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We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…

Dynamical Systems · Mathematics 2025-11-27 Christian Parkinson , Weinan Wang

Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…

Methodology · Statistics 2022-09-19 Yu Gu , Donglin Zeng , Gerardo Heiss , D. Y. Lin

Accurate epidemic forecasting is crucial for outbreak preparedness, but existing data-driven models are often brittle. Typically trained on a single pathogen, they struggle with data scarcity during new outbreaks and fail under distribution…

Machine Learning · Computer Science 2026-02-25 Zewen Liu , Juntong Ni , Bohan Wang , Max S. Y. Lau , Wei Jin

Among various spatio-temporal prediction tasks, epidemic forecasting plays a critical role in public health management. Recent studies have demonstrated the strong potential of spatio-temporal graph neural networks (STGNNs) in extracting…

Machine Learning · Computer Science 2025-12-30 Yufan Zheng , Wei Jiang , Tong Chen , Alexander Zhou , Nguyen Quoc Viet Hung , Choujun Zhan , Hongzhi Yin

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter…

Data Analysis, Statistics and Probability · Physics 2026-04-06 Malik Hassanaly , Corey R. Randall , Peter J. Weddle , Paul J. Gasper , Conlain Kelly , Tanvir R. Tanim , Kandler Smith

Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference…

Methodology · Statistics 2026-02-12 James Neill , Lloyd A. C. Chapman , Chris Jewell

The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…

Quantitative Methods · Quantitative Biology 2024-07-11 Su Yang , Weiqi Chu , Panayotis Kevrekidis

Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for…

Populations and Evolution · Quantitative Biology 2023-12-20 Cameron A. Smith , Ben Ashby

Nosocomial infections have important consequences for patients and hospital staff: they worsen patient outcomes and their management stresses already overburdened health systems. Accurate judgements of whether an infection is nosocomial…

Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…

Methodology · Statistics 2025-04-29 Xiahui Li , Fergus Chadwick , Ben Swallow

Simulation-based Bayesian inference (SBI) can be used to estimate the parameters of complex mechanistic models given observed model outputs without requiring access to explicit likelihood evaluations. A prime example for the application of…

Machine Learning · Computer Science 2022-11-28 Jonas Beck , Michael Deistler , Yves Bernaerts , Jakob Macke , Philipp Berens

Susceptible-Exposed-Infectious-Recovered (SEIR) models with inter-individual variation in susceptibility or exposure to infection were proposed early in the COVID-19 pandemic as a potential element of the mathematical/statistical toolset…

Applications · Statistics 2025-10-28 Ibrahim Mohammed , Chris Robertson , M. Gabriela M. Gomes

Traditional disease transmission models assume that the infectious period is exponentially distributed with a recovery rate fixed in time and across individuals. This assumption provides analytical and computational advantages, however it…

Populations and Evolution · Quantitative Biology 2024-01-30 Laura Di Domenico , Eugenio Valdano , Vittoria Colizza

Stochastic epidemic models which incorporate interactions between space and human mobility are a key tool to inform prioritisation of outbreak control to appropriate locations. However, methods for fitting such models to national-level…

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…

Populations and Evolution · Quantitative Biology 2018-02-07 James N. Walker , Joshua V. Ross , Andrew J. Black

Recent work has shown that different theoretical approaches to the dynamics of the Susceptible-Infected-Susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks.…

Statistical Mechanics · Physics 2012-10-17 Silvio C. Ferreira , Claudio Castellano , Romualdo Pastor-Satorras

Assessing the practical identifiability of epidemic models is essential for determining whether parameters can be meaningfully estimated from observed data. Monte Carlo (MC) methods provide an accessible and intuitive framework; however,…

Methodology · Statistics 2025-10-01 Chiara Mattamira , Olivia Prosper Feldman

We study an individual-based stochastic epidemic model in which infected individuals become susceptible again following each infection. In contrast to classical compartment models, after each infection, the infectivity is a random function…

Probability · Mathematics 2025-04-29 Raphaël Forien , Guodong Pang , Étienne Pardoux , Arsene Brice Zotsa-Ngoufack

Widespread adoption of AI for medical decision making is still hindered due to ethical and safety-related concerns. For AI-based decision support systems in healthcare settings it is paramount to be reliable and trustworthy. Common deep…

Machine Learning · Computer Science 2024-01-26 Adrian Lindenmeyer , Malte Blattmann , Stefan Franke , Thomas Neumuth , Daniel Schneider

Computational models have become a powerful tool in the quantitative sciences to understand the behaviour of complex systems that evolve in time. However, they often contain a potentially large number of free parameters whose values cannot…

Optimization and Control · Mathematics 2023-02-13 Thomas Gaskin , Grigorios A. Pavliotis , Mark Girolami
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