Analytical methods for quantifying environmental connectivity for the control and surveillance of infectious disease spread

The sustained transmission and spread of environmentally mediated infectious diseases is governed in part by the dispersal of parasites, disease vectors and intermediate hosts between sites of transmission. Functional geospatial models can be used to quantify and predict the degree to which environmental features facilitate or limit connectivity between target populations, yet typical models are limited in their geographical and analytical approach, providing simplistic, global measures of connectivity and lacking methods to assess the epidemiological implications of fine-scale heterogeneous landscapes. Here, functional spatial models are applied to problems of surveillance and control of the parasitic blood fluke Schistosoma japonicum and its intermediate snail host Oncomelania haupensis in western China. We advance functional connectivity methods by providing an analytical framework to (i) identify nodes of transmission where the degree of connectedness to other villages, and thus the potential for disease spread, is higher than is estimated using Euclidean distance alone and (ii) (re)organize transmission sites into disease surveillance units based on second-order relationships among nodes using non-Euclidean distance measures, termed effective geographical distance (EGD). Functional environmental models are parametrized using ecological information on the target organisms, and pair-wise distributions of inter-node EGD are estimated. A Monte Carlo rank product analysis is presented to identify nearby nodes under alternative distance models. Nodes are then iteratively embedded into EGD space and clustered using a k-means algorithm to group villages into ecologically meaningful surveillance groups. A consensus clustering approach is taken to derive the most stable cluster structure. The results indicate that novel relationships between nodes are revealed when non-Euclidean, ecologically determined distance measures are used to quantify connectivity in heterogeneous landscapes. These connections are not evident when analysing nodes in Euclidean space, and thus surveillance and control activities planned using Euclidean distance measures may be suboptimal. The methods developed here provide a quantitative framework for assessing the effectiveness of ecologically grounded surveillance systems and of control and prevention strategies for environmentally mediated diseases.     

Spatial dynamics of the 1918 influenza pandemic in England,Wales and the United States

There is still limited understanding of key determinants of spatial spread of influenza. The 1918 pandemic provides an opportunity to elucidate spatial determinants of spread on a large scale.To better characterize the spread of the 1918 major wave, we fitted a range of city-to-city transmission models to mortality data collected for 246 population centres in England and Wales and 47 cities in the US. Using a gravity model for city-to-city contacts, we explored the effect of population size and distance on the spread of disease and tested assumptions regarding density dependence in connectivity between cities. We employed Bayesian Markov Chain Monte Carlo methods to estimate parameters of the model for population, infectivity, distance and density dependence. We inferred the most likely transmission trees for both countries.For England and Wales, a model that estimated the degree of density dependence in connectivity between cities was preferable by deviance information criterion comparison. Early in the major wave, long distance infective interactions predominated, with local infection events more likely as the epidemic became widespread. For the US, with fewer more widely dispersed cities, statistical power was lacking to estimate population size dependence or the degree of density dependence, with the preferred model depending on distance only. We find that parameters estimated from the England and Wales dataset can be applied to the US data with no likelihood penalty.     

Utility of R0 as a predictor of disease invasion in structured populations

Early theoretical work on disease invasion typically assumed large and well-mixed host populations. Many human and wildlife systems, however, have small groups with limited movement among groups. In these situations, the basic reproductive number, R0, is likely to be a poor predictor of a disease pandemic because it typically does not account for group structure and movement of individuals among groups. We extend recent work by combining the movement of hosts, transmission within groups, recovery from infection and the recruitment of new susceptibles into a stochastic model of disease in a host metapopulation. We focus on how recruitment of susceptibles affects disease invasion and how population structure can affect the frequency of superspreading events (SSEs). We show that the frequency of SSEs may decrease with the reduced movement and the group sizes due to the limited number of susceptible individuals available. Classification tree analysis of the model results illustrates the hierarchical nature of disease invasion in host metapopulations. First, the pathogen must effectively transmit within a group (R0>1), and then the pathogen must persist within a group long enough to allow for movement among the groups. Therefore, the factors affecting disease persistence--such as infectious period, group size and recruitment of new susceptibles--are as important as the local transmission rates in predicting the spread of pathogens across a metapopulation.     

