Dynamic SARS-CoV-2 surveillance model combining seroprevalence and wastewater concentrations for post-vaccine disease burden estimates.

BACKGROUND: Despite wide scale assessments, it remains unclear how large-scale severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccination affected the wastewater concentration of the virus or the overall disease burden as measured by hospitalization rates. METHODS: We used weekly SARS-CoV-2 wastewater concentration with a stratified random sampling of seroprevalence, and linked vaccination and hospitalization data, from April 2021-August 2021 in Jefferson County, Kentucky (USA). Our susceptible ( S ), vaccinated ( V ), variant-specific infected ( I 1 and I 2 ), recovered ( R ), and seropositive ( T ) model ( S V I 2 R T ) tracked prevalence longitudinally. This was related to wastewater concentration. RESULTS: Here we show the 64% county vaccination rate translate into about a 61% decrease in SARS-CoV-2 incidence. The estimated effect of SARS-CoV-2 Delta variant emergence is a 24-fold increase of infection counts, which correspond to an over 9-fold increase in wastewater concentration. Hospitalization burden and wastewater concentration have the strongest correlation (r = 0.95) at 1 week lag. CONCLUSIONS: Our study underscores the importance of continuing environmental surveillance post-vaccine and provides a proof-of-concept for environmental epidemiology monitoring of infectious disease for future pandemic preparedness.

It is unclear how large-scale COVID-19 vaccination impacts wastewater concentration or overall disease burden. Here, we developed a mathematical surveillance model that allows estimation of overall vaccine impact based on the amount of SARS-CoV-2 in wastewater, seroprevalence and the number of cases admitted to hospitals between April 2021­August 2021 in Jefferson County, Kentucky USA. We found that a 64% vaccination coverage correlated to a 61% decrease in COVID-19 cases. The emergence of the SARS-CoV-2 Delta variant during the time of the surveillance directly correlated with a sharp increase in infection incidence as well as viral counts in wastewater. The hospitalization burden was closely reflected by the viral count found in the wastewater, indicating that post-vaccine environmental surveillance can be an effective method of estimating changing disease prevalence in future pandemics.

Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks.

We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative binomial distribution. The proof relies on establishing the equivalence, for these specific degree distributions, between the closed pairwise model and a dynamical survival analysis (DSA) model that was previously shown to be exact. Specifically, we demonstrate that the DSA model is equivalent to the well-known edge-based Volz model. Using this result, we also provide reductions of the closed pairwise and Volz models to a single equation that involves only susceptibles. This equation has a useful statistical interpretation in terms of times to infection. We provide some numerical examples to illustrate our results.

Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio.

The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, the Dynamical Survival Analysis (DSA) method has been shown to be an effective tool in analyzing complex non-Markovian epidemic processes that are otherwise difficult to handle using standard methods. One of the advantages of Dynamical Survival Analysis (DSA) is its representation of typical epidemic data in a simple although not explicit form that involves solutions of certain differential equations. In this work we describe how a complex non-Markovian Dynamical Survival Analysis (DSA) model may be applied to a specific data set with the help of appropriate numerical and statistical schemes. The ideas are illustrated with a data example of the COVID-19 epidemic in Ohio.

Projecting COVID-19 cases and hospital burden in Ohio.

As the Coronavirus 2019 disease (COVID-19) started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at The Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: (1) A Dynamical Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. (2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology is also made publicly available. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Wastewater and seroprevalence for pandemic preparedness: variant analysis, vaccination effect, and hospitalization forecasting for SARS-CoV-2, in Jefferson County, Kentucky.

Despite wide scale assessments, it remains unclear how large-scale SARS-CoV-2 vaccination affected the wastewater concentration of the virus or the overall disease burden as measured by hospitalization rates. We used weekly SARS-CoV-2 wastewater concentration with a stratified random sampling of seroprevalence, and linked vaccination and hospitalization data, from April 2021-August 2021 in Jefferson County, Kentucky (USA). Our susceptible (S), vaccinated (V), variant-specific infected I1 and I2, recovered (R), and seropositive (T) model SVI2RT tracked prevalence longitudinally. This was related to wastewater concentration. The 64% county vaccination rate translated into about 61% decrease in SARS-CoV-2 incidence. The estimated effect of SARS-CoV-2 Delta variant emergence was a 24-fold increase of infection counts, which corresponded to an over 9-fold increase in wastewater concentration. Hospitalization burden and wastewater concentration had the strongest correlation (r = 0.95) at 1 week lag. Our study underscores the importance of continued environmental surveillance post-vaccine and provides a proof-of-concept for environmental epidemiology monitoring of infectious disease for future pandemic preparedness.

