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Grzegorz A. Rempala

Publications and source records attributed to Grzegorz A. Rempala.

At least 19 recordsLinked to original sources
arXiv2026

Variable Selection for Infectious Disease Transmission via Penalized Pairwise Accelerated Failure Time Models

In infectious disease transmission, regression and variable selection for time-to-event outcomes are complicated by transmission-induced dependence that violates standard independence assumptions. Pairwise survival analysis addresses this dependence by modeling contact intervals in ordered pairs, defined as the time from the onset of infectiousness in the pair's first individual to their first infectious contact with the second individual. We propose a penalized pairwise accelerated failure time model for contact intervals that accommodates simultaneous covariate effects on infectiousness and susceptibility while jointly representing within-population transmission and infection from external sources. For variable selection with many candidate covariates, we develop adaptive LASSO penalized maximum likelihood estimation with a coordinate descent algorithm, treating distributional baseline parameters as unpenalized nuisance parameters. We establish selection consistency and asymptotic normality of the adaptive LASSO estimator under profile-likelihood regularity conditions in a local asymptotic regime in which information accumulates over all ordered pairs that are ever at risk of transmission during follow-up. Simulation studies show accurate variable selection and improved estimation accuracy compared with the unpenalized estimator and the LASSO. We illustrate the method using 2009 household influenza A (H1N1) surveillance data from Los Angeles County, where the adaptive LASSO produces a sparse, interpretable model and improves the precision of selected covariate effect estimates, including the effect of antiviral prophylaxis on susceptibility.

stat.ME↗
arXiv2026

Kalman Filtering and Smoothing for Improving Precision in Horvitz--Thompson Estimation of Infectious Disease Prevalence

Horvitz--Thompson (HT) estimators can provide unbiased daily estimates of infectious disease prevalence under repeated surveillance by correcting for nonrandom testing induced by scheduled, symptom-based, and contact-tracing components. However, because each HT estimate is based on the testing data available for that day and may involve highly variable inverse probability weights, it can be noisy, have precision that varies over time, and become unavailable during temporary interruptions in testing. The daily HT estimator is modeled as a noisy observation of an underlying prevalence process, with day-specific observation variances estimated using a delete-a-group jackknife. Our primary specification is a joint local linear trend state-space model that extends the standard level-only random walk by adding a latent slope. The Kalman filter improves precision by borrowing information from past estimates. At each time $t$, the process variances are estimated or carried forward using only observations available through time $t$, so the resulting filtered estimate is available in real time. We also describe the corresponding Kalman smoother as a retrospective extension based on the full observed series. When daily HT estimates are missing, the Kalman filter proceeds through prediction-only updates, whereas the corresponding smoother retrospectively reconstructs those periods using later observations. In simulations, the joint Kalman filter substantially improves precision relative to the raw daily HT estimator while preserving the main temporal pattern, and the smoother provides a more stable retrospective summary. In The Ohio State University's fall 2020 SARS-CoV-2 surveillance data, the filter and smoother provide estimates on no-testing days, when the HT estimator provides neither point nor interval estimates, and yield narrower confidence intervals than HT intervals on observed days.

stat.ME↗
arXiv2026

A Counterfactual Framework for Estimating Infectious Disease Prevalence under Repeated Testing with Symptomatic and Contact-Tracing Components

This paper addresses the problem of estimating infectious disease prevalence under longitudinal testing programs that include scheduled, symptomatic, and contact-tracing testing. Our study is motivated by data from The Ohio State University, where a mandatory once-per-week COVID-19 testing and isolation program was implemented during the Fall 2020 semester, supplemented by additional testing for symptomatic individuals and identified contacts. In this setting, the probability of being tested depends on symptoms or contact-tracing status, creating a complex observation process. We develop a counterfactual framework that links the observation process to a hypothetical process in which infection is prevented. This formulation enables unbiased estimation of disease prevalence by modeling the testing process, possibly nonparametrically, without requiring explicit modeling of transmission dynamics, even though the testing and infection processes are jointly dependent.

stat.ME↗
arXiv2026

From Individual-Based Stochastic Epidemics to Heterogeneous SIR Equations

We develop a stochastic framework for a broad class of heterogeneous SIR epidemic models. In the finite-population construction, each initially susceptible individual is assigned a fixed nonnegative susceptibility, and infection occurs when the accumulated population-level infection pressure exceeds an individual random threshold. Infectious periods are independent and exponentially distributed with a common recovery rate. For any susceptibility distribution with finite mean, we prove a uniform-on-compact law of large numbers for the susceptible, infectious, removed, and cumulative infection-pressure processes. In the limit, an individual with susceptibility lambda remains susceptible under cumulative pressure x with probability exp(-x lambda). It follows that the susceptible fraction is given by the Laplace transform of the initial susceptibility distribution, while the incidence rate is governed by the mean susceptibility among those who remain susceptible. The resulting limits recover several familiar heterogeneous SIR systems, including the classical power-law model, and also yield other closed nonlinear incidence forms. The framework therefore provides a unified probabilistic foundation for deterministic epidemic models with persistent individual heterogeneity.

