Accuracy of models for the 2001 foot-and-mouth epidemic

Since 2001 models of the spread of foot-and-mouth disease, supported by the data from the UK epidemic, have been expounded as some of the best examples of problem-driven epidemic models. These claims are generally based on a comparison between model results and epidemic data at fairly coarse spatio-temporal resolution. Here, we focus on a comparison between model and data at the individual farm level, assessing the potential of the model to predict the infectious status of farms in both the short and long terms. Although the accuracy with which the model predicts farms reporting infection is between 5 and 15%, these low levels are attributable to the expected level of variation between epidemics, and are comparable to the agreement between two independent model simulations. By contrast, while the accuracy of predicting culls is higher (20-30%), this is lower than expected from the comparison between model epidemics. These results generally support the contention that the type of the model used in 2001 was a reliable representation of the epidemic process, but highlight the difficulties of predicting the complex human response, in terms of control strategies to the perceived epidemic risk.     

Modelling the initial spread of foot-and-mouth disease through animal movements

Livestock movements in Great Britain (GB) are well recorded and are a unique record of the network of connections among livestock-holding locations. These connections can be critical for disease spread, as in the 2001 epidemic of foot-and-mouth disease (FMD) in the UK. Here, the movement data are used to construct an individual-farm-based model of the initial spread of FMD in GB and determine the susceptibility of the GB livestock industry to future outbreaks under the current legislative requirements. Transmission through movements is modelled, with additional local spread unrelated to the known movements. Simulations show that movements can result in a large nationwide epidemic, but only if cattle are heavily involved, or the epidemic occurs in late summer or early autumn. Inclusion of random local spread can considerably increase epidemic size, but has only a small impact on the spatial extent of the disease. There is a geographical bias in the epidemic size reached, with larger epidemics originating in Scotland and the north of England than elsewhere.     

Molecular epidemiology of the foot-and-mouth disease virus outbreak in the United Kingdom in 2001

The objective of this study was to quantify the extent to which the genetic diversity of foot-and-mouth disease virus (FMDV) arising over the course of infection of an individual animal becomes fixed, is transmitted to other animals, and thereby accumulates over the course of an outbreak. Complete consensus sequences of 23 genomes (each of 8,200 nucleotides) of FMDV were recovered directly from epithelium tissue acquired from 21 farms infected over a nearly 7-month period during the 2001 FMDV outbreak in the United Kingdom. An analysis of these consensus sequences revealed very few apparently ambiguous sites but clear evidence of 197 nucleotide substitutions at 191 different sites. We estimated the rate of nucleotide substitution to be 2.26 x 10(-5) per site per day (95% confidence interval [CI], 1.75 x 10(-5) to 2.80 x 10(-5)) and nucleotide substitutions to accrue in the consensus sequence at an average rate of 1.5 substitutions per farm infection. This is a sufficiently high rate showing that detailed histories of the transmission pathways can be reliably reconstructed. Coalescent methods indicated that the date at which FMDV first infected livestock in the United Kingdom was 7 February 2001 (95% CI, 20 January to 19 February 2001), which was identical to estimates obtained on the basis of purely clinical evidence. Nucleotide changes appeared to have occurred evenly across the genome, and within the open reading frame, the ratio of nonsynonymous-to-synonymous change was 0.09. The ability to recover particular transmission pathways of acutely acting RNA pathogens from genetic data will help resolve uncertainties about how virus is spread and could help in the control of future epidemics.     

Absence of antibodies to foot-and-mouth disease virus in free-ranging roe deer from selected areas of Germany (2001-2002)

Blood samples (n = 223) of free-ranging roe deer (Capreolus capreolus) were collected from selected hunting grounds in Germany between October 2001 and October 2002. Samples originated from Lower Saxony (n = 43) and North-Rhine Westphalia (n = 108) within a 20-km area ("cordon") cordoned off along the border of The Netherlands. This is adjacent to the area of a foot-and-mouth disease outbreak that occurred between 21 March and 22 April 2001 in The Netherlands. Negative control samples were taken from northern Germany (Schleswig-Holstein, n = 72). Two different enzyme-linked immunosorbent assays (ELISAs) were used for the detection of antibodies against foot-and-mouth disease virus (FMDV) serotype O strain Manisa. To confirm ELISA-positive results, a virus neutralization test was performed. All samples tested negative for antibodies against FMDV. These results suggest that FMDV was not transmitted to free-ranging roe deer living in parts of Germany adjacent to the area affected by the 2001 foot-and-mouth disease outbreak in The Netherlands.     

