Accounting for non-stationarity in epidemiology by embedding time-varying parameters in stochastic models

Statistical inference and neural network training based on stochastic difference model for air pollution and associated disease transmission

A polluted air environment can potentially provoke infections of diverse respiratory diseases. The development of mathematical models can study the mechanism of air pollution and its effect on the spread of diseases. The key is to characterize the intrinsic correlation between the disease infection and the change in air pollutant concentration. In this paper, we establish a coupled discrete susceptible-exposed-infectious-susceptible (SEIS) model with demography to characterize the transmission of disease, and the change in the concentration of air pollutants is described in the form of the Beverton-Holt (BH) model with a time-varying inflow rate of air pollutants. Considering the periodic variation characteristics of data, time-varying parameters are defined as specific functional forms. We estimate the change point at which the parameters switch and the parameter values within the switching interval based on Bayesian statistical theory. The data fitting of the model can reflect the seasonal peaks and annual growth trends of values of air quality index (AQI) and the number of influenza-like illnesses (ILI) cases. However, the bias in data fitting indicates a more complex correlation pattern between disease and pollutant concentration changes. To explore unknown mechanisms, we propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining deep learning with difference equations and obtain the curves of the transmission rate and inflow rate functions over time. The results show that neural network models can help us determine time-varying parameters in the model, thereby better reflecting the trend of data changes.

Bayesian workflow for time-varying transmission in stratified compartmental infectious disease transmission models

Compartmental models that describe infectious disease transmission across subpopulations are central for assessing the impact of non-pharmaceutical interventions, behavioral changes and seasonal effects on the spread of respiratory infections. We present a Bayesian workflow for such models, including four features: (1) an adjustment for incomplete case ascertainment, (2) an adequate sampling distribution of laboratory-confirmed cases, (3) a flexible, time-varying transmission rate, and (4) a stratification by age group. Within the workflow, we benchmarked the performance of various implementations of two of these features (2 and 3). For the second feature, we used SARS-CoV-2 data from the canton of Geneva (Switzerland) and found that a quasi-Poisson distribution is the most suitable sampling distribution for describing the overdispersion in the observed laboratory-confirmed cases. For the third feature, we implemented three methods: Brownian motion, B-splines, and approximate Gaussian processes (aGP). We compared their performance in terms of the number of effective samples per second, and the error and sharpness in estimating the time-varying transmission rate over a selection of ordinary differential equation solvers and tuning parameters, using simulated seroprevalence and laboratory-confirmed case data. Even though all methods could recover the time-varying dynamics in the transmission rate accurately, we found that B-splines perform up to four and ten times faster than Brownian motion and aGPs, respectively. We validated the B-spline model with simulated age-stratified data. We applied this model to 2020 laboratory-confirmed SARS-CoV-2 cases and two seroprevalence studies from the canton of Geneva. This resulted in detailed estimates of the transmission rate over time and the case ascertainment. Our results illustrate the potential of the presented workflow including stratified transmission to estimate age-specific epidemiological parameters. The workflow is freely available in the R package HETTMO, and can be easily adapted and applied to other infectious diseases.

An approximate diffusion process for environmental stochasticity in infectious disease transmission modelling

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe, mechanistically, changes in extrinsic environmental factors including public behaviour and seasonal fluctuations. An elegant approach to capturing environmental stochasticity is to model the force of infection as a stochastic process. However, inference in this context requires solving a computationally expensive "missing data" problem, using data-augmentation techniques. We propose to model the time-varying transmission-potential as an approximate diffusion process using a path-wise series expansion of Brownian motion. This approximation replaces the "missing data" imputation step with the inference of the expansion coefficients: a simpler and computationally cheaper task. We illustrate the merit of this approach through three examples: modelling influenza using a canonical SIR model, capturing seasonality using a SIRS model, and the modelling of COVID-19 pandemic using a multi-type SEIR model.

