How to correctly fit an SIR model to data from an SEIR model?

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases.

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 ( ), vaccinated ( ), variant-specific infected ( and ), recovered ( ), and seropositive ( ) model ( ) tracked prevalence longitudinally.

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.

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.

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.

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.

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

Unlabelled: 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.

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.

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.

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.

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.

Bone Morphogenic Proteins Are Immunoregulatory Cytokines Controlling FOXP3 T Cells.

Bone morphogenic proteins (BMPs) are members of the transforming growth factor β (TGF-β) 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 T cells in peripheral lymphoid tissues. BMPR1α signaling promotes molecular circuits supporting acquisition and preservation of T cell phenotype and inhibiting differentiation of pro-inflammatory effector Th1/Th17 CD4 T cell.

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.

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.

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.

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.

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 CD4Foxp3 T cells escape negative selection and in the periphery require continuous suppression by CD4Foxp3 regulatory cells (Tregs). Here, we compare immune repertoires of Treg-deficient and Treg-sufficient mice to find Tregs continuously constraining one-third of mature CD4Foxp3 cells from converting to pathogenic effectors in healthy mice.

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

Cytochrome P450 3A4 isoform () 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.

Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics.

The paper outlines a general approach to deriving quasi-steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis-Menten enzyme kinetics. In particular, it explains how different sets of assumptions about chemical species abundance and reaction rates lead to the standard QSSA, the total QSSA, and the reverse QSSA. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation settings, and several sets of conditions for their validity have been proposed.

Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC.

We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by in city of Isiro, Democratic Republic of the Congo.

Modeling household transmission dynamics: Application to waterborne diarrheal disease in Central Africa.

Introduction: We describe a method for analyzing the within-household network dynamics of a disease transmission. We apply it to analyze the occurrences of endemic diarrheal disease in Cameroon, Central Africa based on observational, cross-sectional data available from household health surveys.

Methods: To analyze the data, we apply formalism of the dynamic SID (susceptible-infected-diseased) process that describes the disease steady-state while adjusting for the household age-structure and environment contamination, such as water contamination.

Estimation of Sobol's Sensitivity Indices under Generalized Linear Models.

We derive explicit formulas for Sobol's sensitivity indices (SSIs) under the generalized linear models (GLMs) with independent or multivariate normal inputs. We argue that the main-effect SSIs provide a powerful tool for variable selection under GLMs with identity links under polynomial regressions. We also show via examples that the SSI-based variable selection results are similar to the ones obtained by the random forest algorithm but without the computational burden of data permutation.