Great cities look small

Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety. Attempts at estimating them often rely on unrealistic over-simplifications such as the assumption of spatial homogeneity. Here we propose a mathematical model of human interactions in terms of a local strategy of maximizing the number of beneficial connections attainable under the constraint of limited individual travelling-time budgets. By incorporating census and openly available online multi-modal transport data, we are able to characterize the connectivity of geometrically and topologically complex cities. Beyond providing a candidate measure of greatness, this model allows one to quantify and assess the impact of transport developments, population growth, and other infrastructure and demographic changes on a city. Supported by validations of gross domestic product and human immunodeficiency virus infection rates across US metropolitan areas, we illustrate the effect of changes in local and city-wide connectivities by considering the economic impact of two contemporary inter- and intra-city transport developments in the UK: High Speed 2 and London Crossrail. This derivation of the model suggests that the scaling of different urban indicators with population size has an explicitly mechanistic origin.     

Anticipating infectious disease re-emergence and elimination: a test of early warning signals using empirically based models

Timely forecasts of the emergence, re-emergence and elimination of human infectious diseases allow for proactive, rather than reactive, decisions that save lives. Recent theory suggests that a generic feature of dynamical systems approaching a tipping point—early warning signals (EWS) due to critical slowing down (CSD)—can anticipate disease emergence and elimination. Empirical studies documenting CSD in observed disease dynamics are scarce, but such demonstration of concept is essential to the further development of model-independent outbreak detection systems. Here, we use fitted, mechanistic models of measles transmission in four cities in Niger to detect CSD through statistical EWS. We find that several EWS accurately anticipate measles re-emergence and elimination, suggesting that CSD should be detectable before disease transmission systems cross key tipping points. These findings support the idea that statistical signals based on CSD, coupled with decision-support algorithms and expert judgement, could provide the basis for early warning systems of disease outbreaks.     

Inferring environmental transmission using phylodynamics: a case-study using simulated evolution of an enteric pathogen

Indirect (environmental) and direct (host–host) transmission pathways cannot easily be distinguished when they co-occur in epidemics, particularly when they occur on similar time scales. Phylodynamic reconstruction is a potential approach to this problem that combines epidemiological information (temporal, spatial information) with pathogen whole-genome sequencing data to infer transmission trees of epidemics. However, factors such as differences in mutation and transmission rates between host and non-host environments may obscure phylogenetic inference from these methods. In this study, we used a network-based transmission model that explicitly models pathogen evolution to simulate epidemics with both direct and indirect transmission. Epidemics were simulated according to factorial combinations of direct/indirect transmission proportions, host mutation rates and conditions of environmental pathogen growth. Transmission trees were then reconstructed using the phylodynamic approach SCOTTI (structured coalescent transmission tree inference) and evaluated. We found that although insufficient diversity sets a lower bound on when accurate phylodynamic inferences can be made, transmission routes and assumed pathogen lifestyle affected pathogen population structure and subsequently influenced both reconstruction success and the likelihood of direct versus indirect pathways being reconstructed. We conclude that prior knowledge of the likely ecology and population structure of pathogens in host and non-host environments is critical to fully using phylodynamic techniques.     

Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity

Dengue, a mosquito-borne virus of humans, infects over 50 million people annually. Infection with any of the four dengue serotypes induces protective immunity to that serotype, but does not confer long-term protection against infection by other serotypes. The immunological interactions between serotypes are of central importance in understanding epidemiological dynamics and anticipating the impact of dengue vaccines. We analysed a 38-year time series with 12 197 serotyped dengue infections from a hospital in Bangkok, Thailand. Using novel mechanistic models to represent different hypothesized immune interactions between serotypes, we found strong evidence that infection with dengue provides substantial short-term cross-protection against other serotypes (approx. 1–3 years). This is the first quantitative evidence that short-term cross-protection exists since human experimental infection studies performed in the 1950s. These findings will impact strategies for designing dengue vaccine studies, future multi-strain modelling efforts, and our understanding of evolutionary pressures in multi-strain disease systems.     