Modeling the time-dependent transmission rate using gaussian pulses for analyzing the COVID-19 outbreaks in the world

In this work, an SEIR epidemic model with time-dependent transmission rate parameters for the multiple waves of COVID-19 infection was investigated. It is assumed that the transmission rate is determined by the superposition of the Gaussian pulses. The interaction of these dynamics is represented by recursive equations. Analysis of the overall dynamics of disease spread is determined by the effective reproduction number R_e(t) produced throughout the infection period. The study managed to show the evolution of the epidemic over time and provided important information about the occurrence of multiple waves of COVID-19 infection in the world and Indonesia.

Estimating the time-dependent effective reproduction number and vaccination rate for COVID-19 in the USA and India

The effective reproduction number, $ R_t $, is a vital epidemic parameter utilized to judge whether an epidemic is shrinking, growing, or holding steady. The main goal of this paper is to estimate the combined $ R_t $ and time-dependent vaccination rate for COVID-19 in the USA and India after the vaccination campaign started. Accounting for the impact of vaccination into a discrete-time stochastic augmented SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model, we estimate the time-dependent effective reproduction number $ (R_t) $ and vaccination rate $ (\xi_t) $ for COVID-19 by using a low pass filter and the Extended Kalman Filter (EKF) approach for the period February 15, 2021 to August 22, 2022 in India and December 13, 2020 to August 16, 2022 in the USA. The estimated $ R_t $ and $ \xi_t $ show spikes and serrations with the data. Our forecasting scenario represents the situation by December 31, 2022 that the new daily cases and deaths are decreasing for the USA and India. We also noticed that for the current vaccination rate, $ R_t $ would remain greater than one by December 31, 2022. Our results are beneficial for the policymakers to track the status of the effective reproduction number, whether it is greater or less than one. As restrictions in these countries ease, it is still important to maintain safety and preventive measures.

A sliding window approach to optimize the time-varying parameters of a spatially-explicit and stochastic model of COVID-19

The implementation of non-pharmaceutical public health interventions can have simultaneous impacts on pathogen transmission rates as well as host mobility rates. For instance, with SARS-CoV-2, masking can influence host-to-host transmission, while stay-at-home orders can influence mobility. Importantly, variations in transmission rates and mobility patterns can influence pathogen-induced hospitalization rates. This poses a significant challenge for the use of mathematical models of disease dynamics in forecasting the spread of a pathogen; to create accurate forecasts in spatial models of disease spread, we must simultaneously account for time-varying rates of transmission and host movement. In this study, we develop a statistical model-fitting algorithm to estimate dynamic rates of SARS-CoV-2 transmission and host movement from geo-referenced hospitalization data. Using simulated data sets, we then test whether our method can accurately estimate these time-varying rates simultaneously, and how this accuracy is influenced by the spatial population structure. Our model-fitting method relies on a highly parallelized process of grid search and a sliding window technique that allows us to estimate time-varying transmission rates with high accuracy and precision, as well as movement rates with somewhat lower precision. Estimated parameters also had lower precision in more rural data sets, due to lower hospitalization rates (i.e., these areas are less data-rich). This model-fitting routine could easily be generalized to any stochastic, spatially-explicit modeling framework, offering a flexible and efficient method to estimate time-varying parameters from geo-referenced data sets.

Analysis of stochastic dynamics in a multistable logistic-type epidemiological model

Motivated by the important problem of analyzing and predicting the spread of epidemics, we propose and study a discrete susceptible-infected model. This logistic-type model accounts such significant parameters as the rate of infection spread due to contacts, mortality caused by disease, and the rate of recovery. We present results of the bifurcation analysis of regular and chaotic survival regimes for interacting susceptible and infected subpopulations. Parametric zones of multistability are found and basins of coexisting attractors are determined. We also discuss the particular role of specific transients. In-phase and anti-phase synchronization in the oscillations of the susceptible and infected parts of the population is studied. An impact of inevitably present random disturbances is studied numerically and by the analytical method of confidence domains. Various mechanisms of noise-induced extinction in this epidemiological model are discussed.

