Prospects for detecting early warning signals in discrete event sequence data : application to epidemiological incidence data

Early warning signals (EWS) identify systems approaching a critical transition, where the system undergoes a sudden change in state. For example, monitoring changes in variance or autocorrelation offers a computationally inexpensive method which can be used in real-time to assess when an infectious disease transitions to elimination. EWS have a promising potential to not only be used to monitor infectious diseases, but also to inform control policies to aid disease elimination. Previously, potential EWS have been identified for prevalence data, however the prevalence of a disease is often not known directly. In this work we identify EWS for incidence data, the standard data type collected by the Centers for Disease Control and Prevention (CDC) or World Health Organization (WHO). We show, through several examples, that EWS calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data. In particular, the variance displays a decreasing trend on the approach to disease elimination, contrary to that expected from critical slowing down theory; this could lead to unreliable indicators of elimination when calculated on real-world data. We derive analytical predictions which can be generalised for many epidemiological systems, and we support our theory with simulated studies of disease incidence. Additionally, we explore EWS calculated on the rate of incidence over time, a property which can be extracted directly from incidence data. We find that although incidence might not exhibit typical critical slowing down properties before a critical transition, the rate of incidence does, presenting a promising new data type for the application of statistical indicators

Rapid simulation of spatial epidemics : a spectral method

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

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

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

Жидкофазные коллоиды серебра и меди, получаемые электронно-лучевым испарением металлов в вакууме

ЭЛЕКТРОННО-ЛУЧЕВАЯ ТЕХНОЛОГИЯКОЛЛОИДЫНАНОЧАСТИЦЫ МЕДИНАНОЧАСТИЦЫ СЕРЕБРАДИСПЕРСНО-УПРОЧНЕННЫЕ МАТЕРИАЛЫНАНОТЕХНОЛОГИ

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

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

Insights from quantitative and mathematical modelling on the proposed 2030 goals for Yaws.

The World Health Organization is currently developing 2030 goals for neglected tropical diseases (NTDs). In these, yaws has been targeted for eradication by 2030, with 50% of member states certified free of yaws transmission by 2023. Here we summarise the yaws modelling literature and discuss the proposed goal and strategy. The current Morges strategy involves rounds of Total Community Treatment (TCT), in which all members of the community are treated, and Total Targeted Treatment (TTT), treating active cases and their contacts. However, modelling and empirical work suggest that latent infections are often not found in the same household as active cases, reducing the utility of household-based contact tracing for a TTT strategy. Economic modelling has also discovered uncertainty in the cost of eradication, requiring further data to give greater information. We also note the need for improved active surveillance in previously endemic countries, in order to plan future intervention efforts and ensure global eradication

Disentangling the influence of livestock vs. farm density on livestock disease epidemics

Susceptible host density is a key factor that influences the success of invading pathogens. However, for diseases affecting livestock, there are two aspects of host density: livestock and farm density, which are seldom considered independently. Traditional approaches of simulating disease outbreaks on real‐world farm data make dissecting the relative importance of farm and livestock density difficult owing to their inherent correlation in many farming regions. We took steps to disentangle these densities and study their relative influences on epidemic size by simulating foot‐and‐mouth disease outbreaks on factorial combinations of cattle and farm populations in artificial county areas, resulting in 50 unique cattle/farm density combinations. In these simulations, increasing cattle density always resulted in larger epidemics, regardless of farm density. Alternatively, increasing farm density only led to larger epidemics in scenarios of high cattle density. We compared these results with simulations performed on real‐world farm data from the United States, where we initiated outbreaks in U.S. counties that varied in county‐level cattle density and farm density. We found a similar, but weaker relationship between cattle density and epidemic size in the U.S. simulations. We tested the sensitivity of these outcomes to variation in pathogen dispersal and farm‐level susceptibility model parameters and found that although variation in these parameters quantitatively influenced the size of the epidemic, they did not qualitatively change the relative influence of cattle vs. farm density in factorial simulations. By reducing the correlation between farm and livestock density in factorial simulations, we were able to clearly demonstrate the increase in epidemic size that occurred as farm sizes grew larger (i.e., through increasing county‐level cattle populations), across levels of farm density. These results suggest livestock production trends in many industrialized countries that concentrate livestock on fewer, but larger farms have the potential to facilitate larger livestock epidemics

Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic

Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic