Generalized reproduction numbers and the prediction of patterns in waterborne disease

Informing policy via dynamic models: Cholera in Haiti

Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.

Emergent encoding of dispersal network topologies in spatial metapopulation models

We address a generalization of the concept of metapopulation capacity for trees and networks acting as the template for ecological interactions. The original measure had been derived from an insightful phenomenological model and is based on the leading eigenvalue of a suitable landscape matrix. It yields a versatile predictor of metapopulation persistence through a threshold value of the eigenvalue determined by ecological features of the focal species. Here, we present an analytical solution to a fundamental microscopic model that incorporates key ingredients of metapopulation dynamics and explicitly distinguishes between individuals comprising the "settled population" and "explorers" seeking colonization. Our approach accounts for general network characteristics (in particular graph-driven directional dispersal which is known to significantly constrain many ecological estimates) and yields a generalized version of the original model, to which it reduces for particular cases. Through examples, including real landscapes used as the template, we compare the predictions from our approach with those of the standard model. Results suggest that in several cases of practical interest, differences are significant. We also examine, with both models, how changes in habitat fragmentation, including removal, addition, or alteration in size, affect metapopulation persistence. The current approach demonstrates a high level of flexibility, enabling the incorporation of diverse "microscopic" elements and their impact on the resulting biodiversity landscape pattern.

Epidemicity of cholera spread and the fate of infection control measures

The fate of ongoing infectious disease outbreaks is predicted through reproduction numbers, defining the long-term establishment of the infection, and epidemicity indices, tackling the reactivity of the infectious pool to new contagions. Prognostic metrics of unfolding outbreaks are of particular importance when designing adaptive emergency interventions facing real-time assimilation of epidemiological evidence. Our aim here is twofold. First, we propose a novel form of the epidemicity index for the characterization of cholera epidemics in spatial models of disease spread. Second, we examine in hindsight the survey of infections, treatments and containment measures carried out for the now extinct 2010–2019 Haiti cholera outbreak, to suggest that magnitude and timing of non-pharmaceutical and vaccination interventions imply epidemiological responses recapped by the evolution of epidemicity indices. Achieving negative epidemicity greatly accelerates fading of infections and thus proves a worthwhile target of containment measures. We also show that, in our model, effective reproduction numbers and epidemicity indices are explicitly related. Therefore, providing an upper bound to the effective reproduction number (significantly lower than the unit threshold) warrants negative epidemicity and, in turn, a rapidly fading outbreak preventing coalescence of sparse local sub-threshold flare-ups.

The epidemicity index of recurrent SARS-CoV-2 infections

Several indices can predict the long-term fate of emerging infectious diseases and the effect of their containment measures, including a variety of reproduction numbers (e.g. [Formula: see text]). Other indices evaluate the potential for transient increases of epidemics eventually doomed to disappearance, based on generalized reactivity analysis. They identify conditions for perturbations to a stable disease-free equilibrium ([Formula: see text]) to grow, possibly causing significant damage. Here, we introduce the epidemicity index e0, a threshold-type indicator: if e0 > 0, initial foci may cause infection peaks even if [Formula: see text]. Therefore, effective containment measures should achieve a negative epidemicity index. We use spatially explicit models to rank containment measures for projected evolutions of the ongoing pandemic in Italy. There, we show that, while the effective reproduction number was below one for a sizable timespan, epidemicity remained positive, allowing recurrent infection flare-ups well before the major epidemic rebounding observed in the fall.

Assessing sub-regional-specific strengths of healthcare systems associated with COVID-19 prevalence, deaths and recoveries in Africa

Introduction

The coronavirus 2019 (COVID-19) has overwhelmed the health systems of several countries, particularly those within the African region. Notwithstanding, the relationship between health systems and the magnitude of COVID-19 in African countries have not received research attention. In this study, we investigated the relationship between the pervasiveness of the pandemic across African countries and their Global Health Security Index (GHSI) scores.

Materials and methods

The study included 54 countries in five regions viz Western (16); Eastern (18); Middle (8); Northern (7); and Southern (5) Africa. The outcome variables in this study were the total confirmed COVID-19 cases (per million); total recoveries (per million); and the total deaths (per million). The data were subjected to Spearman’s rank-order (Spearman’s rho) correlation to determine the monotonic relationship between each of the predictor variables and the outcome variables. The predictor variables that showed a monotonic relationship with the outcome were used to predict respective outcome variables using multiple regressions. The statistical analysis was conducted at a significance level of 0.05.

Results

Our results indicate that total number of COVID-19 cases (per million) has strong correlations (r_s >0.5) with the median age; aged 65 older; aged 70 older; GDP per capita; number of hospital beds per thousand; Human Development Index (HDI); recoveries (per million); and the overall risk environment of a country. All these factors including the country’s commitments to improving national capacity were related to the total number of deaths (per million). Also, strong correlations existed between the total recoveries (per million) and the total number of positive cases; total deaths (per million); median age; aged 70 older; GDP per capita; the number of hospital beds (per thousand); and HDI. The fitted regression models showed strong predictive powers (R-squared>99%) of the variances in the total number of COVID-19 cases (per million); total number of deaths (per million); and the total recoveries (per million).