A Model for Highly Fluctuating Spatio-Temporal Infection Data, with Applications to the COVID Epidemic

Spatio-temporal models need to address specific features of spatio-temporal infection data, such as periods of stable infection levels (endemicity), followed by epidemic phases, as well as infection spread from neighbouring areas. In this paper, we consider a mixture-link model for infection counts that allows alternation between epidemic phases (possibly multiple) and stable endemicity, with higher AR1 coefficients in epidemic phases. This is a form of regime-switching, allowing for non-stationarity in infection levels. We adopt a generalised Poisson model appropriate to the infection count data and avoid transformations (e.g., differencing) to alternative metrics, which have been adopted in many studies. We allow for neighbourhood spillover in infection, which is also governed by adaptive regime-switching. Compared to existing models, the observational (in-sample) model is expected to better reflect the balance between epidemic and endemic tendencies, and short-term extrapolations are likely to be improved. Two case study applications involve COVID area-time data, one for 32 London boroughs (and 96 weeks) since the start of the COVID epidemic, the other for a shorter time span focusing on the epidemic phase in 144 areas of Southeast England associated with the Alpha variant. In both applications, the proposed methods produce a better in-sample fit and out-of-sample short term predictions. The spatial dynamic implications are highlighted in the case studies.

A new estimation method for COVID-19 time-varying reproduction number using active cases

We propose a new method to estimate the time-varying effective (or instantaneous) reproduction number of the novel coronavirus disease (COVID-19). The method is based on a discrete-time stochastic augmented compartmental model that describes the virus transmission. A two-stage estimation method, which combines the Extended Kalman Filter (EKF) to estimate the reported state variables (active and removed cases) and a low pass filter based on a rational transfer function to remove short term fluctuations of the reported cases, is used with case uncertainties that are assumed to follow a Gaussian distribution. Our method does not require information regarding serial intervals, which makes the estimation procedure simpler without reducing the quality of the estimate. We show that the proposed method is comparable to common approaches, e.g., age-structured and new cases based sequential Bayesian models. We also apply it to COVID-19 cases in the Scandinavian countries: Denmark, Sweden, and Norway, where the positive rates were below 5% recommended by WHO.

Improving Dengue Forecasts by Using Geospatial Big Data Analysis in Google Earth Engine and the Historical Dengue Information-Aided Long Short Term Memory Modeling

Simple Summary

Forecasting dengue cases often face challenges from (1) time-effectiveness due to time-consuming satellite data downloading and processing, (2) weak spatial representation due to data dependence on administrative unit-based statistics or weather station-based observations, and (3) stagnant accuracy without historical dengue cases. With the advance of the geospatial big data cloud computing in Google Earth Engine and deep learning, this study proposed an efficient framework of dengue prediction at an epidemiological week basis using geospatial big data analysis in Google Earth Engine and Long Short Term Memory modeling. We focused on the dengue epidemics in the Federal District of Brazil during 2007–2019. Based on Google Earth Engine and epidemiological calendar, we computed the weekly composite for each dengue driving factor, and spatially aggregated the pixel values into dengue transmission areas to generate the time series of driving factors. A multi-step-ahead Long Short Term Memory modeling was used, and the time-differenced natural log-transformed dengue cases and the time series of driving factors were considered as outcomes and explantary factors, respectively, with two modeling scenarios (with and without historical cases). The performance is better when historical cases were used, and the 5-weeks-ahead forecast has the best performance.

Abstract

Timely and accurate forecasts of dengue cases are of great importance for guiding disease prevention strategies, but still face challenges from (1) time-effectiveness due to time-consuming satellite data downloading and processing, (2) weak spatial representation capability due to data dependence on administrative unit-based statistics or weather station-based observations, and (3) stagnant accuracy without the application of historical case information. Geospatial big data, cloud computing platforms (e.g., Google Earth Engine, GEE), and emerging deep learning algorithms (e.g., long short term memory, LSTM) provide new opportunities for advancing these efforts. Here, we focused on the dengue epidemics in the urban agglomeration of the Federal District of Brazil (FDB) during 2007–2019. A new framework was proposed using geospatial big data analysis in the Google Earth Engine (GEE) platform and long short term memory (LSTM) modeling for dengue case forecasts over an epidemiological week basis. We first defined a buffer zone around an impervious area as the main area of dengue transmission by considering the impervious area as a human-dominated area and used the maximum distance of the flight range of Aedes aegypti and Aedes albopictus as a buffer distance. Those zones were used as units for further attribution analyses of dengue epidemics by aggregating the pixel values into the zones. The near weekly composite of potential driving factors was generated in GEE using the epidemiological weeks during 2007–2019, from the relevant geospatial data with daily or sub-daily temporal resolution. A multi-step-ahead LSTM model was used, and the time-differenced natural log-transformed dengue cases were used as outcomes. Two modeling scenarios (with and without historical dengue cases) were set to examine the potential of historical information on dengue forecasts. The results indicate that the performance was better when historical dengue cases were used and the 5-weeks-ahead forecast had the best performance, and the peak of a large outbreak in 2019 was accurately forecasted. The proposed framework in this study suggests the potential of the GEE platform, the LSTM algorithm, as well as historical information for dengue risk forecasting, which can easily be extensively applied to other regions or globally for timely and practical dengue forecasts.

