combination of culling intensity, coverage and duration, the disease can be reduced without driving hosts to extinction.

Data-Driven Risk Assessment from Small Scale Epidemics: Estimation and Model Choice for Spatio-Temporal Data with Application to a Classical Swine Fever Outbreak.

Livestock epidemics have the potential to give rise to significant economic, welfare, and social costs. Incursions of emerging and re-emerging pathogens may lead to small and repeated outbreaks. Analysis of the resulting data is statistically challenging but can inform disease preparedness reducing potential future losses. We present a framework for spatial risk assessment of disease incursions based on data from small localized historic outbreaks. We focus on between-farm spread of livestock pathogens and illustrate our methods by application to data on the small outbreak of Classical Swine Fever (CSF) that occurred in 2000 in East Anglia, UK. We apply models based on continuous time semi-Markov processes, using data-augmentation Markov Chain Monte Carlo techniques within a Bayesian framework to infer disease dynamics and detection from incompletely observed outbreaks. The spatial transmission kernel describing pathogen spread between farms, and the distribution of times between infection and detection, is estimated alongside unobserved exposure times. Our results demonstrate inference is reliable even for relatively small outbreaks when the data-generating model is known. However, associated risk assessments depend strongly on the form of the fitted transmission kernel. Therefore, for real applications, methods are needed to select the most appropriate model in light of the data. We assess standard Deviance Information Criteria (DIC) model selection tools and recently introduced latent residual methods of model assessment, in selecting the functional form of the spatial transmission kernel. These methods are applied to the CSF data, and tested in simulated scenarios which represent field data, but assume the data generation mechanism is known. Analysis of simulated scenarios shows that latent residual methods enable reliable selection of the transmission kernel even for small outbreaks whereas the DIC is less reliable. Moreover, compared with DIC, model choice based on latent residual assessment correlated better with predicted risk.

Complex responses to movement-based disease control: when livestock trading helps.

Livestock disease controls are often linked to movements between farms, for example, via quarantine and pre- or post-movement testing. Designing effective controls, therefore, benefits from accurate assessment of herd-to-herd transmission. Household models of human infections make use of R*, the number of groups infected by an initial infected group, which is a metapopulation level analogue of the basic reproduction number R0 that provides a better characterization of disease spread in a metapopulation. However, existing approaches to calculate R* do not account for individual movements between locations which means we lack suitable tools for livestock systems. We address this gap using next-generation matrix approaches to capture movements explicitly and introduce novel tools to calculate R* in any populations coupled by individual movements. We show that depletion of infectives in the source group, which hastens its recovery, is a phenomenon with important implications for design and efficacy of movement-based controls. Underpinning our results is the observation that R* peaks at intermediate livestock movement rates. Consequently, under movement-based controls, infection could be controlled at high movement rates but persist at intermediate rates. Thus, once control schemes are present in a livestock system, a reduction in movements can counterintuitively lead to increased disease prevalence. We illustrate our results using four important livestock diseases (bovine viral diarrhoea, bovine herpes virus, Johne's disease and Escherichia coli O157) that each persist across different movement rate ranges with the consequence that a change in livestock movements could help control one disease, but exacerbate another.

Using Combined Diagnostic Test Results to Hindcast Trends of Infection from Cross-Sectional Data.

Infectious disease surveillance is key to limiting the consequences from infectious pathogens and maintaining animal and public health. Following the detection of a disease outbreak, a response in proportion to the severity of the outbreak is required. It is thus critical to obtain accurate information concerning the origin of the outbreak and its forward trajectory. However, there is often a lack of situational awareness that may lead to over- or under-reaction. There is a widening range of tests available for detecting pathogens, with typically different temporal characteristics, e.g. in terms of when peak test response occurs relative to time of exposure. We have developed a statistical framework that combines response level data from multiple diagnostic tests and is able to 'hindcast' (infer the historical trend of) an infectious disease epidemic. Assuming diagnostic test data from a cross-sectional sample of individuals infected with a pathogen during an outbreak, we use a Bayesian Markov Chain Monte Carlo (MCMC) approach to estimate time of exposure, and the overall epidemic trend in the population prior to the time of sampling. We evaluate the performance of this statistical framework on simulated data from epidemic trend curves and show that we can recover the parameter values of those trends. We also apply the framework to epidemic trend curves taken from two historical outbreaks: a bluetongue outbreak in cattle, and a whooping cough outbreak in humans. Together, these results show that hindcasting can estimate the time since infection for individuals and provide accurate estimates of epidemic trends, and can be used to distinguish whether an outbreak is increasing or past its peak. We conclude that if temporal characteristics of diagnostics are known, it is possible to recover epidemic trends of both human and animal pathogens from cross-sectional data collected at a single point in time.