Conclusions

The findings from this study suggest that patient-level characteristics such as ageing population (i.e., 65⁺), poverty, underlying co-morbidities–cardiovascular disease (e.g., hypertension), and diabetes through unhealthy behaviours like smoking as well as hospital care (i.e., beds per thousand) can help explain COVID-19 confirmed cases and mortality rates in Africa. Aside from these, other determinants (e.g., population density, the ability of detection, prevention and control) also affect COVID-19 prevalence, deaths and recoveries within African countries and sub-regions.

Scaling of contact networks for epidemic spreading in urban transit systems

Improved mobility not only contributes to more intensive human activities but also facilitates the spread of communicable disease, thus constituting a major threat to billions of urban commuters. In this study, we present a multi-city investigation of communicable diseases percolating among metro travelers. We use smart card data from three megacities in China to construct individual-level contact networks, based on which the spread of disease is modeled and studied. We observe that, though differing in urban forms, network layouts, and mobility patterns, the metro systems of the three cities share similar contact network structures. This motivates us to develop a universal generation model that captures the distributions of the number of contacts as well as the contact duration among individual travelers. This model explains how the structural properties of the metro contact network are associated with the risk level of communicable diseases. Our results highlight the vulnerability of urban mass transit systems during disease outbreaks and suggest important planning and operation strategies for mitigating the risk of communicable diseases.

Sensor-based localization of epidemic sources on human mobility networks

We investigate the source detection problem in epidemiology, which is one of the most important issues for control of epidemics. Mathematically, we reformulate the problem as one of identifying the relevant component in a multivariate Gaussian mixture model. Focusing on the study of cholera and diseases with similar modes of transmission, we calibrate the parameters of our mixture model using human mobility networks within a stochastic, spatially explicit epidemiological model for waterborne disease. Furthermore, we adopt a Bayesian perspective, so that prior information on source location can be incorporated (e.g., reflecting the impact of local conditions). Posterior-based inference is performed, which permits estimates in the form of either individual locations or regions. Importantly, our estimator only requires first-arrival times of the epidemic by putative observers, typically located only at a small proportion of nodes. The proposed method is demonstrated within the context of the 2000-2002 cholera outbreak in the KwaZulu-Natal province of South Africa.

Tracking the source of an epidemic outbreak is of crucial importance as it allows for identification of communities where control efforts should be focused for both short and long-term management and control of the disease. However, such identification is often problematic, time-consuming, and data-intensive. Recently network-based analysis approaches have been established for source detection to account for complex modern spreading, driven substantially by human mobility. Here we develop a probabilistic framework for waterborne disease, that allows investigators to infer the community or the region sparking an outbreak based on a sparse surveillance network. The framework can integrate prior information on the likelihood of a community being the source, for instance as a function of population size or hygiene conditions. Furthermore, we assign an accuracy measure to the resulting source estimate, which is crucial for its practical usability. We test the method in the context of the 2000-2002 cholera outbreak in the KwaZulu-Natal province with promising results. Moreover, we outline a series of guidelines in terms of data needs and preliminary operations to implement the proposed framework in practice.

Modeling epidemic spreading through public transit using time-varying encounter network

Passenger contact in public transit (PT) networks can be a key mediate in the spreading of infectious diseases. This paper proposes a time-varying weighted PT encounter network to model the spreading of infectious diseases through the PT systems. Social activity contacts at both local and global levels are also considered. We select the epidemiological characteristics of coronavirus disease 2019 (COVID-19) as a case study along with smart card data from Singapore to illustrate the model at the metropolitan level. A scalable and lightweight theoretical framework is derived to capture the time-varying and heterogeneous network structures, which enables to solve the problem at the whole population level with low computational costs. Different control policies from both the public health side and the transportation side are evaluated. We find that people's preventative behavior is one of the most effective measures to control the spreading of epidemics. From the transportation side, partial closure of bus routes helps to slow down but cannot fully contain the spreading of epidemics. Identifying "influential passengers" using the smart card data and isolating them at an early stage can also effectively reduce the epidemic spreading.

SEAIR Epidemic spreading model of COVID-19

We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all three versions, which hold when the epidemic is weak. We provide theoretical arguments that eigenvector centrality of a node approximately determines its risk to become infected.

First year with COVID-19: Assessment and prospects

The vision of health for all by Dr. Halfdan Mahler, Director General of the World Health Organization (WHO) 1973 to 1988, guided public health approaches towards improving life for all those mired in poverty and disease. Research on the Neglected Tropical Diseases (NTDs) of the world's poor was advancing strongly when the coronavirus disease 2019 (COVID-19) struck. Although work on the NTDs did not grind to a halt, the situation is reminiscent of the author Stefan Zweig's passionate account of culture destruction in his book The World of Yesterday from 1941, which gives an insight as to how the war ended traditional life. His thoughts parallel the present situation; however, this time societies are not torn apart by war but instead isolated by a pandemic. It comes upon today's scientists to move fast to make COVID-19 less devastating than the Spanish flu of 1918-1920 that killed more than 3% of the world population...

Incorporating Geographic Information Science and Technology in Response to the COVID-19 Pandemic

Incorporating geographic information science and technology (GIS&T) into COVID-19 pandemic surveillance, modeling, and response enhances understanding and control of the disease. Applications of GIS&T include 1) developing spatial data infrastructures for surveillance and data sharing, 2) incorporating mobility data in infectious disease forecasting, 3) using geospatial technologies for digital contact tracing, 4) integrating geographic data in COVID-19 modeling, 5) investigating geographic social vulnerabilities and health disparities, and 6) communicating the status of the disease or status of facilities for return-to-normal operations. Locations and availability of personal protective equipment, ventilators, hospital beds, and other items can be optimized with the use of GIS&T. Challenges include protection of individual privacy and civil liberties and closer collaboration among the fields of geography, medicine, public health, and public policy.

Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures

The spread of coronavirus disease 2019 (COVID-19) in Italy prompted drastic measures for transmission containment. We examine the effects of these interventions, based on modeling of the unfolding epidemic. We test modeling options of the spatially explicit type, suggested by the wave of infections spreading from the initial foci to the rest of Italy. We estimate parameters of a metacommunity Susceptible-Exposed-Infected-Recovered (SEIR)-like transmission model that includes a network of 107 provinces connected by mobility at high resolution, and the critical contribution of presymptomatic and asymptomatic transmission. We estimate a generalized reproduction number ([Formula: see text] = 3.60 [3.49 to 3.84]), the spectral radius of a suitable next-generation matrix that measures the potential spread in the absence of containment interventions. The model includes the implementation of progressive restrictions after the first case confirmed in Italy (February 21, 2020) and runs until March 25, 2020. We account for uncertainty in epidemiological reporting, and time dependence of human mobility matrices and awareness-dependent exposure probabilities. We draw scenarios of different containment measures and their impact. Results suggest that the sequence of restrictions posed to mobility and human-to-human interactions have reduced transmission by 45% (42 to 49%). Averted hospitalizations are measured by running scenarios obtained by selectively relaxing the imposed restrictions and total about 200,000 individuals (as of March 25, 2020). Although a number of assumptions need to be reexamined, like age structure in social mixing patterns and in the distribution of mobility, hospitalization, and fatality, we conclude that verifiable evidence exists to support the planning of emergency measures.

Conditions for transient epidemics of waterborne disease in spatially explicit systems

Waterborne diseases are a diverse family of infections transmitted through ingestion of-or contact with-water infested with pathogens. Outbreaks of waterborne infections often show well-defined spatial signatures that are typically linked to local eco-epidemiological conditions, water-mediated pathogen transport and human mobility. In this work, we apply a spatially explicit network model describing the transmission cycle of waterborne pathogens to determine invasion conditions in metacommunities endowed with a realistic spatial structure. Specifically, we aim to define conditions under which pathogens can temporarily colonize a set of human communities, thus triggering a transient epidemic outbreak. To that end, we apply generalized reactivity analysis, a recently developed methodological framework for the study of transient dynamics in ecological systems subject to external perturbations. The study of pathogen invasion is complemented by the detection of the spatial signatures associated with the perturbations to a disease-free system that are expected to be amplified the most over different time scales. Understanding the drivers of waterborne disease dynamics over time scales that are relevant to epidemic and/or endemic transmission is a crucial, cross-disciplinary challenge, as large portions of the developing world still struggle to cope with the burden of these infections.

Rainfall as a driver of epidemic cholera: Comparative model assessments of the effect of intra-seasonal precipitation events

The correlation between cholera epidemics and climatic drivers, in particular seasonal tropical rainfall, has been studied in a variety of contexts owing to its documented relevance. Several mechanistic models of cholera transmission have included rainfall as a driver by focusing on two possible transmission pathways: either by increasing exposure to contaminated water (e.g. due to worsening sanitary conditions during water excess), or water contamination by freshly excreted bacteria (e.g. due to washout of open-air defecation sites or overflows). Our study assesses the explanatory power of these different modeling structures by formal model comparison using deterministic and stochastic models of the type susceptible-infected-recovered-bacteria (SIRB). The incorporation of rainfall effects is generalized using a nonlinear function that can increase or decrease the relative importance of the large precipitation events. Our modelling framework is tested against the daily epidemiological data collected during the 2015 cholera outbreak within the urban context of Juba, South Sudan. This epidemic is characterized by a particular intra-seasonal double peak on the incidence in apparent relation with particularly strong rainfall events. Our results show that rainfall-based models in both their deterministic and stochastic formulations outperform models that do not account for rainfall. In fact, classical SIRB models are not able to reproduce the second epidemiological peak, thus suggesting that it was rainfall-driven. Moreover we found stronger support across model types for rainfall acting on increased exposure rather than on exacerbated water contamination. Although these results are context-specific, they stress the importance of a systematic and comprehensive appraisal of transmission pathways and their environmental forcings when embarking in the modelling of epidemic cholera.

Hydrological controls on river network connectivity

This study proposes a probabilistic approach for the quantitative assessment of reach- and network-scale hydrological connectivity as dictated by river flow space-time variability. Spatial dynamics of daily streamflows are estimated based on climatic and morphological features of the contributing catchment, integrating a physically based approach that accounts for the stochasticity of rainfall with a water balance framework and a geomorphic recession flow analysis. Ecologically meaningful minimum stage thresholds are used to evaluate the connectivity of individual stream reaches, and other relevant network-scale connectivity metrics. The framework allows a quantitative description of the main hydrological causes and the ecological consequences of water depth dynamics experienced by river networks. The analysis shows that the spatial variability of local-scale hydrological connectivity is strongly affected by the spatial and temporal distribution of climatic variables. Depending on the underlying climatic settings and the critical stage threshold, loss of connectivity can be observed in the headwaters or along the main channel, thereby originating a fragmented river network. The proposed approach provides important clues for understanding the effect of climate on the ecological function of river corridors.

Geographic transmission hubs of the 2009 influenza pandemic in the United States

A key issue in infectious disease epidemiology is to identify and predict geographic sites of epidemic establishment that contribute to onward spread, especially in the context of invasion waves of emerging pathogens. Conventional wisdom suggests that these sites are likely to be in densely-populated, well-connected areas. For pandemic influenza, however, epidemiological data have not been available at a fine enough geographic resolution to test this assumption. Here, we make use of fine-scale influenza-like illness incidence data derived from electronic medical claims records gathered from 834 3-digit ZIP (postal) codes across the US to identify the key geographic establishment sites, or "hubs", of the autumn wave of the 2009 A/H1N1pdm influenza pandemic in the United States. A mechanistic spatial transmission model is fit to epidemic onset times inferred from the data. Hubs are identified by tracing the most probable transmission routes back to a likely first establishment site. Four hubs are identified: two in the southeastern US, one in the central valley of California, and one in the midwestern US. According to the model, 75% of the 834 observed ZIP-level outbreaks in the US were seeded by these four hubs or their epidemiological descendants. Counter-intuitively, the pandemic hubs do not coincide with large and well-connected cities, indicating that factors beyond population density and travel volume are necessary to explain the establishment sites of the major autumn wave of the pandemic. Geographic regions are identified where infection can be statistically traced back to a hub, providing a testable prediction of the outbreak's phylogeography. Our method therefore provides an important way forward to reconcile spatial diffusion patterns inferred from epidemiological surveillance data and pathogen sequence data.

Determinants of Short-term Movement in a Developing Region and Implications for Disease Transmission

BACKGROUND

Human mobility is important for infectious disease spread. However, little is known about how travel varies by demographic groups and how this heterogeneity influences infectious disease risk.

METHODS

We analyzed 10 years of survey data from 15 communities in a remote but rapidly changing region in rural Ecuador where road development in the past 15-20 years has dramatically changed travel. We identify determinants of travel and incorporate them into an infection transmission model.

RESULTS

Individuals living in communities more remote at baseline had lower travel rates compared with less remote villages (adjusted odds ratio [OR] = 0.51; 95% confidence interval [CI] = 0.38, 0.67). Our model predicts that less remote villages are, therefore, at increased disease risk. Though road building and travel increased for all communities, this risk differential remained over 10 years of observation. Our transmission model also suggests that travelers and nontravelers have different roles in disease transmission. Adults travel more than children (adjusted OR = 1.73; 95% CI = 1.30, 2.31) and therefore disseminate infection from population centers to rural communities. Children are more likely than adults to be infected locally (attributable fraction = 0.24 and 0.09, respectively) and were indirectly affected by adult travel patterns.

CONCLUSIONS

These results reinforce the importance of large population centers for regional transmission and show that children and adults may play different roles in disease spread. Changing transportation infrastructure and subsequent economic and social transitions are occurring worldwide, potentially causing increased regional risk of disease.

Epidemicity thresholds for water-borne and water-related diseases

Determining the conditions that favor pathogen establishment in a host community is key to disease control and eradication. However, focusing on long-term dynamics alone may lead to an underestimation of the threats imposed by outbreaks triggered by short-term transient phenomena. Achieving an effective epidemiological response thus requires to look at different timescales, each of which may be endowed with specific management objectives. In this work we aim to determine epidemicity thresholds for some prototypical examples of water-borne and water-related diseases, a diverse family of infections transmitted either directly through water infested with pathogens or by vectors whose lifecycles are closely associated with water. From a technical perspective, while conditions for endemicity are determined via stability analysis, epidemicity thresholds are defined through generalized reactivity analysis, a recently proposed method that allows the study of the short-term instability properties of ecological systems. Understanding the drivers of water-borne and water-related disease dynamics over timescales that may be relevant to epidemic and/or endemic transmission is a challenge of the utmost importance, as large portions of the developing world are still struggling with the burden imposed by these infections.

River networks as ecological corridors: A coherent ecohydrological perspective

This paper draws together several lines of argument to suggest that an ecohydrological framework, i.e. laboratory, field and theoretical approaches focused on hydrologic controls on biota, has contributed substantially to our understanding of the function of river networks as ecological corridors. Such function proves relevant to: the spatial ecology of species; population dynamics and biological invasions; the spread of waterborne disease. As examples, we describe metacommunity predictions of fish diversity patterns in the Mississippi-Missouri basin, geomorphic controls imposed by the fluvial landscape on elevational gradients of species' richness, the zebra mussel invasion of the same Mississippi-Missouri river system, and the spread of proliferative kidney disease in salmonid fish. We conclude that spatial descriptions of ecological processes in the fluvial landscape, constrained by their specific hydrologic and ecological dynamics and by the ecosystem matrix for interactions, i.e. the directional dispersal embedded in fluvial and host/pathogen mobility networks, have already produced a remarkably broad range of significant results. Notable scientific and practical perspectives are thus open, in the authors' view, to future developments in ecohydrologic research.