Quantifying Non-Stationarity with Information Theory

We introduce an index based on information theory to quantify the stationarity of a stochastic process. The index compares on the one hand the information contained in the increment at the time scale τ of the process at time t with, on the other hand, the extra information in the variable at time t that is not present at time t−τ. By varying the scale τ, the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale. Not only is this index able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is. We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements.

Dynamics of the COVID-19 epidemic in Ireland under mitigation

BACKGROUND

In Ireland and across the European Union the COVID-19 epidemic waves, driven mainly by the emergence of new variants of the SARS-CoV-2 have continued their course, despite various interventions from governments. Public health interventions continue in their attempts to control the spread as they wait for the planned significant effect of vaccination.

METHODS

To tackle this challenge and the observed non-stationary aspect of the epidemic we used a modified SEIR stochastic model with time-varying parameters, following Brownian process. This enabled us to reconstruct the temporal evolution of the transmission rate of COVID-19 with the non-specific hypothesis that it follows a basic stochastic process constrained by the available data. This model is coupled with Bayesian inference (particle Markov Chain Monte Carlo method) for parameter estimation and utilized mainly well-documented Irish hospital data.

RESULTS

In Ireland, mitigation measures provided a 78-86% reduction in transmission during the first wave between March and May 2020. For the second wave in October 2020, our reduction estimation was around 20% while it was 70% for the third wave in January 2021. This third wave was partly due to the UK variant appearing in Ireland. In June 2020 we estimated that sero-prevalence was 2.0% (95% CI: 1.2-3.5%) in complete accordance with a sero-prevalence survey. By the end of April 2021, the sero-prevalence was greater than 17% due in part to the vaccination campaign. Finally we demonstrate that the available observed confirmed cases are not reliable for analysis owing to the fact that their reporting rate has as expected greatly evolved.

CONCLUSION

We provide the first estimations of the dynamics of the COVID-19 epidemic in Ireland and its key parameters. We also quantify the effects of mitigation measures on the virus transmission during and after mitigation for the three waves. Our results demonstrate that Ireland has significantly reduced transmission by employing mitigation measures, physical distancing and lockdown. This has to date avoided the saturation of healthcare infrastructures, flattened the epidemic curve and likely reduced mortality. However, as we await for a full roll out of a vaccination programme and as new variants potentially more transmissible and/or more infectious could continue to emerge and mitigation measures change silent transmission, challenges remain.

Estimation of the reproduction number of influenza A(H1N1)pdm09 in South Korea using heterogeneous models

Background

The reproduction number is one of the most crucial parameters in determining disease dynamics, providing a summary measure of the transmission potential. However, estimating this value is particularly challenging owing to the characteristics of epidemic data, including non-reproducibility and incompleteness.

Methods

In this study, we propose mathematical models with different population structures; each of these models can produce data on the number of cases of the influenza A(H1N1)pdm09 epidemic in South Korea. These structured models incorporating the heterogeneity of age and region are used to estimate the reproduction numbers at various terminal times. Subsequently, the age- and region-specific reproduction numbers are also computed to analyze the differences illustrated in the incidence data.

Results

Incorporation of the age-structure or region-structure allows for robust estimation of parameters, while the basic SIR model provides estimated values beyond the reasonable range with severe fluctuation. The estimated duration of infectious period using age-structured model is around 3.8 and the reproduction number was estimated to be 1.6. The estimated duration of infectious period using region-structured model is around 2.1 and the reproduction number was estimated to be 1.4. The estimated age- and region-specific reproduction numbers are consistent with cumulative incidence for corresponding groups.