Comparing transmission potential networks based on social network surveys,close contacts and environmental overlap in rural Madagascar

Social and spatial network analysis is an important approach for investigating infectious disease transmission, especially for pathogens transmitted directly between individuals or via environmental reservoirs. Given the diversity of ways to construct networks, however, it remains unclear how well networks constructed from different data types effectively capture transmission potential. We used empirical networks from a population in rural Madagascar to compare social network survey and spatial data-based networks of the same individuals. Close contact and environmental pathogen transmission pathways were modelled with the spatial data. We found that naming social partners during the surveys predicted higher close-contact rates and the proportion of environmental overlap on the spatial data-based networks. The spatial networks captured many strong and weak connections that were missed using social network surveys alone. Across networks, we found weak correlations among centrality measures (a proxy for superspreading potential). We conclude that social network surveys provide important scaffolding for understanding disease transmission pathways but miss contact-specific heterogeneities revealed by spatial data. Our analyses also highlight that the superspreading potential of individuals may vary across transmission modes. We provide detailed methods to construct networks for close-contact transmission pathogens when not all individuals simultaneously wear GPS trackers.     

A unifying framework for quantifying the nature of animal interactions

Collective phenomena, whereby agent–agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite both types of interaction fundamentally influencing animal behaviour, there has hitherto been no unifying framework for the models proposed in both areas. Here, we construct a general method for inferring population-level spatial patterns from underlying individual movement and interaction processes, a key ingredient in building a statistical mechanics for ecological systems. We show that resource selection functions, as well as several examples of collective motion models, arise as special cases of our framework, thus bringing together resource selection analysis and collective animal behaviour into a single theory. In particular, we focus on combining the various mechanistic models of territorial interactions in the literature with step selection functions, by incorporating interactions into the step selection framework and demonstrating how to derive territorial patterns from the resulting models. We demonstrate the efficacy of our model by application to a population of insectivore birds in the Amazon rainforest.     

Mechanistic movement models reveal ecological drivers of tick-borne pathogen spread

Identifying ecological drivers of tick-borne pathogen spread has great value for tick-borne disease management. However, theoretical investigations into the consequences of host movement behaviour on pathogen spread dynamics in heterogeneous landscapes remain limited because spatially explicit epidemiological models that incorporate more realistic mechanisms governing host movement are rare. We built a mechanistic movement model to investigate how the interplay between multiple ecological drivers affects the risk of tick-borne pathogen spread across heterogeneous landscapes. We used the model to generate simulations of tick dispersal by migratory birds and terrestrial hosts across theoretical landscapes varying in resource aggregation, and we performed a sensitivity analysis to explore the impacts of different parameters on the infected tick spread rate, tick infection prevalence and infected tick density. Our findings highlight the importance of host movement and tick population dynamics in explaining the infected tick spread rate into new regions. Tick infection prevalence and infected tick density were driven by predictors related to the infection process and tick population dynamics, respectively. Our results suggest that control strategies aiming to reduce tick burden on tick reproduction hosts and encounter rate between immature ticks and pathogen amplification hosts will be most effective at reducing tick-borne disease risk.     

Connectivity sustains disease transmission in environments with low potential for endemicity: modelling schistosomiasis with hydrologic and social connectivities

Social interaction and physical interconnections between populations can influence the spread of parasites. The role that these pathways play in sustaining the transmission of parasitic diseases is unclear, although increasingly realistic metapopulation models are being used to study how diseases persist in connected environments. We use a mathematical model of schistosomiasis transmission for a distributed set of heterogeneous villages to show that the transport of parasites via social (host movement) and environmental (parasite larvae movement) pathways has consequences for parasite control, spread and persistence. We find that transmission can be sustained regionally throughout a group of connected villages even when individual village conditions appear not to support endemicity. Optimum transmission is determined by an interplay between different transport pathways, and not necessarily by those that are the most dispersive (e.g. disperse social contacts may not be optimal for transmission). We show that the traditional targeting of villages with high infection, without regard to village interconnections, may not lead to optimum control. These findings have major implications for effective disease control, which needs to go beyond considering local variations in disease intensity, to also consider the degree to which populations are interconnected.     

