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In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic, and of disease models generally. Most works follow the susceptible-infected-removed (SIR)…

Numerical Analysis · Mathematics 2022-05-18 Nicola Guglielmi , Elisa Iacomini , Alex Viguerie

A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…

Populations and Evolution · Quantitative Biology 2010-10-05 A. Noviello , F. Romeo , R. De Luca

The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the…

Populations and Evolution · Quantitative Biology 2022-01-17 Giulia Bertaglia , Lorenzo Pareschi

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…

Populations and Evolution · Quantitative Biology 2015-09-03 Joel C. Miller , Erik M. Volz

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…

Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have…

Methodology · Statistics 2026-05-12 Caitlin Ward , Rob Deardon , Alexandra M. Schmidt

Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact…

Applications · Statistics 2019-08-20 Md Mahsin , Rob Deardon , Patrick Brown

Coupling within-host infection dynamics with population-level transmission remains a major challenge in infectious disease modeling, especially for airborne pathogens with potential to spread indoor. The frequent emergence of such diseases…

Analysis of PDEs · Mathematics 2025-12-18 Andrew Omame , Sarafa Iyaniwura

Understanding infectious disease spread remains a critical public health challenge, particularly given the interplay between household dynamics and community transmission patterns. Traditional epidemiological models often oversimplify these…

Populations and Evolution · Quantitative Biology 2026-01-21 Houda Yaqine , Christiane Fuchs

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of…

Tracking the spread of infectious disease during a pandemic has posed a great challenge to the governments and health sectors on a global scale. To facilitate informed public health decision-making, the concerned parties usually rely on…

Methodology · Statistics 2023-06-05 Tejasv Bedi , Yanxun Xu , Qiwei Li

The spread of COVID-19 has been greatly impacted by regulatory policies and behavior patterns that vary across counties, states, and countries. Population-level dynamics of COVID-19 can generally be described using a set of ordinary…

Applications · Statistics 2022-04-11 Joshua P. Keller , Tianjian Zhou , Andee Kaplan , G. Brooke Anderson , Wen Zhou

This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…

Dynamical Systems · Mathematics 2020-01-01 Dang H Nguyen , Nhu N Nguyen , George Yin

Stochastic infectious disease models capture uncertainty in public health outcomes and have become increasingly popular in epidemiological practice. However, calibrating these models to observed data is challenging with existing methods for…

Methodology · Statistics 2024-12-18 Prayag Chatha , Fan Bu , Jeffrey Regier , Evan Snitkin , Jon Zelner

We study an individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity. Each individual is associated with a random infection-age dependent…

Probability · Mathematics 2025-10-21 Guodong Pang , Etienne Pardoux

Forecasting disease spread is a critical tool to help public health officials design and plan public health interventions. However, the expected future state of an epidemic is not necessarily well defined as disease spread is inherently…

Populations and Evolution · Quantitative Biology 2026-05-05 Mariah C. Boudreau , Andrea J. Allen , Nicholas J. Roberts , Antoine Allard , Laurent Hébert-Dufresne

Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…

Physics and Society · Physics 2022-06-07 Christopher A. Browne , Daniel B. Amchin , Joanna Schneider , Sujit S. Datta

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…

Numerical Analysis · Mathematics 2026-03-02 M. Soledad Aronna , Mariana Bergonzi , Ernesto Kofman

We propose an SEIR-type meta-population model to simulate and monitor the Covid-19 epidemic evolution. The basic model consists of seven compartments, namely susceptible (S), exposed (E), three infective classes, recovered (R), and deceased…

Populations and Evolution · Quantitative Biology 2020-11-18 Vinicius V. L. Albani , Roberto M. Velho , Jorge P. Zubelli

The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case…

Quantitative Methods · Quantitative Biology 2025-01-23 Hannah Craddock , Simon EF Spencer , Xavier Didelot