Prolonging herd immunity to cholera via vaccination: Accounting for human mobility and waning vaccine effects

BACKGROUND

Oral cholera vaccination is an approach to preventing outbreaks in at-risk settings and controlling cholera in endemic settings. However, vaccine-derived herd immunity may be short-lived due to interactions between human mobility and imperfect or waning vaccine efficacy. As the supply and utilization of oral cholera vaccines grows, critical questions related to herd immunity are emerging, including: who should be targeted; when should revaccination be performed; and why have cholera outbreaks occurred in recently vaccinated populations?

METHODS AND FINDINGS

We use mathematical models to simulate routine and mass oral cholera vaccination in populations with varying degrees of migration, transmission intensity, and vaccine coverage. We show that migration and waning vaccine efficacy strongly influence the duration of herd immunity while birth and death rates have relatively minimal impacts. As compared to either periodic mass vaccination or routine vaccination alone, a community could be protected longer by a blended "Mass and Maintain" strategy. We show that vaccination may be best targeted at populations with intermediate degrees of mobility as compared to communities with very high or very low population turnover. Using a case study of an internally displaced person camp in South Sudan which underwent high-coverage mass vaccination in 2014 and 2015, we show that waning vaccine direct effects and high population turnover rendered the camp over 80% susceptible at the time of the cholera outbreak beginning in October 2016.

CONCLUSIONS

Oral cholera vaccines can be powerful tools for quickly protecting a population for a period of time that depends critically on vaccine coverage, vaccine efficacy over time, and the rate of population turnover through human mobility. Due to waning herd immunity, epidemics in vaccinated communities are possible but become less likely through complementary interventions or data-driven revaccination strategies.

Challenges in developing methods for quantifying the effects of weather and climate on water-associated diseases: A systematic review

Infectious diseases attributable to unsafe water supply, sanitation and hygiene (e.g. Cholera, Leptospirosis, Giardiasis) remain an important cause of morbidity and mortality, especially in low-income countries. Climate and weather factors are known to affect the transmission and distribution of infectious diseases and statistical and mathematical modelling are continuously developing to investigate the impact of weather and climate on water-associated diseases. There have been little critical analyses of the methodological approaches. Our objective is to review and summarize statistical and modelling methods used to investigate the effects of weather and climate on infectious diseases associated with water, in order to identify limitations and knowledge gaps in developing of new methods. We conducted a systematic review of English-language papers published from 2000 to 2015. Search terms included concepts related to water-associated diseases, weather and climate, statistical, epidemiological and modelling methods. We found 102 full text papers that met our criteria and were included in the analysis. The most commonly used methods were grouped in two clusters: process-based models (PBM) and time series and spatial epidemiology (TS-SE). In general, PBM methods were employed when the bio-physical mechanism of the pathogen under study was relatively well known (e.g. Vibrio cholerae); TS-SE tended to be used when the specific environmental mechanisms were unclear (e.g. Campylobacter). Important data and methodological challenges emerged, with implications for surveillance and control of water-associated infections. The most common limitations comprised: non-inclusion of key factors (e.g. biological mechanism, demographic heterogeneity, human behavior), reporting bias, poor data quality, and collinearity in exposures. Furthermore, the methods often did not distinguish among the multiple sources of time-lags (e.g. patient physiology, reporting bias, healthcare access) between environmental drivers/exposures and disease detection. Key areas of future research include: disentangling the complex effects of weather/climate on each exposure-health outcome pathway (e.g. person-to-person vs environment-to-person), and linking weather data to individual cases longitudinally.

Modeling Key Drivers of Cholera Transmission Dynamics Provides New Perspectives for Parasitology

Hydroclimatological and anthropogenic factors are key drivers of waterborne disease transmission. Information on human settlements and host mobility on waterways along which pathogens and hosts disperse, and relevant hydroclimatological processes, can be acquired remotely and included in spatially explicit mathematical models of disease transmission. In the case of epidemic cholera, such models allowed the description of complex disease patterns and provided insight into the course of ongoing epidemics. The inclusion of spatial information in models of disease transmission can aid in emergency management and the assessment of alternative interventions. Here, we review the study of drivers of transmission via spatially explicit approaches and argue that, because many parasitic waterborne diseases share the same drivers as cholera, similar principles may apply.

Trends in the Mechanistic and Dynamic Modeling of Infectious Diseases

The dynamics of infectious disease epidemics are driven by interactions between individuals with differing disease status (e.g., susceptible, infected, immune). Mechanistic models that capture the dynamics of such “dependent happenings” are a fundamental tool of infectious disease epidemiology. Recent methodological advances combined with access to new data sources and computational power have resulted in an explosion in the use of dynamic models in the analysis of emerging and established infectious diseases. Increasing use of models to inform practical public health decision making has challenged the field to develop new methods to exploit available data and appropriately characterize the uncertainty in the results. Here, we discuss recent advances and areas of active research in the mechanistic and dynamic modeling of infectious disease. We highlight how a growing emphasis on data and inference, novel forecasting methods, and increasing access to “big data” are changing the field of infectious disease dynamics. We showcase the application of these methods in phylodynamic research, which combines mechanistic models with rich sources of molecular data to tie genetic data to population-level disease dynamics. As dynamics and mechanistic modeling methods mature and are increasingly tied to principled statistical approaches, the historic separation between the infectious disease dynamics and “traditional” epidemiologic methods is beginning to erode; this presents new opportunities for cross pollination between fields and novel applications.