The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak

The case-reproduction ratio for the spread of an infectious disease is a critically important concept for understanding dynamics of epidemics and for evaluating impact of control measures on spread of infection. Reliable estimation of this ratio is a problem central to epidemiology and is most often accomplished by fitting dynamic models to data and estimating combinations of parameters that equate to the case-reproduction ratio. Here, we develop a novel parameter-free method that permits direct estimation of the history of transmission events recoverable from detailed observation of a particular epidemic. From these reconstructed 'epidemic trees', case-reproduction ratios can be estimated directly. We develop a bootstrap algorithm that generates percentile intervals for these estimates that shows the procedure to be both precise and robust to possible uncertainties in the historical reconstruction. Identifying and 'pruning' branches from these trees whose occurrence might have been prevented by implementation of more stringent control measures permits estimation of the possible efficacy of these alternative measures. Examination of the cladistic structure of these trees as a function of the distance of each case from its infection source reveals useful insights about the relationship between long-distance transmission events and epidemic size. We demonstrate the utility of these methods by applying them to data from the 2001 foot-and-mouth disease outbreak in the UK.     

Linear relationship between Gaeumannomyces graminis var. tritici (Ggt) genotypic frequencies and disease severity on wheat roots in the field

In order to investigate potential links existing between Gaeumannomyces graminis var. tritici (Ggt) population structure and disease development during polyetic take-all epidemics in sequences of Ggt host cereals, seven epidemics in fields with different cropping histories were monitored during the seasons 2001/2002 (two fields), 2002/2003 (two fields) and 2003/2004 (three fields). Take-all incidence and severity were measured at stem elongation and Ggt populations were characterized. The 73 isolates collected in the two fields in 2001/2002 were distributed into two multilocus genotypes, G1 and G2 according to amplified fragment length polymorphism analysis. A monolocus molecular marker amplified by F-12 random amplification polymorphism DNA primer sizing between 1.9 and 2.0 kb that gave strictly the same distinction between the two multilocus genotypes was further applied to measure G1/G2 frequencies among Ggt populations in all fields (266 isolates). The ratios of G1 to G2 differed between fields with different cropping histories. A linear relationship between G2 frequency among Ggt populations and disease severity at stem elongation was measured during the three cropping seasons. When take-all decline was observed, G2 frequencies were low in first wheat crops, highest in short-term sequences and intermediate in longer sequences of consecutive crops of Ggt host cereals. This pattern could be the result of population selection by environmental conditions, in particular by microbial antagonism during the parasitic phase of the fungus. In order to better understand take-all epidemic dynamics, the distinction between these two genotypes could be a basis to develop models that link approaches of quantitative epidemiology and advances in population genetics of Ggt.     

Non-exponential tolerance to infection in epidemic systems--modeling, inference, and assessment

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.     

Sequence-based prediction for vaccine strain selection and identification of antigenic variability in foot-and-mouth disease virus

Identifying when past exposure to an infectious disease will protect against newly emerging strains is central to understanding the spread and the severity of epidemics, but the prediction of viral cross-protection remains an important unsolved problem. For foot-and-mouth disease virus (FMDV) research in particular, improved methods for predicting this cross-protection are critical for predicting the severity of outbreaks within endemic settings where multiple serotypes and subtypes commonly co-circulate, as well as for deciding whether appropriate vaccine(s) exist and how much they could mitigate the effects of any outbreak. To identify antigenic relationships and their predictors, we used linear mixed effects models to account for variation in pairwise cross-neutralization titres using only viral sequences and structural data. We identified those substitutions in surface-exposed structural proteins that are correlates of loss of cross-reactivity. These allowed prediction of both the best vaccine match for any single virus and the breadth of coverage of new vaccine candidates from their capsid sequences as effectively as or better than serology. Sub-sequences chosen by the model-building process all contained sites that are known epitopes on other serotypes. Furthermore, for the SAT1 serotype, for which epitopes have never previously been identified, we provide strong evidence--by controlling for phylogenetic structure--for the presence of three epitopes across a panel of viruses and quantify the relative significance of some individual residues in determining cross-neutralization. Identifying and quantifying the importance of sites that predict viral strain cross-reactivity not just for single viruses but across entire serotypes can help in the design of vaccines with better targeting and broader coverage. These techniques can be generalized to any infectious agents where cross-reactivity assays have been carried out. As the parameterization uses pre-existing datasets, this approach quickly and cheaply increases both our understanding of antigenic relationships and our power to control disease.     

