Bayesian Noise Modelling for State Estimation of the Spread of COVID-19 in Saudi Arabia with Extended Kalman Filters.

The epistemic uncertainty in coronavirus disease (COVID-19) model-based predictions using complex noisy data greatly affects the accuracy of pandemic trend and state estimations. Quantifying the uncertainty of COVID-19 trends caused by different unobserved hidden variables is needed to evaluate the accuracy of the predictions for complex compartmental epidemiological models. A new approach for estimating the measurement noise covariance from real COVID-19 pandemic data has been presented based on the marginal likelihood (Bayesian evidence) for Bayesian model selection of the stochastic part of the Extended Kalman filter (EKF), with a sixth-order nonlinear epidemic model, known as the SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Dead) compartmental model. This study presents a method for testing the noise covariance in cases of dependence or independence between the infected and death errors, to better understand their impact on the predictive accuracy and reliability of EKF statistical models. The proposed approach is able to reduce the error in the quantity of interest compared to the arbitrarily chosen values in the EKF estimation.

Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models.

During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an SIR-type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

A Bayesian two-stage group sequential scheme for ordinal endpoints

Ordinal endpoints are common in clinical studies. For example, many clinical trials for evaluating COVID-19 infection therapies have adopted an ordinal scale as recommended by the World Health Organization. Despite their importance in clinical studies, design methods for ordinal endpoints are limited;in practice, a dichotomized approach is often used for simplicity. Here, we introduce a Bayesian group sequential scheme to assess ordinal endpoints, which considers a proportional-odds (PO) model, a nonproportional-odds (NPO) model, and a PO/NPO-switch model to handle various scenarios. Extensive simulations are conducted to demonstrate desirable performance, and the R package BayesOrdDesign has been made publicly available.

The Maxwell-Burr X Distribution: Its Properties and Applications to the COVID-19 Mortality Rate in Thailand

A novel distribution, the Maxwell-Burr X (M-BX) distribution, was proposed. This distribution was an extension of the Burr X distribution by applying the Maxwell generalized family of distributions. The cumulative distribution function, probability density function, survival function, hazard function and quantile function of the M-BX distribution were defined. Some important properties and the parameters of its estimates were discussed. A simulation study was conducted from the basis of quantile function to ascertain the performance of maximum likelihood estimators. The M-BX distribution were also applied to model two lifetime data sets relating to the COVID-19 mortality rate in Thailand during different periods to express the flexibility of the distribution against other competing distributions. According to information criteria, AIC, CAIC, BIC, and HQIC, the M-BX distribution gave the best fit among all chosen distributions. © 2023, Thai Statistical Association. All rights reserved.

Model selection with decision support model for US natural gas consumption forecasting

Reliable prediction of natural gas consumption helps make the right decisions ensuring sustainable economic growth. This problem is addressed here by introducing a hybrid mathematical model defined as the Choquet integral-based model. Model selection is based on decision support model to consider the model performance more comprehensively. Different from the previous literature, we focus on the interaction between models when combine models. This paper adds grey accumulation generating operator to Holt-Winters model to capture more information in time series, and the grey wolf optimizer obtains the associated parameters. The proposed model can deal with seasonal (short-term) variability using season auto-regression moving average computation. Besides, it uses the long short term memory neural network to deal with long-term variability. The effectiveness of the developed model is validated on natural gas consumption due to the COVID-19 pandemic in the USA. For this, the model is customized using the publicly available datasets relevant to the USA energy sector. The model shows better robustness and outperforms other similar models since it consider the interaction between models. This means that it ensures reliable perdition, taking the highly uncertain factor (e.g., the COVID-19) into account. © 2023 Elsevier Ltd