Quantifying the relationship between sub-population wastewater samples and community-wide SARS-CoV-2 seroprevalence.

Robust epidemiological models relating wastewater to community disease prevalence are lacking. Assessments of SARS-CoV-2 infection rates have relied primarily on convenience sampling, which does not provide reliable estimates of community disease prevalence due to inherent biases. This study conducted serial stratified randomized samplings to estimate the prevalence of SARS-CoV-2 antibodies in 3717 participants, and obtained weekly samples of community wastewater for SARS-CoV-2 concentrations in Jefferson County, KY (USA) from August 2020 to February 2021. Using an expanded Susceptible-Infected-Recovered model, the longitudinal estimates of the disease prevalence were obtained and compared with the wastewater concentrations using regression analysis. The model analysis revealed significant temporal differences in epidemic peaks. The results showed that in some areas, the average incidence rate, based on serological sampling, was 50 % higher than the health department rate, which was based on convenience sampling. The model-estimated average prevalence rates correlated well with the wastewater (correlation = 0.63, CI (0.31,0.83)). In the regression analysis, a one copy per ml-unit increase in weekly average wastewater concentration of SARS-CoV-2 corresponded to an average increase of 1-1.3 cases of SARS-CoV-2 infection per 100,000 residents. The analysis indicates that wastewater may provide robust estimates of community spread of infection, in line with the modeled prevalence estimates obtained from stratified randomized sampling, and is therefore superior to publicly available health data.

Projecting COVID-19 Cases and Subsequent Hospital Burden in Ohio.

As the Coronavirus 2019 (COVID-19) disease started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at the Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: 1) A Dynamic Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. 2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology has been made available publicly. Highlights: We present a novel statistical approach called Dynamic Survival Analysis (DSA) to model an epidemic curve with incomplete data. The DSA approach is advantageous over standard statistical methods primarily because it does not require prior knowledge of the size of the susceptible population, the overall prevalence of the disease, and also the shape of the epidemic curve.The principal motivation behind the study was to obtain predictions of case counts of COVID-19 and the resulting hospital burden in the state of Ohio during the early phase of the pandemic.The proposed methodology was applied to the COVID-19 incidence data in the state of Ohio to support the Ohio Department of Health (ODH) and the Ohio Hospital Association (OHA) with predictions of hospital burden in each of the Hospital Catchment Areas (HCAs) of the state.

Dynamic survival analysis for non-Markovian epidemic models.

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method's versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.

Quantifying the Population-Level Effect of the COVID-19 Mass Vaccination Campaign in Israel: A Modeling Study.

Background: Estimating real-world vaccine effectiveness is challenging as a variety of population factors can impact vaccine effectiveness. We aimed to assess the population-level reduction in cumulative severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases, hospitalizations, and mortality due to the BNT162b2 mRNA coronavirus disease 2019 (COVID-19) vaccination campaign in Israel during January-February 2021. Methods: A susceptible-infected-recovered/removed (SIR) model and a Dynamic Survival Analysis (DSA) statistical approach were used. Daily counts of individuals who tested positive and of vaccine doses administered, obtained from the Israeli Ministry of Health, were used to calibrate the model. The model was parameterized using values derived from a previous phase of the pandemic during which similar lockdown and other preventive measures were implemented in order to take into account the effect of these prevention measures on COVID-19 spread. Results: Our model predicted for the total population a reduction of 648 585 SARS-CoV-2 cases (75% confidence interval [CI], 25 877-1 396 963) during the first 2 months of the vaccination campaign. The number of averted hospitalizations for moderate to severe conditions was 16 101 (75% CI, 2010-33 035), and reduction of death was estimated at 5123 (75% CI, 388-10 815) fatalities. Among children aged 0-19 years, we estimated a reduction of 163 436 (75% CI, 0-433 233) SARS-CoV-2 cases, which we consider to be an indirect effect of the vaccine. Conclusions: Our results suggest that the rapid vaccination campaign prevented hundreds of thousands of new cases as well as thousands of hospitalizations and fatalities and has probably averted a major health care crisis.

