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Compartmental models like the Susceptible-Infected-Recovered (SIR)\cite{Kermack1927} and its extensions such as the Susceptible-Exposed-Infected-Recovered (SEIRS)\cite{Ottar2020,Ignazio2021,Grimm2021,Paoluzzi2021} are commonly used to model…

Populations and Evolution · Quantitative Biology 2025-07-14 Kasturi Banerjee , Subhankar Ray , Jayalakshmi Shamanna

This chapter surveys univariate and multivariate methods for infectious disease outbreak detection. The setting considered is a prospective one: data arrives sequentially as part of the surveillance systems maintained by public health…

Methodology · Statistics 2017-11-27 Benjamin Allévius , Michael Höhle

Probabilistic models for infectious disease dynamics are useful for understanding the mechanism underlying the spread of infection. When the likelihood function for these models is expensive to evaluate, traditional likelihood-based…

Methodology · Statistics 2013-02-18 Roman Jandarov , Murali Haran , Ottar Bjørnstad , Bryan Grenfell

The epidemic spreading on arbitrary complex networks is studied in SIR (Susceptible Infected Recovered) compartment model. We propose our implementation of a Naive SIR algorithm for epidemic simulation spreading on networks that uses data…

Data Structures and Algorithms · Computer Science 2015-03-20 Nino Antulov-Fantulin , Alen Lancic , Hrvoje Stefancic , Mile Sikic

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces the complex spreading patterns of a pandemic to a wave-like propagation from…

Sheep pox is a highly transmissible disease which can cause serious loss of livestock and can therefore have major economic impact. We present data from sheep pox epidemics which occurred between 1994 and 1998. The data include weekly…

Populations and Evolution · Quantitative Biology 2017-09-06 C. Malesios , N. Demiris , Z. Abas , K. Dadousis , T. Koutroumanidis

In this paper, we develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure…

Populations and Evolution · Quantitative Biology 2015-04-01 Derdei Bichara , Yun Kang , Carlos Castillo-Chavez , Richard Horan , Charles Perrings

Infectious diseases on farms pose both public and animal health risks, so understanding how they spread between farms is crucial for developing disease control strategies to prevent future outbreaks. We develop novel Bayesian nonparametric…

Applications · Statistics 2021-08-24 R. G. Seymour , T. Kypraios , P. D. O'Neill , T. J. Hagenaars

We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible (SIRS) model on smallworld graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase…

Statistical Mechanics · Physics 2021-03-26 Daniel Malz , Andrea Pizzi , Andreas Nunnenkamp , Johannes Knolle

SARS-CoV2, which causes coronavirus disease (COVID-19) is continuing to spread globally and has become a pandemic. People have lost their lives due to the virus and the lack of counter measures in place. Given the increasing caseload and…

In this paper we introduce a statistical inference framework for estimating the contagion source from a partially observed contagion spreading process on an arbitrary network structure. The framework is based on a maximum likelihood…

Social and Information Networks · Computer Science 2015-03-12 Nino Antulov-Fantulin , Alen Lancic , Hrvoje Stefancic , Mile Sikic , Tomislav Smuc

The spatial propagation of many livestock infectious diseases critically depends on the animal movements among premises; so the knowledge of movement data may help us to detect, manage and control an outbreak. The identification of robust…

Populations and Evolution · Quantitative Biology 2012-10-03 Paolo Bajardi , Alain Barrat , Lara Savini , Vittoria Colizza

Epidemic spread in single-host systems strongly depends on the population's contact network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species…

Populations and Evolution · Quantitative Biology 2017-12-06 Shai Pilosof , Gili Greenbaum , Boris R. Krasnov , Yuval R. Zelnik

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based…

Dynamical Systems · Mathematics 2013-02-22 Prapanporn Rattana , Konstantin B. Blyuss , Ken T. D. Eames , Istvan Z. Kiss

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

Stochastic compartmental models are important tools for understanding the course of infectious diseases epidemics in populations and in prospective evaluation of intervention policies. However, calculating the likelihood for discretely…

Computation · Statistics 2018-07-26 Lam Si Tung Ho , Forrest W. Crawford , Marc A. Suchard

Accurate forecasting of viral disease outbreaks is crucial for guiding public health responses and preventing widespread loss of life. In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a promising framework that can…

Quantitative Methods · Quantitative Biology 2025-08-12 Bikram Das , Rupchand Sutradhar , D C Dalal

Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to…

Populations and Evolution · Quantitative Biology 2023-12-04 Gaël Beaunée , Pauline Ezanno , Alain Joly , Pierre Nicolas , Elisabeta Vergu

Infectious zoonotic disease emergence, through spillover events, is of global concern and has the potential to cause significant harm to society, as recently demonstrated by COVID-19. More than 70% of the 400 infectious diseases that…

Populations and Evolution · Quantitative Biology 2024-09-26 Maryam Golchin , Moreno Di Marco , Paul Horwood , Dean Paini , Andrew Hoskins , R. I. Hickson

We propose an SIR epidemic model coupled with opinion dynamics to study an epidemic and opinions spreading in a network of communities. Our model couples networked SIR epidemic dynamics with opinions towards the severity of the epidemic,…

Systems and Control · Electrical Eng. & Systems 2025-06-23 Baike She , Humphrey C. H. Leung , Shreyas Sundaram , Philip E. Paré