An Optimal Model Selection for COVID 19 Disease Classification

In the current scenario, the pandemic created by coronavirus is on the boom, and that is why it becomes very critical to control and cure this disease. The currently available technique for coronavirus disease 2019 (COVID-19) testing, i.e., reverse transcription polymerase chain reaction (RT-PCR), turns out to be a lot of time-consuming and requires modern labs, equipment, and highly trained medical staff that are rare to get. Chest computerized tomography (CT) is however available with a lot of ease, and it will be fruitful if these machines are used for COVID-19 testing. During this pandemic, there is an absolute need for an efficient and readily accessible way for COVID-19 patients classification, and CT is one of the best ways to do so. Keeping that in fact, this chapter introduces a study for understanding which deep learning models give the best result when classifying COVID-19 patients using chest CT images. For this study, ResNet 50, ResNet 101, DenseNet 121, DenseNet 169, and DenseNet 201 are compared with each other on the basis of classification accuracy, and it has been observed that DenseNet 169 has the tendency to yield best results with the accuracy of 96%. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

An Optimal Model Selection for COVID 19 Disease Classification

In the current scenario, the pandemic created by coronavirus is on the boom, and that is why it becomes very critical to control and cure this disease. The currently available technique for coronavirus disease 2019 (COVID-19) testing, i.e., reverse transcription polymerase chain reaction (RT-PCR), turns out to be a lot of time-consuming and requires modern labs, equipment, and highly trained medical staff that are rare to get. Chest computerized tomography (CT) is however available with a lot of ease, and it will be fruitful if these machines are used for COVID-19 testing. During this pandemic, there is an absolute need for an efficient and readily accessible way for COVID-19 patients classification, and CT is one of the best ways to do so. Keeping that in fact, this chapter introduces a study for understanding which deep learning models give the best result when classifying COVID-19 patients using chest CT images. For this study, ResNet 50, ResNet 101, DenseNet 121, DenseNet 169, and DenseNet 201 are compared with each other on the basis of classification accuracy, and it has been observed that DenseNet 169 has the tendency to yield best results with the accuracy of 96%. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

A modified SEIR model with a jump in the transmission parameter applied to COVID-19 data on Wuhan.

In December 2019, Wuhan, the capital of Hubei Province, was struck by an outbreak of COVID-19. Numerous studies have been conducted to fit COVID-19 data and make statistical inferences. In applications, functions of the parameters in the model are usually used to assess severity of the outbreak. Because of the strategies applied during the struggle against the pandemic, the trend of the parameters changes abruptly. However, time-varying parameters with a jump have received scant attention in the literature. In this study, a modified SEIR model is proposed to fit the actual situation of the COVID-19 epidemic. In the proposed model, the dynamic propagation system is modified because of the high infectivity during incubation, and a time-varying parametric strategy is suggested to account for the utility of the intervention. A corresponding model selection algorithm based on the information criterion is also suggested to detect the jump in the transmission parameter. A real data analysis based on the COVID-19 epidemic in Wuhan and a simulation study demonstrate the plausibility and validity of the proposed method.

Regional and temporal differences in the relation between SARS-CoV-2 biomarkers in wastewater and estimated infection prevalence - Insights from long-term surveillance.

Wastewater-based epidemiology provides a conceptual framework for the evaluation of the prevalence of public health related biomarkers. In the context of the Coronavirus disease-2019, wastewater monitoring emerged as a complementary tool for epidemic management. In this study, we evaluated data from six wastewater treatment plants in the region of Saxony, Germany. The study period lasted from February to December 2021 and covered the third and fourth regional epidemic waves. We collected 1065 daily composite samples and analyzed SARS-CoV-2 RNA concentrations using reverse transcription-quantitative polymerase chain reaction (RT-qPCR). Regression models quantify the relation between RNA concentrations and disease prevalence. We demonstrated that the relation is site and time specific. Median loads per diagnosed case differed by a factor of 3-4 among sites during both waves and were on average 45 % higher during the third wave. In most cases, log-log-transformed data achieved better regression performance than non-transformed data and local calibration outperformed global models for all sites. The inclusion of lag/lead time, discharge and detection probability improved model performance in all cases significantly, but the importance of these components was also site and time specific. In all cases, models with lag/lead time and log-log-transformed data obtained satisfactory goodness-of-fit with adjusted coefficients of determination higher than 0.5. Back-estimation of testing efficiency from wastewater data confirmed state-wide prevalence estimation from individual testing statistics, but revealed pronounced differences throughout the epidemic waves and among the different sites.