Analysis of individual-level data from 2018-2020 Ebola outbreak in Democratic Republic of the Congo.

The 2018-2020 Ebola virus disease epidemic in Democratic Republic of the Congo (DRC) resulted in 3481 cases (probable and confirmed) and 2299 deaths. In this paper, we use a novel statistical method to analyze the individual-level incidence and hospitalization data on DRC Ebola victims. Our analysis suggests that an increase in the rate of quarantine and isolation that has shortened the infectiousness period by approximately one day during the epidemic's third and final wave was likely responsible for the eventual containment of the outbreak. The analysis further reveals that the total effective population size or the average number of individuals at risk for the disease exposure in three epidemic waves over the period of 24 months was around 16,000-a much smaller number than previously estimated and likely an evidence of at least partial protection of the population at risk through ring vaccination and contact tracing as well as adherence to strict quarantine and isolation policies.

A machine learning model for nowcasting epidemic incidence.

Due to delay in reporting, the daily national and statewide COVID-19 incidence counts are often unreliable and need to be estimated from recent data. This process is known in economics as nowcasting. We describe in this paper a simple random forest statistical model for nowcasting the COVID-19 daily new infection counts based on historic data along with a set of simple covariates, such as the currently reported infection counts, day of the week, and time since first reporting. We apply the model to adjust the daily infection counts in Ohio, and show that the predictions from this simple data-driven method compare favorably both in quality and computational burden to those obtained from the state-of-the-art hierarchical Bayesian model employing a complex statistical algorithm. The interactive notebook for performing nowcasting is available online at https://tinyurl.com/simpleMLnowcasting.

Binary Classification for Failure Risk Assessment.

Survival analysis is tremendously powerful, and is a popular methodology for analyzing time to event models in bioinformatics. Furthermore, several of its extensions can simultaneously perform variable selection in conjunction with model estimation. While this flexibility is extremely desirable, under certain scenarios, binary class variable selection and classification methods might provide more reliable risk estimates. Synthetic simulations and real data case studies suggest that when (1) randomly censored points comprise only a small portion of data, (2) biological markers are weak, (3) it is desired to compute risk across predetermined time intervals, and (4) the assumptions of the competing time to event models are violated, binary class models tend to perform superior. In practice, it might be prudent to test both model families to guarantee adequate analysis. Here we describe the pipeline of binary class feature selection and classification for time to event risk assessment.

Incorporating age and delay into models for biophysical systems.

In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this paper, we consider relaxing this assumption by incorporating age-dependent random time delays (distributed according to a given probability distribution) into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of partial differential equations (PDEs) in the large-volume limit, as opposed to ordinary differential equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms. In order to describe the ideas, we use a simple transcription process as a running example. We, however, note that the methods developed in this paper apply to a wide class of biophysical systems.

Bone Morphogenic Proteins Are Immunoregulatory Cytokines Controlling FOXP3+ Treg Cells.

Bone morphogenic proteins (BMPs) are members of the transforming growth factor ß (TGF-ß) cytokine family promoting differentiation, homeostasis, and self-renewal of multiple tissues. We show that signaling through the bone morphogenic protein receptor 1α (BMPR1α) sustains expression of FOXP3 in Treg cells in peripheral lymphoid tissues. BMPR1α signaling promotes molecular circuits supporting acquisition and preservation of Treg cell phenotype and inhibiting differentiation of pro-inflammatory effector Th1/Th17 CD4+ T cell. Mechanistically, increased expression of KDM6B (JMJD3) histone demethylase, an antagonist of the polycomb repressive complex 2, underlies lineage-specific changes of T cell phenotypes associated with abrogation of BMPR1α signaling. These results reveal that BMPs are immunoregulatory cytokines mediating maturation and stability of peripheral FOXP3+ regulatory T cells (Treg cells) and controlling generation of iTreg cells. Thus, we establish that BMPs, a large cytokine family, are an essential link between stromal tissues and the adaptive immune system involved in sustaining tissue homeostasis by promoting immunological tolerance.