Conclusions

Numerical results reveal that the introduction of heterogeneity into the population to represent the general characteristics of dynamics is essential for the robust estimation of parameters.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

The stationarity bias in research on the environmental determinants of health

An implicit assumption often made in research on the environmental determinants of health is that the relationships between environmental factors and their health effects are stable over space and time. This is the assumption of stationarity. The health impacts of environmental factors, however, may vary not only over space and time but also over the value ranges of the environmental factors under investigation. Few studies to date have examined how often the stationarity assumption is violated and when violated, to what extent findings might be misleading. Using selected studies as examples, this paper explores how the stationarity assumption can lead to misleading conclusions about health-environment relationships that may in turn have serious health consequences or policy implications. It encourages researchers to embrace nonstationarity and recognize its meaning because it helps direct our attention to the ignored factors or processes that may enhance our understanding of the phenomena under investigation.

Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation

We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realization. This forms the basis of our Data Augmented MCMC, which consists of augmenting parameter space with the unobserved PRM value. The resulting simple Metropolis-Hastings sampler acts as an efficient simulation-based inference method, that can easily be transferred from model to model. Compared with a recent Data Augmentation method based on Gibbs sampling of individual infection histories, PRM-augmented MCMC scales much better with epidemic size and is far more flexible. It is also found to be competitive with Particle MCMC for moderate epidemics when using approximate simulations. PRM-augmented MCMC also yields a posteriori estimates of the PRM, that represent process stochasticity, and which can be used to validate the model. A pattern of deviation from the PRM prior distribution will indicate that the model underfits the data and help to understand the cause. We illustrate this by fitting a non-seasonal model to some simulated seasonal case count data. Applied to the Zika epidemic of 2013 in French Polynesia, our approach shows that a simple SEIR model cannot correctly reproduce both the initial sharp increase in the number of cases as well as the final proportion of seropositive. PRM augmentation thus provides a coherent story for Stochastic Epidemic Model inference, where explicitly inferring process stochasticity helps with model validation.

Parallel trends in the transmission of SARS-CoV-2 and retail/recreation and public transport mobility during non-lockdown periods

Recent literature strongly supports the hypothesis that mobility restriction and social distancing play a crucial role in limiting the transmission of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). During the first wave of the coronavirus disease 2019 (COVID-19) pandemic, it was shown that mobility restriction reduced transmission significantly. This study found that, in the period between the first two waves of the COVID-19 pandemic, there was high positive correlation between trends in the transmission of SARS-CoV-2 and mobility. These two trends oscillated simultaneously, and increased mobility following the relaxation of lockdown rules was significantly associated with increased transmission. From a public health perspective, these results highlight the importance of tracking changes in mobility when relaxing mitigation measures in order to anticipate future changes in the spread of SARS-CoV-2.

Range of reproduction number estimates for COVID-19 spread

To monitor local and global COVID-19 outbreaks, and to plan containment measures, accessible and comprehensible decision-making tools need to be based on the growth rates of new confirmed infections, hospitalization or case fatality rates. Growth rates of new cases form the empirical basis for estimates of a variety of reproduction numbers, dimensionless numbers whose value, when larger than unity, describes surging infections and generally worsening epidemiological conditions. Typically, these determinations rely on noisy or incomplete data gained over limited periods of time, and on many parameters to estimate. This paper examines how estimates from data and models of time-evolving reproduction numbers of national COVID-19 infection spread change by using different techniques and assumptions. Given the importance acquired by reproduction numbers as diagnostic tools, assessing their range of possible variations obtainable from the same epidemiological data is relevant. We compute control reproduction numbers from Swiss and Italian COVID-19 time series adopting both data convolution (renewal equation) and a SEIR-type model. Within these two paradigms we run a comparative analysis of the possible inferences obtained through approximations of the distributions typically used to describe serial intervals, generation, latency and incubation times, and the delays between onset of symptoms and notification. Our results suggest that estimates of reproduction numbers under these different assumptions may show significant temporal differences, while the actual variability range of computed values is rather small.