Multiple partition Markov model for B.1.1.7, B.1.351, B.1.617.2, and P.1 variants of SARS-CoV 2 virus.

With tools originating from Markov processes, we investigate the similarities and differences between genomic sequences in FASTA format coming from four variants of the SARS-CoV 2 virus, B.1.1.7 (UK), B.1.351 (South Africa), B.1.617.2 (India), and P.1 (Brazil). We treat the virus' sequences as samples of finite memory Markov processes acting in A = { a , c , g , t } . We model each sequence, revealing some heterogeneity between sequences belonging to the same variant. We identified the five most representative sequences for each variant using a robust notion of classification, see Fernández et al. (Math Methods Appl Sci 43(13):7537-7549. 10.1002/mma.5705 ). Using a notion derived from a metric between processes, see García et al. (Appl Stoch Models Bus Ind 34(6):868-878. 10.1002/asmb.2346), we identify four groups, each group representing a variant. It is also detected, by this metric, global proximity between the variants B.1.351 and B.1.1.7. With the selected sequences, we assemble a multiple partition model, see Cordeiro et al. (Math Methods Appl Sci 43(13):7677-7691. 10.1002/mma.6079), revealing in which states of the state space the variants differ, concerning the mechanisms for choosing the next element in A. Through this model, we identify that the variants differ in their transition probabilities in eleven states out of a total of 256 states. For these eleven states, we reveal how the transition probabilities change from variant (group of variants) to variant (group of variants). In other words, we indicate precisely the stochastic reasons for the discrepancies.

Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study.

Background: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission. Methods: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates. Results: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi. Conclusions: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.

Detection of arrhythmia using weightage-based supervised learning system for COVID-19

COVID-19 disease has became a global pandemic in the last few years. This disease was highly contagious, and it quickly spread throughout several countries. Its infection can lead to severe implications for its victims, including cardiovascular issues. This complication develops in some people with a history of cardiovascular illness, whereas it emerges in others after COVID-19 infection. Cardiovascular problems are the primary cause of mortality in COVID-19 patients and are used to predict disease prognosis. Identifying arrhythmia from abnormalities in patient ECG signals is one approach to the detection of cardiovascular disorders. This is a laborious and time-consuming procedure that can be automated. The proposed method selects the most suitable model for this task. The selection is made through the weightage generated from the user’s requirements. The proposed method uses supervised learning to identify abnormalities in ECG waves. The models provided by the selection system during tests were able to meet user requirements. The models achieved up to 97% accuracy and 97% precision in predictive tasks.

STRUCTURAL AND PRACTICAL IDENTIFIABILITY ANALYSES ON THE TRANSMISSION DYNAMICS OF COVID-19 IN THE UNITED STATES∗

We formulate an epidemic model to capture essential epidemiology of COVID-19 and major public health interventions. We start with a system of differential equations involving six compartments, and we use the Goodman and Weare affine invariant ensemble Markov Chain Monte Carlo algorithm (GWMCMC) to identify a simplified version of the full model that consists of only four compartments. We examine well-posedness of the relevant parameter estimation problem for the given observations using the U.S. epidemic data;study the reliability of model selection;analyze the structural identifiability of the selected model;and conduct a practical identifiability analysis on the selected model using the GWMCMC algorithm. Our study shows that the selected model is structurally identifiable for the confirmed cases, and for small measurement errors, key parameters such as the transmission rate are practically identifiable. We also analyze the stability of the selected model and prove the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium by constructing appropriate Lyapunov functions. Our numerical experiments show that the U.S. will undergo damped transit oscillations towards the endemicity. © 2022, Wilmington Scientific Publisher. All rights reserved.