High dimensional model representation of log likelihood ratio: binary classification with SNP data.

BACKGROUND: Developing binary classification rules based on SNP observations has been a major challenge for many modern bioinformatics applications, e.g., predicting risk of future disease events in complex conditions such as cancer. Small-sample, high-dimensional nature of SNP data, weak effect of each SNP on the outcome, and highly non-linear SNP interactions are several key factors complicating the analysis. Additionally, SNPs take a finite number of values which may be best understood as ordinal or categorical variables, but are treated as continuous ones by many algorithms. METHODS: We use the theory of high dimensional model representation (HDMR) to build appropriate low dimensional glass-box models, allowing us to account for the effects of feature interactions. We compute the second order HDMR expansion of the log-likelihood ratio to account for the effects of single SNPs and their pairwise interactions. We propose a regression based approach, called linear approximation for block second order HDMR expansion of categorical observations (LABS-HDMR-CO), to approximate the HDMR coefficients. We show how HDMR can be used to detect pairwise SNP interactions, and propose the fixed pattern test (FPT) to identify statistically significant pairwise interactions. RESULTS: We apply LABS-HDMR-CO and FPT to synthetically generated HAPGEN2 data as well as to two GWAS cancer datasets. In these examples LABS-HDMR-CO enjoys superior accuracy compared with several algorithms used for SNP classification, while also taking pairwise interactions into account. FPT declares very few significant interactions in the small sample GWAS datasets when bounding false discovery rate (FDR) by 5%, due to the large number of tests performed. On the other hand, LABS-HDMR-CO utilizes a large number of SNP pairs to improve its prediction accuracy. In the larger HAPGEN2 dataset FTP declares a larger portion of SNP pairs used by LABS-HDMR-CO as significant. CONCLUSION: LABS-HDMR-CO and FPT are interesting methods to design prediction rules and detect pairwise feature interactions for SNP data. Reliably detecting pairwise SNP interactions and taking advantage of potential interactions to improve prediction accuracy are two different objectives addressed by these methods. While the large number of potential SNP interactions may result in low power of detection, potentially interacting SNP pairs, of which many might be false alarms, can still be used to improve prediction accuracy.

High dimensional model representation of log-likelihood ratio: binary classification with expression data.

BACKGROUND: Binary classification rules based on a small-sample of high-dimensional data (for instance, gene expression data) are ubiquitous in modern bioinformatics. Constructing such classifiers is challenging due to (a) the complex nature of underlying biological traits, such as gene interactions, and (b) the need for highly interpretable glass-box models. We use the theory of high dimensional model representation (HDMR) to build interpretable low dimensional approximations of the log-likelihood ratio accounting for the effects of each individual gene as well as gene-gene interactions. We propose two algorithms approximating the second order HDMR expansion, and a hypothesis test based on the HDMR formulation to identify significantly dysregulated pairwise interactions. The theory is seen as flexible and requiring only a mild set of assumptions. RESULTS: We apply our approach to gene expression data from both synthetic and real (breast and lung cancer) datasets comparing it also against several popular state-of-the-art methods. The analyses suggest the proposed algorithms can be used to obtain interpretable prediction rules with high prediction accuracies and to successfully extract significantly dysregulated gene-gene interactions from the data. They also compare favorably against their competitors across multiple synthetic data scenarios. CONCLUSION: The proposed HDMR-based approach appears to produce a reliable classifier that additionally allows one to describe how individual genes or gene-gene interactions affect classification decisions. Both real and synthetic data analyses suggest that our methods can be used to identify gene networks with dysregulated pairwise interactions, and are therefore appropriate for differential networks analysis.

Survival dynamical systems: individual-level survival analysis from population-level epidemic models.