On the critical behaviour of simple epidemics.

We show how ideas and models which were originally introduced to gain an understanding of critical phenomena can be used to interpret the dynamics of epidemics of communicable disease in real populations. Specifically, we present an analysis of the dynamics of disease outbreaks for three common communicable infections from a small isolated island population. The strongly fluctuating nature of the temporal incidence of disease is captured by the model, and comparisons between exponents calculated from the data and from simulations are made. A forest-fire model with sparks is used to classify the observed scaling dynamics of the epidemics and provides a unified picture of the epidemiology which conventional epidemiological analysis is unable to reproduce. This study suggests that power-law scaling can emerge in natural systems when they are driven on widely separated time-scales, in accordance with recent analytic renormalization group calculations.     

Recent Evolutionary History of Human Immunodeficiency Virus Type 1 Subtype B: Reconstruction of Epidemic Onset Based on Sequence Distances to the Common Ancestor

We obtained and studied HIV-1 sequences with a known sampling year from three outbreaks of the HIV-1 epidemic: 141 env V3 (270 nt) sampled between 1984 and 1992 and 117 pol prot/RT (804 nt) sequences sampled between 1986 and 1999 from Dutch homosexual men and injecting drug users (IDUs), as well as 77 env V3 sequences sampled between 1983 and 1994 in the United States. Since retrospective serological and/or epidemiological data on these populations are available, providing estimates of the dates of the onset of the HIV-1 epidemics, we had the opportunity to test different phylogenetic models for their accuracy in deriving the recent evolutionary history of HIV-1 subtype B and the onset date of the HIV-1 epidemic. We observed that, in any given year, individual sequences vary widely in their distances to the common ancestor, and sequences close to the ancestors were found decades after the onset of the epidemic. Nevertheless, the mean evolutionary distances of virus strains to ancestors were increasing significantly during the course of the studied epidemics, which indicates that the molecular clock is operational in the recent evolution of HIV-1. When the relationship between the sampling years of sequences and their nucleotide distances to the common ancestor was extrapolated to the past, analysis of pol sequences provided accurate estimates of the onset years of the epidemics, whereas analysis of V3 sequences by the maximum-likelihood or neighbor-joining methods led to an overestimation of the age of the epidemics. Separate analysis of nonsynonymous and synonymous distances revealed that this overestimation results from nonsynonymous substitutions, whose numbers were not increasing significantly in all three virus populations over the observation period. In contrast, analysis of synonymous env V3 distances provided accurate estimates of the onset years for the outbreaks we studied. Received: 26 October 2001 / Accepted: 8 November 2001     

The role of mathematical modelling in the control of the 2001 FMD epidemic in the UK

Mathematical models played an important role in guiding the development of the control policies in the 2001 foot-and-mouth disease epidemic in the UK. The variety of approaches that helped to guide the policy can sometimes be confusing. Here, the different modelling exercises that were developed over the course of the epidemic are reviewed, describing the difficulties in interpreting the available data and the appropriateness of the various assumptions.     

Modeling Age-Specific Mortality for Countries with Generalized HIV Epidemics

Background

In a given population the age pattern of mortality is an important determinant of total number of deaths, age structure, and through effects on age structure, the number of births and thereby growth. Good mortality models exist for most populations except those experiencing generalized HIV epidemics and some developing country populations. The large number of deaths concentrated at very young and adult ages in HIV-affected populations produce a unique ‘humped’ age pattern of mortality that is not reproduced by any existing mortality models. Both burden of disease reporting and population projection methods require age-specific mortality rates to estimate numbers of deaths and produce plausible age structures. For countries with generalized HIV epidemics these estimates should take into account the future trajectory of HIV prevalence and its effects on age-specific mortality. In this paper we present a parsimonious model of age-specific mortality for countries with generalized HIV/AIDS epidemics.

Methods and Findings

The model represents a vector of age-specific mortality rates as the weighted sum of three independent age-varying components. We derive the age-varying components from a Singular Value Decomposition of the matrix of age-specific mortality rate schedules. The weights are modeled as a function of HIV prevalence and one of three possible sets of inputs: life expectancy at birth, a measure of child mortality, or child mortality with a measure of adult mortality. We calibrate the model with 320 five-year life tables for each sex from the World Population Prospects 2010 revision that come from the 40 countries of the world that have and are experiencing a generalized HIV epidemic. Cross validation shows that the model is able to outperform several existing model life table systems.