Disease and disaster: Optimal deployment of epidemic control facilities in a spatially heterogeneous population with changing behaviour

Epidemics of water-borne infections often follow natural disasters and extreme weather events that disrupt water management processes. The impact of such epidemics may be reduced by deployment of transmission control facilities such as clinics or decontamination plants. Here we use a relatively simple mathematical model to examine how demographic and environmental heterogeneities, population behaviour, and behavioural change in response to the provision of facilities, combine to determine the optimal configurations of limited numbers of facilities to reduce epidemic size, and endemic prevalence. We show that, if the presence of control facilities does not affect behaviour, a good general rule for responsive deployment to minimise epidemic size is to place them in exactly the locations where they will directly benefit the most people. However, if infected people change their behaviour to seek out treatment then the deployment of facilities offering treatment can lead to complex effects that are difficult to foresee. So careful mathematical analysis is the only way to get a handle on the optimal deployment. Behavioural changes in response to control facilities can also lead to critical facility numbers at which there is a radical change in the optimal configuration. So sequential improvement of a control strategy by adding facilities to an existing optimal configuration does not always produce another optimal configuration. We also show that the pre-emptive deployment of control facilities has conflicting effects. The configurations that minimise endemic prevalence are very different to those that minimise epidemic size. So cost-benefit analysis of strategies to manage endemic prevalence must factor in the frequency of extreme weather events and natural disasters.

A Theoretical Analysis of the Geography of Schistosomiasis in Burkina Faso Highlights the Roles of Human Mobility and Water Resources Development in Disease Transmission

We study the geography of schistosomiasis across Burkina Faso by means of a spatially explicit model of water-based disease dynamics. The model quantitatively addresses the geographic stratification of disease burden in a novel framework by explicitly accounting for drivers and controls of the disease, including spatial information on the distributions of population and infrastructure, jointly with a general description of human mobility and climatic/ecological drivers. Spatial patterns of disease are analysed by the extraction and the mapping of suitable eigenvectors of the Jacobian matrix subsuming the stability of the disease-free equilibrium. The relevance of the work lies in the novel mapping of disease burden, a byproduct of the parametrization induced by regional upscaling, by model-guided field validations and in the predictive scenarios allowed by exploiting the range of possible parameters and processes. Human mobility is found to be a primary control at regional scales both for pathogen invasion success and the overall distribution of disease burden. The effects of water resources development highlighted by systematic reviews are accounted for by the average distances of human settlements from water bodies that are habitats for the parasite's intermediate host. Our results confirm the empirical findings about the role of water resources development on disease spread into regions previously nearly disease-free also by inspection of empirical prevalence patterns. We conclude that while the model still needs refinements based on field and epidemiological evidence, the proposed framework provides a powerful tool for large-scale public health planning and schistosomiasis management.

Evaluating Spatial Interaction Models for Regional Mobility in Sub-Saharan Africa

Simple spatial interaction models of human mobility based on physical laws have been used extensively in the social, biological, and physical sciences, and in the study of the human dynamics underlying the spread of disease. Recent analyses of commuting patterns and travel behavior in high-income countries have led to the suggestion that these models are highly generalizable, and as a result, gravity and radiation models have become standard tools for describing population mobility dynamics for infectious disease epidemiology. Communities in Sub-Saharan Africa may not conform to these models, however; physical accessibility, availability of transport, and cost of travel between locations may be variable and severely constrained compared to high-income settings, informal labor movements rather than regular commuting patterns are often the norm, and the rise of mega-cities across the continent has important implications for travel between rural and urban areas. Here, we first review how infectious disease frameworks incorporate human mobility on different spatial scales and use anonymous mobile phone data from nearly 15 million individuals to analyze the spatiotemporal dynamics of the Kenyan population. We find that gravity and radiation models fail in systematic ways to capture human mobility measured by mobile phones; both severely overestimate the spatial spread of travel and perform poorly in rural areas, but each exhibits different characteristic patterns of failure with respect to routes and volumes of travel. Thus, infectious disease frameworks that rely on spatial interaction models are likely to misrepresent population dynamics important for the spread of disease in many African populations.

Human mobility underlies many social, biological, and physical phenomena, including the spread of infectious diseases. Analyses in high-income countries have led to the notion that populations obey universal rules of mobility that are effectively captured by spatial interaction models. However, communities in Africa may not conform to these rules since the availability of transport and geographic barriers may impose different constraints compared to high-income settings. We use anonymous mobile phone data from ~15 million subscribers to quantify different spatial and temporal scales of mobility within Kenya and test their performance with respect to this measurement of human travel. We find that standard models systematically fail to describe regional mobility in Kenya, with poor performance in rural areas. Epidemiological models that rely on these frameworks may therefore fail to capture important aspects of population dynamics driving disease spread in many African populations.

