MS03 - MEPI-10

Mathematical Epidemiology: Infectious disease modeling across time, space, and scale (Part 1)

Tuesday, July 15 at 10:20am

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Note: this minisymposia has multiple sessions. The other session is: and Part-2.

Meredith Greer, Prashant Kumar Srivastava, Michael Robert (Bates College), Prashant Kumar Srivastava (Indian Institute of Technology, Patna) and Michael Robert (Virginia Tech)

Description:

Work within the mathematical epidemiology subgroup focuses on critical questions about the emergence, spread, and control of infectious diseases at multiple scales, and to study these questions, we must develop and implement a variety of tools. In this mini-symposium, we feature work across a broad spectrum of infectious disease modeling research and highlight work that members of the SMB Mathematical Epidemiology subgroup have been doing over the past year. This minisymposium will feature work addressing issues in parameter estimation, population heterogeneity, and modeling control efforts, among other important topics, and feature the work of a diverse group of mathematical biologists who are implementing traditional and novel methods to study questions in mathematical epidemiology.

Iulia Martina Bulai

University of Torino, Italy

"Modeling fast information and slow(er) disease spreading"

In the era of social networks, when information travels fast between continents, it is of paramount importance to understand how the evolution of a disease can be affected by human behavioral dynamics influenced by information diffusion. For decades, from the early 20th century, the evolution of epidemics are modelled and studied via ordinary differential equations (ODEs) systems. The compartmental models are important tools for a better understanding of infectious diseases and they have been introduce in 1927 by Kermack and McKendrick [1], in fact they can be used to predict how the disease spread, or obtain information on the duration of an epidemic, the number of infected individuals, etc., but also to identify optimal strategies for control the disease. In this work, [2], we focus on the interplay between fast information spreading and slow(er) disease spreading using techniques from Geometric Singular Perturbation Theory (GSPT). Since the pioneering papers written by N. Fenichel [3], GSPT has proven extremely suitable to describe systems evolving on multiple time scales, and analyse their transient and asymptotic behaviours. Here, we introduce an SIRS compartmental model with demography and fast information and misinformation spreading in the population. Considering the speed at which information spreads in the age of social media, we let our system evolve on two time scales, a fast one, corresponding to the information “layer” and a slow one, corresponding to the epidemic “layer”. We completely characterize the possible asymptotic behaviours of the system we propose with techniques of GSPT. In particular, we emphasise how the inclusion of (mis)information spreading can radically alter the asymptotic behaviour of the epidemic, depending on whether a non-negligible part of the population is misinformed or skeptical of misinformation. References [1] W.O. Kermack, A.G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A115700–721 (1927). [2] I.M. Bulai, M. Sensi, S. Sottile, A geometric analysis of the SIRS compartmental model with fast information and misinformation spreading, Chaos Solitons Fractals, 185, Article 115104 (2024). [3] N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of Differential Equations, 31(1), 53-98, (1979).

Konstantinos Mamis

University of Washington

"Modeling correlated uncertainties in stochastic compartmental models"

In compartmental models of epidemiology, stochastic fluctuations are often considered in parameters such as contact rate to account for uncertainties originating from environmental factors, variability in human behavior patterns, and also changes in the pathogen itself. The usual choice for modeling stochastic fluctuations is white noise; however, white noise cannot incorporate the correlations arising in human social behavior. The mean reverting Ornstein–Uhlenbeck (OU) process is a more adequate model for the stochastic contact rate that includes correlations in time. The main objection to the use of white or OU noises is that they may result in contact rate taking negative values, since they are unbounded Gaussian processes. For this reason, the correlated and lognormally distributed logarithmic Ornstein-Uhlenbeck (logOU) noise has been proposed for contact rate perturbation. Furthermore, logOU noise can model the presence of superspreaders in the population because of its long distribution tail. For a stochastic Susceptibles-Infected-Susceptibles (SIS) model, we are able to analytically determine the stationary probability density of the infected, for white and Ornstein-Uhlenbeck noises. This allows us to give a complete description of the model’s asymptotic behavior and the noise-induced transitions it undergoes as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the logOU noise, where the probability density is not available in closed form, we study the noise-induced transitions using Monte Carlo simulations. This enables us to compare the model’s predictions on the severity of the disease outbreak for the different types of noise.

Elizabeth Amona

Virginia Commonwealth University

"Essential Workers at Risk: An Agent-Based Model with Bayesian Uncertainty Quantification"

Essential workers face elevated infection risks due to their critical roles during pandemics, and protecting them remains a significant challenge for public health planning. This study develops an Agent-Based Modeling (ABM) framework to evaluate targeted intervention strategies, explicitly capturing structured interactions across families, workplaces, and schools. We simulate key scenarios—including unrestricted movement, school closures, mobility restrictions specific to essential workers, and workforce rotation—to assess their impact on disease transmission dynamics. To enhance model robustness, we integrate Bayesian Uncertainty Quantification (UQ), systematically capturing variability in transmission rates, recovery times, and mortality estimates. Our comparative analysis demonstrates that while general mobility restrictions reduce overall transmission, a workforce rotation strategy for essential workers, when combined with quarantine enforcement, most effectively limits workplace outbreaks and secondary family infections. Unlike other interventions, this approach preserves a portion of the susceptible population, resulting in a more controlled and sustainable epidemic trajectory. These findings offer critical insights for optimizing intervention strategies that mitigate disease spread while maintaining essential societal functions.

Dongju Lim

KAIST

"History-dependent framework of infectious disease dynamics"

Infectious disease dynamics is inherently history-dependent; when an individual is exposed to an infectious disease affects when that individual becomes infectious. However, this inherent characteristic was disregarded in previous studies using a simple history-independent ODE model, leading to significant bias in estimating key epidemiological parameters such as reproduction numbers. In this talk, we address this bias by utilizing a model that describes the history-dependent dynamics, achieving more accurate and precise parameter estimates, solely from confirmed case data. Furthermore, we address another crucial limitation of history-dependent models; they rely heavily on accurate initial conditions. While initial conditions were estimated under unrealistic history-independent assumptions in existing studies, we discovered that this approach yields biased estimates. To address this, we introduce a new history-dependent method for estimating initial conditions based on the formula that involves time-varying likelihoods of transitioning from exposure to infectious. This method reduced error in estimating initial conditions by 55% in real-world COVID-19 data. Taken together, our results offer a framework that completely describes the history-dependent dynamics of infectious disease.

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Annual Meeting for the Society for Mathematical Biology, 2025.