Conclusions

We present a flexible, parsimonious model of age-specific mortality for countries with generalized HIV epidemics. Combined with the outputs of existing epidemiological and demographic models, this model makes it possible to project future age-specific mortality profiles and number of deaths for countries with generalized HIV epidemics.     

Sensitivity Analysis of an Individual-Based Model for Simulation of Influenza Epidemics

Individual-based epidemiology models are increasingly used in the study of influenza epidemics. Several studies on influenza dynamics and evaluation of intervention measures have used the same incubation and infectious period distribution parameters based on the natural history of influenza. A sensitivity analysis evaluating the influence of slight changes to these parameters (in addition to the transmissibility) would be useful for future studies and real-time modeling during an influenza pandemic.In this study, we examined individual and joint effects of parameters and ranked parameters based on their influence on the dynamics of simulated epidemics. We also compared the sensitivity of the model across synthetic social networks for Montgomery County in Virginia and New York City (and surrounding metropolitan regions) with demographic and rural-urban differences. In addition, we studied the effects of changing the mean infectious period on age-specific epidemics. The research was performed from a public health standpoint using three relevant measures: time to peak, peak infected proportion and total attack rate. We also used statistical methods in the design and analysis of the experiments.The results showed that: (i) minute changes in the transmissibility and mean infectious period significantly influenced the attack rate; (ii) the mean of the incubation period distribution appeared to be sufficient for determining its effects on the dynamics of epidemics; (iii) the infectious period distribution had the strongest influence on the structure of the epidemic curves; (iv) the sensitivity of the individual-based model was consistent across social networks investigated in this study and (v) age-specific epidemics were sensitive to changes in the mean infectious period irrespective of the susceptibility of the other age groups. These findings suggest that small changes in some of the disease model parameters can significantly influence the uncertainty observed in real-time forecasting and predicting of the characteristics of an epidemic.     

Spatial and temporal invasion dynamics of the 2014–2017 Zika and chikungunya epidemics in Colombia

Zika virus (ZIKV) and chikungunya virus (CHIKV) were recently introduced into the Americas resulting in significant disease burdens. Understanding their spatial and temporal dynamics at the subnational level is key to informing surveillance and preparedness for future epidemics. We analyzed anonymized line list data on approximately 105,000 Zika virus disease and 412,000 chikungunya fever suspected and laboratory-confirmed cases during the 2014–2017 epidemics. We first determined the week of invasion in each city. Out of 1,122, 288 cities met criteria for epidemic invasion by ZIKV and 338 cities by CHIKV. We analyzed risk factors for invasion using linear and logistic regression models. We also estimated that the geographic origin of both epidemics was located in Barranquilla, north Colombia. We assessed the spatial and temporal invasion dynamics of both viruses to analyze transmission between cities using a suite of (i) gravity models, (ii) Stouffer’s rank models, and (iii) radiation models with two types of distance metrics, geographic distance and travel time between cities. Invasion risk was best captured by a gravity model when accounting for geographic distance and intermediate levels of density dependence; Stouffer’s rank model with geographic distance performed similarly well. Although a few long-distance invasion events occurred at the beginning of the epidemics, an estimated distance power of 1.7 (95% CrI: 1.5–2.0) from the gravity models suggests that spatial spread was primarily driven by short-distance transmission. Similarities between the epidemics were highlighted by jointly fitted models, which were preferred over individual models when the transmission intensity was allowed to vary across arboviruses. However, ZIKV spread considerably faster than CHIKV.     