Tracking R of COVID-19: A new real-time estimation using the Kalman filter

We develop a new method for estimating the effective reproduction number of an infectious disease (R ) and apply it to track the dynamics of COVID-19. The method is based on the fact that in the SIR model,R is linearly related to the growth rate of the number of infected individuals. This time-varying growth rate is estimated using the Kalman filter from data on new cases. The method is easy to implement in standard statistical software, and it performs well even when the number of infected individuals is imperfectly measured, or the infection does not follow the SIR model. Our estimates ofR for COVID-19 for 124 countries across the world are provided in an interactive online dashboard, and they are used to assess the effectiveness of non-pharmaceutical interventions in a sample of 14 European countries.

Tracking [Formula: see text] of COVID-19: A new real-time estimation using the Kalman filter

We develop a new method for estimating the effective reproduction number of an infectious disease ([Formula: see text]) and apply it to track the dynamics of COVID-19. The method is based on the fact that in the SIR model, [Formula: see text] is linearly related to the growth rate of the number of infected individuals. This time-varying growth rate is estimated using the Kalman filter from data on new cases. The method is easy to implement in standard statistical software, and it performs well even when the number of infected individuals is imperfectly measured, or the infection does not follow the SIR model. Our estimates of [Formula: see text] for COVID-19 for 124 countries across the world are provided in an interactive online dashboard, and they are used to assess the effectiveness of non-pharmaceutical interventions in a sample of 14 European countries.

Tracking [Formula: see text] of COVID-19: A new real-time estimation using the Kalman filter

We develop a new method for estimating the effective reproduction number of an infectious disease ([Formula: see text]) and apply it to track the dynamics of COVID-19. The method is based on the fact that in the SIR model, [Formula: see text] is linearly related to the growth rate of the number of infected individuals. This time-varying growth rate is estimated using the Kalman filter from data on new cases. The method is easy to implement in standard statistical software, and it performs well even when the number of infected individuals is imperfectly measured, or the infection does not follow the SIR model. Our estimates of [Formula: see text] for COVID-19 for 124 countries across the world are provided in an interactive online dashboard, and they are used to assess the effectiveness of non-pharmaceutical interventions in a sample of 14 European countries.

Ecological Dynamics: Integrating Empirical, Statistical, and Analytical Methods

Understanding ecological processes and predicting long-term dynamics are ongoing challenges in ecology. To address these challenges, we suggest an approach combining mathematical analyses and Bayesian hierarchical statistical modeling with diverse data sources. Novel mathematical analysis of ecological dynamics permits a process-based understanding of conditions under which systems approach equilibrium, experience large oscillations, or persist in transient states. This understanding is improved by combining ecological models with empirical observations from a variety of sources. Bayesian hierarchical models explicitly couple process-based models and data, yielding probabilistic quantification of model parameters, system characteristics, and associated uncertainties. We outline relevant tools from dynamical analysis and hierarchical modeling and argue for their integration, demonstrating the value of this synthetic approach through a simple predator-prey example.

Estimation of temporal covariances in pathogen dynamics using Bayesian multivariate autoregressive models

It is well recognised that animal and plant pathogens form complex ecological communities of interacting organisms within their hosts, and there is growing interest in the health implications of such pathogen interactions. Although community ecology approaches have been used to identify pathogen interactions at the within-host scale, methodologies enabling robust identification of interactions from population-scale data such as that available from health authorities are lacking. To address this gap, we developed a statistical framework that jointly identifies interactions between multiple viruses from contemporaneous non-stationary infection time series. Our conceptual approach is derived from a Bayesian multivariate disease mapping framework. Importantly, our approach captures within- and between-year dependencies in infection risk while controlling for confounding factors such as seasonality, demographics and infection frequencies, allowing genuine pathogen interactions to be distinguished from simple correlations. We validated our framework using a broad range of synthetic data. We then applied it to diagnostic data available for five respiratory viruses co-circulating in a major urban population between 2005 and 2013: adenovirus, human coronavirus, human metapneumovirus, influenza B virus and respiratory syncytial virus. We found positive and negative covariances indicative of epidemiological interactions among specific virus pairs. This statistical framework enables a community ecology perspective to be applied to infectious disease epidemiology with important utility for public health planning and preparedness.