Optimal two-dimensional layout of industrial facilities

Layout is an important aspect of the design of industrial plants. In this paper a mathematical model is presented for the design of efficient and generic industrial layouts where a simultaneous solution of the block and detailed layout problem is considered. The optimal plant layout is obtained based on the minimization of the connectivity cost. Connectivity can describe simple pipe connections, guided vehicles or conveyors amongst others. Different topological characteristics are considered such as different equipment orientations, distance restrictions, non-overlapping constraints, different equipment connectivity inputs and outputs, irregular equipment shapes and space availability over a two-dimensional continuous area. In operational terms, production together with operational sections are modelled as well as safety and operability restrictions. A Mixed-Integer Linear Problem (MILP) is developed where binary variables are introduced to characterize topological choices and continuous variables describe the distances and locations involved. To conclude, the applicability of the proposed formulation is illustrated via a set of representative examples.     

Parameterizing state–space models for infectious disease dynamics by generalized profiling: measles in Ontario

Parameter estimation for infectious disease models is important for basic understanding (e.g. to identify major transmission pathways), for forecasting emerging epidemics, and for designing control measures. Differential equation models are often used, but statistical inference for differential equations suffers from numerical challenges and poor agreement between observational data and deterministic models. Accounting for these departures via stochastic model terms requires full specification of the probabilistic dynamics, and computationally demanding estimation methods. Here, we demonstrate the utility of an alternative approach, generalized profiling, which provides robustness to violations of a deterministic model without needing to specify a complete probabilistic model. We introduce novel means for estimating the robustness parameters and for statistical inference in this framework. The methods are applied to a model for pre-vaccination measles incidence in Ontario, and we demonstrate the statistical validity of our inference through extensive simulation. The results confirm that school term versus summer drives seasonality of transmission, but we find no effects of short school breaks and the estimated basic reproductive ratio ℛ₀ greatly exceeds previous estimates. The approach applies naturally to any system for which candidate differential equations are available, and avoids many challenges that have limited Monte Carlo inference for state–space models.     

Disease transmission in territorial populations: the small-world network of Serengeti lions

Territoriality in animal populations creates spatial structure that is thought to naturally buffer disease invasion. Often, however, territorial populations also include highly mobile, non-residential individuals that potentially serve as disease superspreaders. Using long-term data from the Serengeti Lion Project, we characterize the contact network structure of a territorial wildlife population and address the epidemiological impact of nomadic individuals. As expected, pride contacts are dominated by interactions with neighbouring prides and interspersed by encounters with nomads as they wander throughout the ecosystem. Yet the pride–pride network also includes occasional long-range contacts between prides, making it surprisingly small world and vulnerable to epidemics, even without nomads. While nomads increase both the local and global connectivity of the network, their epidemiological impact is marginal, particularly for diseases with short infectious periods like canine distemper virus. Thus, territoriality in Serengeti lions may be less protective and non-residents less important for disease transmission than previously considered.     

Comparing approaches for modelling indirect contact transmission of infectious diseases

Mathematical models describing indirect contact transmission are an important component of infectious disease mitigation and risk assessment. A model that tracks microorganisms between compartments by coupled ordinary differential equations or a Markov chain is benchmarked against a mechanistic interpretation of the physical transfer of microorganisms from surfaces to fingers and subsequently to a susceptible person''s facial mucosal membranes. The primary objective was to compare these models in their estimates of doses and changes in microorganism concentrations on hands and fomites over time. The abilities of the models to capture the impact of episodic events, such as hand hygiene, and of contact patterns were also explored. For both models, greater doses were estimated for the asymmetrical scenarios in which a more contaminated fomite was touched more often. Differing representations of hand hygiene in the Markov model did not notably impact estimated doses but affected pathogen concentration dynamics on hands. When using the Markov model, losses due to hand hygiene should be handled as separate events as opposed to time-averaging expected losses. The discrete event model demonstrated the effect of hand-to-mouth contact timing on the dose. Understanding how model design influences estimated doses is important for advancing models as reliable risk assessment tools.     