Downy mildew (Plasmopara viticola) epidemics on grapevine under climate change

As climate is a key agro‐ecosystem driving force, climate change could have a severe impact on agriculture. Many assessments have been carried out to date on the possible effects of climate change (temperature, precipitation and carbon dioxide concentration changes) on plant physiology. At present however, likely effects on plant pathogens have not been investigated deeply. The aim of this work was to simulate future scenarios of downy mildew (Plasmopara viticola) epidemics on grape under climate change, by combining a disease model to output from two general circulation models (GCMs). Model runs corresponding to the SRES‐A2 emissions scenario, characterized by high projections of both population and greenhouse gas emissions from present to 2100, were chosen in order to investigate impacts of worst‐case scenarios, among those currently available from IPCC. Three future decades were simulated (2030, 2050, 2080), using as baseline historical series of meteorological data collected from 1955 to 2001 in Acqui Terme, an important grape‐growing area in the north‐west of Italy. Both GCMs predicted increase of temperature and decrease of precipitation in this region. The simulations obtained by combining the disease model to the two GCM outputs predicted an increase of the disease pressure in each decade: more severe epidemics were a direct consequence of more favourable temperature conditions during the months of May and June. These negative effects of increasing temperatures more than counterbalanced the effects of precipitation reductions, which alone would have diminished disease pressure. Results suggested that, as adaptation response to future climate change, more attention would have to be paid in the management of early downy mildew infections; two more fungicide sprays were necessary under the most negative climate scenario, compared with present management regimes. At the same time, increased knowledge on the effects of climate change on host–pathogen interactions will be necessary to improve current predictions.     

Modeling routes of chronic wasting disease transmission: environmental prion persistence promotes deer population decline and extinction

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsin's CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R(0), may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the host's life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress.     

Vaccination against Foot-And-Mouth Disease: Do Initial Conditions Affect Its Benefit?

When facing incursion of a major livestock infectious disease, the decision to implement a vaccination programme is made at the national level. To make this decision, governments must consider whether the benefits of vaccination are sufficient to outweigh potential additional costs, including further trade restrictions that may be imposed due to the implementation of vaccination. However, little consensus exists on the factors triggering its implementation on the field. This work explores the effect of several triggers in the implementation of a reactive vaccination-to-live policy when facing epidemics of foot-and-mouth disease. In particular, we tested whether changes in the location of the incursion and the delay of implementation would affect the epidemiological benefit of such a policy in the context of Scotland. To reach this goal, we used a spatial, premises-based model that has been extensively used to investigate the effectiveness of mitigation procedures in Great Britain. The results show that the decision to vaccinate, or not, is not straightforward and strongly depends on the underlying local structure of the population-at-risk. With regards to disease incursion preparedness, simply identifying areas of highest population density may not capture all complexities that may influence the spread of disease as well as the benefit of implementing vaccination. However, if a decision to vaccinate is made, we show that delaying its implementation in the field may markedly reduce its benefit. This work provides guidelines to support policy makers in their decision to implement, or not, a vaccination-to-live policy when facing epidemics of infectious livestock disease.     

Disease contact tracing in random and clustered networks

The efficacy of contact tracing, be it between individuals (e.g. sexually transmitted diseases or severe acute respiratory syndrome) or between groups of individuals (e.g. foot-and-mouth disease; FMD), is difficult to evaluate without precise knowledge of the underlying contact structure; i.e. who is connected to whom? Motivated by the 2001 FMD epidemic in the UK, we determine, using stochastic simulations and deterministic 'moment closure' models of disease transmission on networks of premises (nodes), network and disease properties that are important for contact tracing efficiency. For random networks with a high average number of connections per node, little clustering of connections and short latency periods, contact tracing is typically ineffective. In this case, isolation of infected nodes is the dominant factor in determining disease epidemic size and duration. If the latency period is longer and the average number of connections per node small, or if the network is spatially clustered, then the contact tracing performs better and an overall reduction in the proportion of nodes that are removed during an epidemic is observed.     

Disease Prevention versus Data Privacy: Using Landcover Maps to Inform Spatial Epidemic Models

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock.     

The potential effects of climate change on winter mortality in England and Wales

In Britain death rates from several important causes, particularly circulatory and respiratory diseases, rise markedly during the colder winter months. This close association between temperature and mortality suggests that climate change as a result of global warming may lead to a future reduction in excess winter deaths. This paper gives a brief introductory review of the literature on the links between cold conditions and health, and statistical models are subsequently developed of the associations between temperature and monthly mortality rates for the years 1968 to 1988 for England and Wales. Other factors, particularly the occurrence of influenza epidemics, are also taken into account. Highly significant negative associations were found between temperature and death rates from all causes and from chronic bronchitis, pneumonia, ischaemic heart disease and cerebrovascular disease. The statistical models developed from this analysis were used to compare death rates for current conditions with those that might be expected to occur in a future warmer climate. The results indicate that the higher temperatures predicted for 2050 might result in nearly 9000 fewer winter deaths each year with the largest contribution being from mortality from ischaemic heart disease. However, these preliminary estimates might change when further research is able to make into account a number of additional factors affecting the relationship between mortality and climate.