math.PR↗
arXiv2026

Approximating Peak Prevalence in Multistage SIR Epidemics

Estimating peak prevalence is a central problem in epidemic modeling because it determines the period of greatest infectious burden and is closely linked to health-care demand. In multistage SIR models, however, peak prevalence is generally less tractable than in the classical model with exponentially distributed infectious periods. Motivated by the use of weighted infectious-stage aggregates as surrogates for prevalence, we investigate the relationship between the prevalence peak and the maximum of a weighted stage functional in deterministic SI$(k)$R epidemic models. We show that this relationship depends critically on how the stage-progression rate is scaled as the number of infectious stages increases. Under naive scaling, in which the progression rate remains fixed, the weighted peak is asymptotically equivalent to the prevalence peak and the commonly used factor-two approximation fails. Under Erlang scaling, which preserves the mean infectious period, the multistage model converges to a delay formulation in which prevalence and the weighted stage functional become unweighted and triangularly weighted moving averages of incidence. This limiting representation provides a theoretical basis for the factor-two approximation and identifies the regimes in which it is accurate. It also explains why this approximation deteriorates as epidemic waves become more sharply peaked. We derive analytical error bounds and develop curvature-based and parameter-based corrections that substantially improve accuracy. Numerical studies confirm these improvements across a broad range of epidemiological parameters. Overall, the results show when weighted-stage peaks can be used reliably as proxies for peak prevalence and how the resulting estimates can be refined when the standard approximation loses accuracy.

q-bio.PE↗
arXiv2025

Inference for stochastic reaction networks via logistic regression

Identifying network structure and inferring parameters are central challenges in modeling chemical reaction networks. In this study, we propose likelihood-based methods grounded in multinomial logistic regression to infer both stoichiometries and network connectivity structure from full time-series trajectories of stochastic chemical reaction networks. When complete molecular count trajectories are observed for all species, stoichiometric coefficients are identifiable, provided each reaction occurs at least once during the observation window. However, identifying catalytic species remains difficult, as their molecular counts remain unchanged before and after each reaction event. Through three illustrative stochastic models involving catalytic interactions in open networks, we demonstrate that the logistic regression framework, when applied properly, can recover the full network structure, including stoichiometric relationships. We further apply Bayesian logistic regression to estimate model parameters in real-world epidemic settings, using the COVID-19 outbreak in the Greater Seoul area of South Korea as a case study. Our analysis focuses on a Susceptible--Infected--Recovered (SIR) network model that incorporates demographic effects. To address the challenge of partial observability, particularly the availability of data only for the infectious subset of the population, we develop a method that integrates Bayesian logistic regression with differential equation models. This approach enables robust inference of key SIR parameters from observed COVID-19 case trajectories. Overall, our findings demonstrate that simple, likelihood-based techniques such as logistic regression can recover meaningful mechanistic insights from both synthetic and empirical time-series data.

q-bio.QM↗
arXiv2024

Poisson Network SIR Epidemic Model

We extend the classical Susceptible-Infected-Recovered (SIR) model to a network-based framework where the degree distribution of nodes follows a Poisson distribution. This extension incorporates an additional parameter representing the mean node degree, allowing for the inclusion of heterogeneity in contact patterns. Using this enhanced model, we analyze epidemic data from the 2018-20 Ebola outbreak in the Democratic Republic of the Congo, employing a survival approach combined with the Hamiltonian Monte Carlo method. Our results suggest that network-based models can more effectively capture the heterogeneity of epidemic dynamics compared to traditional compartmental models, without introducing unduly overcomplicated compartmental framework.

q-bio.PE↗
arXiv2024

Infinitesimal Homeostasis in Mass-Action Systems

Homeostasis occurs in a biological system when a chosen output variable remains approximately constant despite changes in an input variable. In this work we specifically focus on biological systems which may be represented as chemical reaction networks and consider their infinitesimal homeostasis, where the derivative of the input-output function is zero. The specific challenge of chemical reaction networks is that they often obey various conservation laws complicating the standard input-output analysis. We derive several results that allow to verify the existence of infinitesimal homeostasis points both in the absence of conservation and under conservation laws where conserved quantities serve as input parameters. In particular, we introduce the notion of infinitesimal concentration robustness, where the output variable remains nearly constant despite fluctuations in the conserved quantities. We provide several examples of chemical networks which illustrate our results both in deterministic and stochastic settings.