A Systematic Bayesian Integration of Epidemiological and Genetic Data.

Genetic sequence data on pathogens have great potential to inform inference of their transmission dynamics ultimately leading to better disease control. Where genetic change and disease transmission occur on comparable timescales additional information can be inferred via the joint analysis of such genetic sequence data and epidemiological observations based on clinical symptoms and diagnostic tests. Although recently introduced approaches represent substantial progress, for computational reasons they approximate genuine joint inference of disease dynamics and genetic change in the pathogen population, capturing partially the joint epidemiological-evolutionary dynamics. Improved methods are needed to fully integrate such genetic data with epidemiological observations, for achieving a more robust inference of the transmission tree and other key epidemiological parameters such as latent periods. Here, building on current literature, a novel Bayesian framework is proposed that infers simultaneously and explicitly the transmission tree and unobserved transmitted pathogen sequences. Our framework facilitates the use of realistic likelihood functions and enables systematic and genuine joint inference of the epidemiological-evolutionary process from partially observed outbreaks. Using simulated data it is shown that this approach is able to infer accurately joint epidemiological-evolutionary dynamics, even when pathogen sequences and epidemiological data are incomplete, and when sequences are available for only a fraction of exposures. These results also characterise and quantify the value of incomplete and partial sequence data, which has important implications for sampling design, and demonstrate the abilities of the introduced method to identify multiple clusters within an outbreak. The framework is used to analyse an outbreak of foot-and-mouth disease in the UK, enhancing current understanding of its transmission dynamics and evolutionary process.

Climate-driven tipping-points could lead to sudden, high-intensity parasite outbreaks.

Parasitic nematodes represent one of the most pervasive and significant challenges to grazing livestock, and their intensity and distribution are strongly influenced by climate. Parasite levels and species composition have already shifted under climate change, with nematode parasite intensity frequently low in newly colonized areas, but sudden large-scale outbreaks are becoming increasingly common. These outbreaks compromise both food security and animal welfare, yet there is a paucity of predictions on how climate change will influence livestock parasites. This study aims to assess how climate change can affect parasite risk. Using a process-based approach, we determine how changes in temperature-sensitive elements of outbreaks influence parasite dynamics, to explore the potential for climate change to influence livestock helminth infections. We show that changes in temperate-sensitive parameters can result in nonlinear responses in outbreak dynamics, leading to distinct 'tipping-points' in nematode parasite burdens. Through applying two mechanistic models, of varying complexity, our approach demonstrates that these nonlinear responses are robust to the inclusion of a number of realistic processes that are present in livestock systems. Our study demonstrates that small changes in climatic conditions around critical thresholds may result in dramatic changes in parasite burdens.

An explicit immunogenetic model of gastrointestinal nematode infection in sheep.

Gastrointestinal nematodes are a global cause of disease and death in humans, wildlife and livestock. Livestock infection has historically been controlled with anthelmintic drugs, but the development of resistance means that alternative controls are needed. The most promising alternatives are vaccination, nutritional supplementation and selective breeding, all of which act by enhancing the immune response. Currently, control planning is hampered by reliance on the faecal egg count (FEC), which suffers from low accuracy and a nonlinear and indirect relationship with infection intensity and host immune responses. We address this gap by using extensive parasitological, immunological and genetic data on the sheep-Teladorsagia circumcincta interaction to create an immunologically explicit model of infection dynamics in a sheep flock that links host genetic variation with variation in the two key immune responses to predict the observed parasitological measures. Using our model, we show that the immune responses are highly heritable and by comparing selective breeding based on low FECs versus high plasma IgA responses, we show that the immune markers are a much improved measure of host resistance. In summary, we have created a model of host-parasite infections that explicitly captures the development of the adaptive immune response and show that by integrating genetic, immunological and parasitological understanding we can identify new immune-based markers for diagnosis and control.