On the predictive ability of mechanistic models for the Haitian cholera epidemic

Predictive models of epidemic cholera need to resolve at suitable aggregation levels spatial data pertaining to local communities, epidemiological records, hydrologic drivers, waterways, patterns of human mobility and proxies of exposure rates. We address the above issue in a formal model comparison framework and provide a quantitative assessment of the explanatory and predictive abilities of various model settings with different spatial aggregation levels and coupling mechanisms. Reference is made to records of the recent Haiti cholera epidemics. Our intensive computations and objective model comparisons show that spatially explicit models accounting for spatial connections have better explanatory power than spatially disconnected ones for short-to-intermediate calibration windows, while parsimonious, spatially disconnected models perform better with long training sets. On average, spatially connected models show better predictive ability than disconnected ones. We suggest limits and validity of the various approaches and discuss the pathway towards the development of case-specific predictive tools in the context of emergency management.

Detection of Vibrio cholerae O1 and O139 in environmental waters of rural Bangladesh: a flow-cytometry-based field trial

Presence of Vibrio cholerae serogroups O1 and O139 in the waters of the rural area of Matlab, Bangladesh, was investigated with quantitative measurements performed with a portable flow cytometer. The relevance of this work relates to the testing of a field-adapted measurement protocol that might prove useful for cholera epidemic surveillance and for validation of mathematical models. Water samples were collected from different water bodies that constitute the hydrological system of the region, a well-known endemic area for cholera. Water was retrieved from ponds, river waters, and irrigation canals during an inter-epidemic time period. Each sample was filtered and analysed with a flow cytometer for a fast determination of V. cholerae cells contained in those environments. More specifically, samples were treated with O1- and O139-specific antibodies, which allowed precise flow-cytometry-based concentration measurements. Both serogroups were present in the environmental waters with a consistent dominance of V. cholerae O1. These results extend earlier studies where V. cholerae O1 and O139 were mostly detected during times of cholera epidemics using standard culturing techniques. Furthermore, our results confirm that an important fraction of the ponds' host populations of V. cholerae are able to self-sustain even when cholera cases are scarce. Those contaminated ponds may constitute a natural reservoir for cholera endemicity in the Matlab region. Correlations of V. cholerae concentrations with environmental factors and the spatial distribution of V. cholerae populations are also discussed.

Glucose- but not rice-based oral rehydration therapy enhances the production of virulence determinants in the human pathogen Vibrio cholerae

Despite major attempts to prevent cholera transmission, millions of people worldwide still must address this devastating disease. Cholera research has so far mainly focused on the causative agent, the bacterium Vibrio cholerae, or on disease treatment, but rarely were results from both fields interconnected. Indeed, the treatment of this severe diarrheal disease is mostly accomplished by oral rehydration therapy (ORT), whereby water and electrolytes are replenished. Commonly distributed oral rehydration salts also contain glucose. Here, we analyzed the effects of glucose and alternative carbon sources on the production of virulence determinants in the causative agent of cholera, the bacterium Vibrio cholerae during in vitro experimentation. We demonstrate that virulence gene expression and the production of cholera toxin are enhanced in the presence of glucose or similarly transported sugars in a ToxR-, TcpP- and ToxT-dependent manner. The virulence genes were significantly less expressed if alternative non-PTS carbon sources, including rice-based starch, were utilized. Notably, even though glucose-based ORT is commonly used, field studies indicated that rice-based ORT performs better. We therefore used a spatially explicit epidemiological model to demonstrate that the better performing rice-based ORT could have a significant impact on epidemic progression based on the recent outbreak of cholera in Haiti. Our results strongly support a change of carbon source for the treatment of cholera, especially in epidemic settings.

Cholera research has so far mainly focused on the causative agent, the bacterium Vibrio cholerae, or on disease treatment, but rarely were results from both fields interconnected. Indeed, the treatment of this severe diarrheal disease is mostly accomplished by oral rehydration therapy (ORT). ORT aims at rehydrating patients through the provision of water and oral rehydration salts; the latter being composed of electrolytes as well as glucose as a carbon source. Although glucose-based ORS is commonly used to treat diarrheal diseases and is recommended by the WHO, field studies on cholera indicated that rice-based ORT performs better than glucose-based ORT. Here, we investigated the impact that glucose, starch, or other carbon sources exert on V. cholerae. We demonstrated that glucose leads to an increased expression of the major virulence genes in the pathogen and, accordingly, to an enhanced production of cholera toxin during in vitro experimentation. Because the cholera toxin is primarily responsible for the severe symptoms that are associated with the disease, our study highlights the negative effects of glucose-based ORT. Next, we used a spatially explicit epidemiological model to demonstrate that the better performing rice-based ORS could have a significant impact on epidemic progression based on the recent outbreak of cholera in Haiti.

Validation of three geolocation strategies for health-facility attendees for research and public health surveillance in a rural setting in western Kenya

Understanding the spatial distribution of disease is critical for effective disease control. Where formal address networks do not exist, tracking spatial patterns of clinical disease is difficult. Geolocation strategies were tested at rural health facilities in western Kenya. Methods included geocoding residence by head of compound, participatory mapping and recording the self-reported nearest landmark. Geocoding was able to locate 72·9% [95% confidence interval (CI) 67·7–77·6] of individuals to within 250 m of the true compound location. The participatory mapping exercise was able to correctly locate 82·0% of compounds (95% CI 78·9–84·8) to a 2 × 2·5 km area with a 500 m buffer. The self-reported nearest landmark was able to locate 78·1% (95% CI 73·8–82·1) of compounds to the correct catchment area. These strategies tested provide options for quickly obtaining spatial information on individuals presenting at health facilities.