Disease-causing microorganisms, including viruses, bacteria, protozoa and fungi, form complex communities within animals and plants. These microorganisms can coexist harmoniously or even beneficially, or they may competitively interact for host resources. Well-studied examples include interactions between viruses and bacteria in the respiratory tract. Whilst ecological studies have revealed that some pathogens do interact within their hosts, identifying interactions from available population scale data from health authorities is challenging. This is exacerbated by a lack of large-scale data describing the infection patterns of multiple pathogens within single populations over long time frames. Furthermore, methods for evaluating whether infection frequencies of different pathogens fluctuate together or not over time cannot readily account for alternative explanations. For example, human pathogens may have related seasonal patterns depending on the age groups they infect and the weather conditions they survive in, and not because they are interacting. We developed a robust statistical framework to identify pathogen-pathogen interactions from population scale diagnostic data. This framework serves as a crucial step in identifying such important interactions and will guide new studies to elucidate their underpinning mechanisms. This will have important consequences for public health preparedness and the design of effective disease control interventions.

Correction: Accounting for non-stationarity in epidemiology by embedding time-varying parameters in stochastic models

[This corrects the article DOI: 10.1371/journal.pcbi.1006211.].

Real-time analysis of the diphtheria outbreak in forcibly displaced Myanmar nationals in Bangladesh

BACKGROUND

Between August and December 2017, more than 625,000 Rohingya from Myanmar fled into Bangladesh, settling in informal makeshift camps in Cox's Bazar district and joining 212,000 Rohingya already present. In early November, a diphtheria outbreak hit the camps, with 440 reported cases during the first month. A rise in cases during early December led to a collaboration between teams from Médecins sans Frontières-who were running a provisional diphtheria treatment centre-and the London School of Hygiene and Tropical Medicine with the goal to use transmission dynamic models to forecast the potential scale of the outbreak and the resulting resource needs.

METHODS

We first adjusted for delays between symptom onset and case presentation using the observed distribution of reporting delays from previously reported cases. We then fit a compartmental transmission model to the adjusted incidence stratified by age group and location. Model forecasts with a lead time of 2 weeks were issued on 12, 20, 26 and 30 December and communicated to decision-makers.

RESULTS

The first forecast estimated that the outbreak would peak on 19 December in Balukhali camp with 303 (95% posterior predictive interval 122-599) cases and would continue to grow in Kutupalong camp, requiring a bed capacity of 316 (95% posterior predictive interval (PPI) 197-499). On 19 December, a total of 54 cases were reported, lower than forecasted. Subsequent forecasts were more accurate: on 20 December, we predicted a total of 912 cases (95% PPI 367-2183) and 136 (95% PPI 55-327) hospitalizations until the end of the year, with 616 cases actually reported during this period.

CONCLUSIONS

Real-time modelling enabled feedback of key information about the potential scale of the epidemic, resource needs and mechanisms of transmission to decision-makers at a time when this information was largely unknown. By 20 December, the model generated reliable forecasts and helped support decision-making on operational aspects of the outbreak response, such as hospital bed and staff needs, and with advocacy for control measures. Although modelling is only one component of the evidence base for decision-making in outbreak situations, suitable analysis and forecasting techniques can be used to gain insights into an ongoing outbreak.

Comparison of stochastic and deterministic frameworks in dengue modelling

We perform estimations of compartment models for dengue transmission in rural Cambodia with increasing complexity regarding both model structure and the account for stochasticity. On the one hand, we successively account for three embedded sources of stochasticity: observation noise, demographic variability and environmental hazard. On the other hand, complexity in the model structure is increased by introducing vector-borne transmission, explicit asymptomatic infections and interacting virus serotypes. Using two sources of case data from dengue epidemics in Kampong Cham (Cambodia), models are estimated in the bayesian framework, with Markov Chain Monte Carlo and Particle Markov Chain Monte Carlo. We highlight the advantages and drawbacks of the different formulations in a practical setting. Although in this case the deterministic models provide a good approximation of the mean trajectory for a low computational cost, the stochastic frameworks better reflect and account for parameter and simulation uncertainty.