Empirical Quantitative Analysis of COVID-19 Forecasting Models

COVID-19 has been a public health emergency of international concern since early 2020. Reliable forecasting is critical to diminish the impact of this disease. To date, a large number of different forecasting models have been proposed, mainly including statistical models, compartmental models, and deep learning models. However, due to various uncertain factors across different regions such as economics and government policy, no forecasting model appears to be the best for all scenarios. In this paper, we perform quantitative analysis of COVID-19 forecasting of confirmed cases and deaths across different regions in the United States with different forecasting horizons, and evaluate the relative impacts of the following three dimensions on the predictive performance (improvement and variation) through different evaluation metrics: model selection, hyperparameter tuning, and the length of time series required for training. We find that if a dimension brings about higher performance gains, if not well-tuned, it may also lead to harsher performance penalties. Furthermore, model selection is the dominant factor in determining the predictive performance. It is responsible for both the largest improvement and the largest variation in performance in all prediction tasks across different regions. While practitioners may perform more complicated time series analysis in practice, they should be able to achieve reasonable results if they have adequate insight into key decisions like model selection. © 2021 IEEE.

Forecasting Facing Economic Shifts, Climate Change and Evolving Pandemics

By its emissions of greenhouse gases, economic activity is the source of climate change which affects pandemics that in turn can impact badly on economies. Across the three highly interacting disciplines in our title, time-series observations are measured at vastly different data frequencies: very low frequency at 1000-year intervals for paleoclimate, through annual, monthly to intra-daily for current climate;weekly and daily for pandemic data;annual, quarterly and monthly for economic data, and seconds or nano-seconds in finance. Nevertheless, there are important commonalities to economic, climate and pandemic time series. First, time series in all three disciplines are subject to non-stationarities from evolving stochastic trends and sudden distributional shifts, as well as data revisions and changes to data measurement systems. Next, all three have imperfect and incomplete knowledge of their data generating processes from changing human behaviour, so must search for reasonable empirical modeling approximations. Finally, all three need forecasts of likely future outcomes to plan and adapt as events unfold, albeit again over very different horizons. We consider how these features shape the formulation and selection of forecasting models to tackle their common data features yet distinct problems. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Examining Type 1 Diabetes Mathematical Models Using Experimental Data.

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with ß-cells and the other with no ß-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1-4, depending on the diabetes severity of each group, with severity increasing from group 1-4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no ß-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with ß-cells required more parameters to match the data and we fitted the ß-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1-3 ranging from 2.10 to 4.05. Our results suggest that the model without ß-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

The Emergence of SARS-CoV-2 Variants of Concern Is Driven by Acceleration of the Substitution Rate.

The ongoing SARS-CoV-2 pandemic has seen an unprecedented amount of rapidly generated genome data. These data have revealed the emergence of lineages with mutations associated to transmissibility and antigenicity, known as variants of concern (VOCs). A striking aspect of VOCs is that many of them involve an unusually large number of defining mutations. Current phylogenetic estimates of the substitution rate of SARS-CoV-2 suggest that its genome accrues around two mutations per month. However, VOCs can have 15 or more defining mutations and it is hypothesized that they emerged over the course of a few months, implying that they must have evolved faster for a period of time. We analyzed genome sequence data from the GISAID database to assess whether the emergence of VOCs can be attributed to changes in the substitution rate of the virus and whether this pattern can be detected at a phylogenetic level using genome data. We fit a range of molecular clock models and assessed their statistical performance. Our analyses indicate that the emergence of VOCs is driven by an episodic increase in the substitution rate of around 4-fold the background phylogenetic rate estimate that may have lasted several weeks or months. These results underscore the importance of monitoring the molecular evolution of the virus as a means of understanding the circumstances under which VOCs may emerge.

Spatiotemporal variable selection and air quality impact assessment of COVID-19 lockdown.