Incorporating heterogeneity into the transmission dynamics of a waterborne disease model

We formulate a mathematical model that captures the essential dynamics of waterborne disease transmission to study the effects of heterogeneity on the spread of the disease. The effects of heterogeneity on some important mathematical features of the model such as the basic reproduction number, type reproduction number and final outbreak size are analysed accordingly. We conduct a real-world application of this model by using it to investigate the heterogeneity in transmission in the recent cholera outbreak in Haiti. By evaluating the measure of heterogeneity between the administrative departments in Haiti, we discover a significant difference in the dynamics of the cholera outbreak between the departments.

Metapopulation persistence and species spread in river networks

River networks define ecological corridors characterised by unidirectional streamflow, which may impose downstream drift to aquatic organisms or affect their movement. Animals and plants manage to persist in riverine ecosystems, though, which in fact harbour high biological diversity. Here, we study metapopulation persistence in river networks analysing stage-structured populations that exploit different dispersal pathways, both along-stream and overland. Using stability analysis, we derive a novel criterion for metapopulation persistence in arbitrarily complex landscapes described as spatial networks. We show how dendritic geometry and overland dispersal can promote population persistence, and that their synergism provides an explanation of the so-called `drift paradox'. We also study the geography of the initial spread of a species and place it in the context of biological invasions. Applications concerning the persistence of stream salamanders in the Shenandoah river, and the spread of two invasive species in the Mississippi-Missouri are also discussed.

Epidemic cholera spreads like wildfire

Cholera is on the rise globally, especially epidemic cholera which is characterized by intermittent and unpredictable outbreaks that punctuate periods of regional disease fade-out. These epidemic dynamics remain however poorly understood. Here we examine records for epidemic cholera over both contemporary and historical timelines, from Africa (1990–2006) and former British India (1882–1939). We find that the frequency distribution of outbreak size is fat-tailed, scaling approximately as a power-law. This pattern which shows strong parallels with wildfires is incompatible with existing cholera models developed for endemic regions, as it implies a fundamental role for stochastic transmission and local depletion of susceptible hosts. Application of a recently developed forest-fire model indicates that epidemic cholera dynamics are located above a critical phase transition and propagate in similar ways to aggressive wildfires. These findings have implications for the effectiveness of control measures and the mechanisms that ultimately limit the size of outbreaks.

Examining rainfall and cholera dynamics in Haiti using statistical and dynamic modeling approaches

Haiti has been in the midst of a cholera epidemic since October 2010. Rainfall is thought to be associated with cholera here, but this relationship has only begun to be quantitatively examined. In this paper, we quantitatively examine the link between rainfall and cholera in Haiti for several different settings (including urban, rural, and displaced person camps) and spatial scales, using a combination of statistical and dynamic models. Statistical analysis of the lagged relationship between rainfall and cholera incidence was conducted using case crossover analysis and distributed lag nonlinear models. Dynamic models consisted of compartmental differential equation models including direct (fast) and indirect (delayed) disease transmission, where indirect transmission was forced by empirical rainfall data. Data sources include cholera case and hospitalization time series from the Haitian Ministry of Public Health, the United Nations Water, Sanitation and Health Cluster, International Organization for Migration, and Hôpital Albert Schweitzer. Rainfall data was obtained from rain gauges from the U.S. Geological Survey and Haiti Regeneration Initiative, and remote sensing rainfall data from the National Aeronautics and Space Administration Tropical Rainfall Measuring Mission. A strong relationship between rainfall and cholera was found for all spatial scales and locations examined. Increased rainfall was significantly correlated with increased cholera incidence 4-7 days later. Forcing the dynamic models with rainfall data resulted in good fits to the cholera case data, and rainfall-based predictions from the dynamic models closely matched observed cholera cases. These models provide a tool for planning and managing the epidemic as it continues.

Spatially explicit conditions for waterborne pathogen invasion

Waterborne pathogens cause many possibly lethal human diseases. We derive the condition for pathogen invasion and subsequent disease outbreak in a territory with specific, space-inhomogeneous characteristics (hydrological, ecological, demographic, and epidemiological). The criterion relies on a spatially explicit model accounting for the density of susceptible and infected individuals and the pathogen concentration in a network of communities linked by human mobility and the water system. Pathogen invasion requires that a dimensionless parameter, the dominant eigenvalue of a generalized reproductive matrix J0, be larger than unity. Conditions for invasion are studied while crucial parameters (population density distribution, contact and water contamination rates, pathogen growth rates) and the characteristics of the networks (connectivity, directional transport, water retention times, mobility patterns) are varied. We analyze both simple, prototypical test cases and realistic landscapes, in which optimal channel networks mimic the water systems and gravitational models describe human mobility. Also, we show that the dominant eigenvector of J0 effectively portrays the geography of epidemic outbreaks, that is, the areas of the studied territory that will be initially affected by an epidemic. This is important for planning an efficient spatial allocation of interventions (e.g., improving sanitation and providing emergency aid and medicines).