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We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is…

Populations and Evolution · Quantitative Biology 2015-01-06 Andrew J. Black , J. V. Ross

In many epidemiological contexts, disease occurrences and their rates are naturally modelled by counting processes and their intensities, allowing an analysis based on martingale methods. These methods lend themselves to extensions of…

Statistics Theory · Mathematics 2007-06-13 Larry Goldstein , Bryan Langholz

Approximate variational inference has shown to be a powerful tool for modeling unknown complex probability distributions. Recent advances in the field allow us to learn probabilistic models of sequences that actively exploit spatial and…

Machine Learning · Statistics 2016-06-15 Maximilian Soelch , Justin Bayer , Marvin Ludersdorfer , Patrick van der Smagt

This paper investigates the dynamics of infectious diseases with a non-exponentially distributed infectious period. This is achieved by considering a multi-stage infection model on networks. Using pairwise approximation with a standard…

Physics and Society · Physics 2015-11-23 N. Sherborne , K. B. Blyuss , I. Z. Kiss

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network…

Artificial Intelligence · Computer Science 2015-03-13 Yoshiharu Maeno

Intuitively, sampling is likely to be more efficient for prevalence estimation, if the cases (or positives) have a relatively higher representation in the sample than in the population. In case the virus is transmitted via personal…

Applications · Statistics 2020-11-18 Li-Chun Zhang

Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…

Methodology · Statistics 2022-11-29 Jenny Huang , Raphaël Morsomme , David Dunson , Jason Xu

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time…

Computation · Statistics 2017-02-14 Jonathan Fintzi , Xiang Cui , Jon Wakefield , Vladimir N. Minin

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…

Statistical Mechanics · Physics 2025-10-07 Javier Aguilar , Miguel A. Muñoz , Sandro Azaele

Two simple agent based models are often employed in epidemic studies: the susceptible-infected (SI) and the susceptible-infected-susceptible (SIS). Both models describe the time evolution of infectious diseases in networks in which vertices…

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…

For many infectious disease outbreaks, the at-risk population changes their behavior in response to the outbreak severity, causing the transmission dynamics to change in real-time. Behavioral change is often ignored in epidemic modeling…

Methodology · Statistics 2023-10-25 Caitlin Ward , Rob Deardon , Alexandra M. Schmidt

Timely and robust influenza incidence forecasting is critical for public health decision-making. This paper presents MAESTRO (Multi-modal Adaptive Estimation for Temporal Respiratory Disease Outbreak), a novel, unified framework that…

Machine Learning · Computer Science 2025-09-22 Hong Liu , Kerui Cen , Yanxing Chen , Zige Liu , Dong Chen , Zifeng Yang , Chitin Hon

We tackle limitations of ordinary differential equation-driven Susceptible-Infections-Removed (SIR) models and their extensions that have recently be employed for epidemic nowcasting and forecasting. In particular, we deal with challenges…

Computation · Statistics 2026-02-10 Angelos Alexopoulos , Paul Birrell , Daniela De Angelis

Modern longitudinal data, for example from wearable devices, measures biological signals on a fixed set of participants at a diverging number of time points. Traditional statistical methods are not equipped to handle the computational…

Methodology · Statistics 2023-03-23 Lan Luo , Jingshen Wang , Emily C. Hector

The statistics of outbreaks in a model for the propagation of meningococcal diseases is analyzed, taking into account the possibility that the population is fragmented into weakly connected patches. It is shown that, depending on the size…

Populations and Evolution · Quantitative Biology 2007-05-23 F. Guinea , V. A. A. Jansen , N. Stollenwerk

During an infectious disease pandemic, it is critical to share electronic medical records or models (learned from these records) across regions. Applying one region's data/model to another region often have distribution shift issues that…

Machine Learning · Computer Science 2021-03-12 Ye Ye , Andrew Gu

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and…

Populations and Evolution · Quantitative Biology 2023-11-09 Maxwell H. Wang , Jukka-Pekka Onnela

Recent work has focused attention on statistical inference for the population distribution of the number of sexual partners based on survey data. The characteristics of these distributions are of interest as components of mathematical…

Disordered Systems and Neural Networks · Physics 2007-05-23 Mark S. Handcock , James Holland Jones , Martina Morris

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
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