During the first wave of the COVID-19 pandemics in 2020, lockdown policies reduced human mobility in many countries globally. This significantly reduces car traffic-related emissions. In this paper, we consider the impact of the Italian restrictions (lockdown) on the air quality in the Lombardy Region. In particular, we consider public data on concentrations of particulate matters (PM10 and PM2.5) and nitrogen dioxide, pre/during/after lockdown. To reduce the effect of confounders, we use detailed regression function based on meteorological, land and calendar information. Spatial and temporal correlations are handled using a multivariate spatiotemporal model in the class of hidden dynamic geostatistical models (HDGM). Due to the large size of the design matrix, variable selection is made using a hybrid approach coupling the well known LASSO algorithm with the cross-validation performance of HDGM. The impact of COVID-19 lockdown is heterogeneous in the region. Indeed, there is high statistical evidence of nitrogen dioxide concentration reductions in metropolitan areas and near trafficked roads where also PM10 concentration is reduced. However, rural, industrial, and mountain areas do not show significant reductions. Also, PM2.5 concentrations lack significant reductions irrespective of zone. The post-lockdown restart shows unclear results.

Strategy to identify priority groups for COVID-19 vaccination: A population based cohort study.

BACKGROUND: Evidence from COVID-19 outbreak shows that individuals with specific chronic diseases are at higher risk of severe prognosis after infection. Public health authorities are developing vaccination programmes with priorities that minimize the risk of mortality and severe events in individuals and communities. We propose an evidence-based strategy that targets the frailest subjects whose timely vaccination is likely to minimize future deaths and preserve the resilience of the health service by preventing infections. METHODS: The cohort includes 146,087 cases with COVID-19 diagnosed in 2020 in Milan (3.49 million inhabitants). Individual level data on 42 chronic diseases and vital status updated as of January 21, 2021, were available in administrative data. Analyses were performed in three sub-cohorts of age (16-64, 65-79 and 80+ years) and comorbidities affecting mortality were selected by means of LASSO cross-validated conditional logistic regression. Simplified models based on previous results identified high-risk categories worth targeting with highest priority. Results adjusted by age and gender, were reported in terms of odds ratios and 95%CI. RESULTS: The final models include as predictors of mortality (7,667 deaths, 5.2%) 10, 12, and 5 chronic diseases, respectively. The older age categories shared, as risk factors, chronic renal failure, chronic heart failure, cerebrovascular disease, Parkinson disease and psychiatric diseases. In the younger age category, predictors included neoplasm, organ transplantation and psychiatric conditions. Results were consistent with those obtained on mortality at 60 days from diagnosis (6,968 deaths). CONCLUSION: This approach defines a two-level stratification for priorities in the vaccination that can easily be applied by health authorities, eventually adapted to local results in terms of number and types of comorbidities, and rapidly updated with current data. After the early phase of vaccination, data on effectiveness and safety will give the opportunity to revise prioritization and discuss the future approach in the remaining population.

COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling.

Epidemiological models are widely used to analyze the spread of diseases such as the global COVID-19 pandemic caused by SARS-CoV-2. However, all models are based on simplifying assumptions and often on sparse data. This limits the reliability of parameter estimates and predictions. In this manuscript, we demonstrate the relevance of these limitations and the pitfalls associated with the use of overly simplistic models. We considered the data for the early phase of the COVID-19 outbreak in Wuhan, China, as an example, and perform parameter estimation, uncertainty analysis and model selection for a range of established epidemiological models. Amongst others, we employ Markov chain Monte Carlo sampling, parameter and prediction profile calculation algorithms. Our results show that parameter estimates and predictions obtained for several established models on the basis of reported case numbers can be subject to substantial uncertainty. More importantly, estimates were often unrealistic and the confidence/credibility intervals did not cover plausible values of critical parameters obtained using different approaches. These findings suggest, amongst others, that standard compartmental models can be overly simplistic and that the reported case numbers provide often insufficient information for obtaining reliable and realistic parameter values, and for forecasting the evolution of epidemics.