In this paper, we show that solutions to ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models can be interpreted as survival or cumulative hazard functions when analysing data on individuals sampled from the population. We refer to the individual-level survival and hazard functions derived from population-level equations as a survival dynamical system (SDS). To illustrate how population-level dynamics imply probability laws for individual-level infection and recovery times that can be used for statistical inference, we show numerical examples based on synthetic data. In these examples, we show that an SDS analysis compares favourably with a complete-data maximum-likelihood analysis. Finally, we use the SDS approach to analyse data from a 2009 influenza A(H1N1) outbreak at Washington State University.

Dormant pathogenic CD4+ T cells are prevalent in the peripheral repertoire of healthy mice.

Thymic central tolerance eliminates most immature T cells with autoreactive T cell receptors (TCR) that recognize self MHC/peptide complexes. Regardless, an unknown number of autoreactive CD4+Foxp3- T cells escape negative selection and in the periphery require continuous suppression by CD4+Foxp3+ regulatory cells (Tregs). Here, we compare immune repertoires of Treg-deficient and Treg-sufficient mice to find Tregs continuously constraining one-third of mature CD4+Foxp3- cells from converting to pathogenic effectors in healthy mice. These dormant pathogenic clones frequently express TCRs activatable by ubiquitous autoantigens presented by class II MHCs on conventional dendritic cells, including self-peptides that select them in the thymus. Our data thus suggest that identification of most potentially autoreactive CD4+ T cells in the peripheral repertoire is critical to harness or redirect these cells for therapeutic advantage.

Ligand-Free Estrogen Receptor α (ESR1) as Master Regulator for the Expression of CYP3A4 and Other Cytochrome P450 Enzymes in the Human Liver.

Cytochrome P450 3A4 isoform (CYP3A4) transcription is controlled by hepatic transcription factors (TFs), but how TFs dynamically interact remains uncertain. We hypothesize that several TFs form a regulatory network with nonlinear, dynamic, and hierarchical interactions. To resolve complex interactions, we have applied a computational approach for estimating Sobol's sensitivity indices (SSI) under generalized linear models to existing liver RNA expression microarray data (GSE9588) and RNA-seq data from genotype-tissue expression (GTEx), generating robust importance ranking of TF effects and interactions. The SSI-based analysis identified TFs and interacting TF pairs, triplets, and quadruplets involved in CYP3A4 expression. In addition to known CYP3A4 TFs, estrogen receptor α (ESR1) emerges as key TF with the strongest main effect and as the most frequently included TF interacting partner. Model predictions were validated using small interfering RNA (siRNA)/short hairpin RNA (shRNA) gene knockdown and clustered regularly interspaced short palindromic repeats (CRISPR)-mediated transcriptional activation of ESR1 in biliary epithelial Huh7 cells and human hepatocytes in the absence of estrogen. Moreover, ESR1 and known CYP3A4 TFs mutually regulate each other. Detectable in both male and female hepatocytes without added estrogen, the results demonstrate a role for unliganded ESR1 in CYP3A4 expression consistent with unliganded ESR1 signaling reported in other cell types. Added estrogen further enhances ESR1 effects. We propose a hierarchical regulatory network for CYP3A4 expression directed by ESR1 through self-regulation, cross regulation, and TF-TF interactions. We also demonstrate that ESR1 regulates the expression of other P450 enzymes, suggesting broad influence of ESR1 on xenobiotics metabolism in human liver. Further studies are required to understand the mechanisms underlying role of ESR1 in P450 regulation. SIGNIFICANCE STATEMENT: This study focuses on identifying key transcription factors and regulatory networks for CYP3A4, the main drug metabolizing enzymes in liver. We applied a new computational approach (Sobol's sensitivity analysis) to existing hepatic gene expression data to determine the role of transcription factors in regulating CYP3A4 expression, and used molecular genetics methods (siRNA/shRNA gene knockdown and CRISPR-mediated transcriptional activation) to test these interactions in life cells. This approach reveals a robust network of TFs, including their putative interactions and the relative impact of each interaction. We find that ESR1 serves as a key transcription factor function in regulating CYP3A4, and it appears to be acting at least in part in a ligand-free fashion.