Effect of data quality on estimates of farm infectiousness trends in the UK 2001 foot-and-mouth disease epidemic

Most of the mathematical models that were developed to study the UK 2001 foot-and-mouth disease epidemic assumed that the infectiousness of infected premises was constant over their infectious periods. However, there is some controversy over whether this assumption is appropriate. Uncertainty about which farm infected which in 2001 means that the only method to determine if there were trends in farm infectiousness is the fitting of mechanistic mathematical models to the epidemic data. The parameter values that are estimated using this technique, however, may be influenced by missing and inaccurate data. In particular to the UK 2001 epidemic, this includes unreported infectives, inaccurate farm infection dates and unknown farm latent periods. Here, we show that such data degradation prevents successful determination of trends in farm infectiousness.     

Estimating epidemic coupling between populations from the time to invasion

Identifying the mechanisms by which diseases spread among populations is important for understanding and forecasting patterns of epidemics and pandemics. Estimating transmission coupling among populations is challenging because transmission events are difficult to observe in practice, and connectivity among populations is often obscured by local disease dynamics. We consider the common situation in which an epidemic is seeded in one population and later spreads to a second population. We present a method for estimating transmission coupling between the two populations, assuming they can be modelled as susceptible–infected–removed (SIR) systems. We show that the strength of coupling between the two populations can be estimated from the time taken for the disease to invade the second population. Confidence in the estimate is low if only a single invasion event has been observed, but is substantially improved if numerous independent invasion events are observed. Our analysis of this simplest, idealized scenario represents a first step toward developing and verifying methods for estimating epidemic coupling among populations in an ever-more-connected global human population.     

Connectivity and piezoelectric-pyroelectric composites

Connectivity is a critical parameter in composites designed for use as piezoelectric transducers or as pyroelectric detectors. There are ten important connectivity patterns in diphasic solids, ranging from a 0-0 unconnected checkerboard pattern to a 3-3 pattern in which both phases are three dimensionally self-connected. Processing methods for manufacturing some of these patterns are described. Series and parallel models for composite piezoelectrics and pyroelectrics lead to several interesting results, such as a diphasic pyroelectric in which neither phase is pyroelectric. The models are also helpful in interpreting the structure-property relations in single-phase materials where the crystal structures mimic certain connectivity patterns.     

Spatial generalized linear mixed models of electric power outages due to hurricanes and ice storms

This paper presents new statistical models that predict the number of hurricane- and ice storm-related electric power outages likely to occur in each 3 km×3 km grid cell in a region. The models are based on a large database of recent outages experienced by three major East Coast power companies in six hurricanes and eight ice storms. A spatial generalized linear mixed modeling (GLMM) approach was used in which spatial correlation is incorporated through random effects. Models were fitted using a composite likelihood approach and the covariance matrix was estimated empirically. A simulation study was conducted to test the model estimation procedure, and model training, validation, and testing were done to select the best models and assess their predictive power. The final hurricane model includes number of protective devices, maximum gust wind speed, hurricane indicator, and company indicator covariates. The final ice storm model includes number of protective devices, ice thickness, and ice storm indicator covariates. The models should be useful for power companies as they plan for future storms. The statistical modeling approach offers a new way to assess the reliability of electric power and other infrastructure systems in extreme events.     

Statistical evaluation of resilient models characterizing coarse granular materials

Consistent material modeling is a prerequisite for a mechanistic approach to pavement design. The scope of this investigation was to statistically evaluate the efficiency of various resilient models commonly encountered in highway engineering. These models were categorized as describing either resilient modulus or shear and volumetric strains. Triaxial tests using constant and cyclic confining pressure were performed on coarse granular materials of various gradings (maximum particle size 90 mm). Two statistical methods, the extra sum of squares F-test and the Akaike information criterion, were used for model comparison. Concerning resilient modulus, the Uzan model provided, in general, a statistically significant improvement compared to the k–θ model. However, this improvement is lost if a constant Poisson ratio is used to predict shear and volumetric strains. In case of the shear–volumetric approach, no single model was most likely to be the best model for all gradings studied.