q-bio.QM↗
arXiv2023

Equivalence of Mass Action and Poisson Network SIR Epidemic Models

This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a century ago by Kermack and McKendrick. We demonstrate that the decline pattern in susceptibles is identical for both models. This equivalence carries practical implications: the susceptibles decay curve, often referred to as the epidemic or incidence curve, is frequently used in empirical studies to forecast epidemic dynamics. Although the curves for susceptibles align perfectly, those for infections do differ. Yet, the infection curves tend to converge and become almost indistinguishable in high-degree networks. In summary, our analysis suggests that under many practical scenarios, it is acceptable to use the classical SIR model as a close approximation to the Poisson SIR network model.

q-bio.PE↗
arXiv2023

Overcoming Repeated Testing Schedule Bias in Estimates of Disease Prevalence

During the COVID-19 pandemic, many institutions such as universities and workplaces implemented testing regimens with every member of some population tested longitudinally, and those testing positive isolated for some time. Although the primary purpose of such regimens was to suppress disease spread by identifying and isolating infectious individuals, testing results were often also used to obtain prevalence and incidence estimates. Such estimates are helpful in risk assessment and institutional planning and various estimation procedures have been implemented, ranging from simple test-positive rates to complex dynamical modeling. Unfortunately, the popular test-positive rate is a biased estimator of prevalence under many seemingly innocuous longitudinal testing regimens with isolation. We illustrate how such bias arises and identify conditions under which the test-positive rate is unbiased. Further, we identify weaker conditions under which prevalence is identifiable and propose a new estimator of prevalence under longitudinal testing. We evaluate the proposed estimation procedure via simulation study and illustrate its use on a dataset derived by anonymizing testing data from The Ohio State University.

stat.ME↗
arXiv2023

Individual molecules dynamics in reaction network models

In a stochastic reaction network setting we consider the problem of tracking the fate of individual molecules. We show that using the classical large volume limit results, we may approximate the dynamics of a single tracked molecule in a simple and computationally efficient way. We give examples on how this approach may be used to obtain various characteristics of single-molecule dynamics (for instance, the distribution of the number of infections in a single individual in the course of an epidemic or the activity time of a single enzyme molecule). Moreover, we show how to approximate the overall dynamics of species of interest in the full system with a collection of independent single-molecule trajectories, and give explicit bounds for the approximation error in terms of the reaction rates. This approximation, which is well defined for all times, leads to an efficient and fully parallelizable simulation technique for which we provide some numerical examples.

math.PR↗
arXiv2022

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

We prove that the exact closure of SIR pairwise epidemic equations on a configuration model network is possible if and only if the degree distribution is Poisson, Binomial, or Negative Binomial. The proof relies on establishing, for these specific degree distributions, the equivalence of the closed pairwise model and the so-called dynamical survival analysis (DSA) edge-based model which was previously shown to be exact. Indeed, as we show here, the DSA model is equivalent to the well-known edge-based Volz model. We use this result to provide reductions of the closed pairwise and Volz models to the same single equation involving only susceptibles, which has a useful statistical interpretation in terms of the times to infection. We illustrate our findings with some numerical examples.

q-bio.PE↗
arXiv2022

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, DSA 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 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 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.

q-bio.PE↗
arXiv2022

Dynamic Survival Analysis for non-Markovian Epidemic Models

We present a new method for analyzing stochastic epidemic models under minimal assumptions. The method, dubbed DSA, is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of PDE 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 the FMD in the United Kingdom and the COVID-19 in India show good accuracy and confirm method's versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modeling, analyzing and interpreting epidemic data with the help of the DSA approach.

q-bio.PE↗
arXiv2021

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.

q-bio.QM↗
arXiv2020

Forecasting elections using compartmental models of infection

Forecasting elections -- a challenging, high-stakes problem -- is the subject of much uncertainty, subjectivity, and media scrutiny. To shed light on this process, we develop a method for forecasting elections from the perspective of dynamical systems. Our model borrows ideas from epidemiology, and we use polling data from United States elections to determine its parameters. Surprisingly, our general model performs as well as popular forecasters for the 2012 and 2016 U.S. races for president, senators, and governors. Although contagion and voting dynamics differ, our work suggests a valuable approach to elucidate how elections are related across states. It also illustrates the effect of accounting for uncertainty in different ways, provides an example of data-driven forecasting using dynamical systems, and suggests avenues for future research on political elections. We conclude with our forecasts for the senatorial and gubernatorial races on 6~November 2018, which we posted on 5 November 2018.

physics.soc-ph↗
arXiv2020

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 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.

q-bio.PE↗