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In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…

Probability · Mathematics 2014-04-29 Frank G. Ball , David J. Sirl , Pieter Trapman

To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…

Dynamical Systems · Mathematics 2024-07-03 Saswata Das , Mohammad Hossein Samaei , Caterina Scoglio

Recent outbreaks of infectious diseases have been monitored closely from an epidemiological and microbiological perspective. Extracting from this wealth of data the information that is relevant for the evolution of the pathogen and predict…

Populations and Evolution · Quantitative Biology 2024-10-10 Baptiste Filoche , Stefan Hohenegger

We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and by considering human interventions (such as quarantining or social distancing) as control…

Systems and Control · Electrical Eng. & Systems 2022-11-21 Tamas G. Molnar , Andrew W. Singletary , Gabor Orosz , Aaron D. Ames

Mathematical and computational modeling approaches are increasingly used as quantitative tools in the analysis and forecasting of infectious disease epidemics. The growing need for realism in addressing complex public health questions is…

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…

Probability · Mathematics 2015-12-08 Frank G Ball , Edward S Knock , Philip D O'Neill

We consider an SEIR epidemic model on a network also allowing random contacts, where recovered individuals could either recover naturally or be diagnosed. Upon diagnosis, manual contact tracing is triggered such that each infected network…

Physics and Society · Physics 2024-06-06 Dongni Zhang , Tom Britton

Spatial epidemiology identifies the drivers of elevated population-level disease risks, using disease counts, exposures and known confounders at the areal unit level. Poisson regression models are typically used for inference, which…

Methodology · Statistics 2026-02-03 Duncan Lee , Vinny Davies

We investigate the use of hybrid techniques in complex processes of infectious diseases. Since predictive disease models in biomedicine require a multiscale approach for understanding the molecule-cell-tissue-organ-body interactions,…

Logic in Computer Science · Computer Science 2012-08-21 Pietro Liò , Emanuela Merelli , Nicola Paoletti

We study the impact of parameter estimation and state measurement errors on a control framework for optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic…

Systems and Control · Electrical Eng. & Systems 2024-08-08 Baike She , Lei Xin , Shreyas Sundaram , Philip E. Paré

Early outbreak data analysis is critical for informing about their potential impact and interventions. However, data obtained early in outbreaks are often sensitive and subject to strict privacy restrictions. Thus, federated analysis, which…

Applications · Statistics 2026-01-27 Simon Busch-Moreno , Moritz U. G. Kraemer

This paper is concerned with the growth rate of SIR (Susceptible-Infectious-Recovered) epidemics with general infectious period distribution on random intersection graphs. This type of graph is characterized by the presence of cliques…

Probability · Mathematics 2025-08-13 Carolina Fransson

We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is…

Populations and Evolution · Quantitative Biology 2026-03-31 J. Ilnytskyi , T. Patsahan

We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early…

Populations and Evolution · Quantitative Biology 2026-01-06 Mohamed El Khalifi

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

Global pandemics, such as the recent COVID-19 crisis, highlight the need for stochastic epidemic models that can capture the randomness inherent in the spread of disease. Such models must be accompanied by methods for estimating parameters…

Quantitative Methods · Quantitative Biology 2026-04-13 Vincent Wieland , Nils Wassmuth , Lorenzo Contento , Martin Kühn , Jan Hasenauer

We present the generalised mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic system, where the population of infective nodes and links are…

Dynamical Systems · Mathematics 2016-05-11 G. Röst , Z. Vizi , I. Z. Kiss

We introduce a Python package for modeling and studying the spread of infectious diseases using an agent-based SEIR style epidemiological model with a focus on university campuses. This document explains the epidemiological model used in…

Populations and Evolution · Quantitative Biology 2020-11-13 Matthew Zalesak , Samitha Samaranayake

We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…

Probability · Mathematics 2014-09-24 Svante Janson , Malwina Luczak , Peter Windridge

We are currently facing a highly critical case of a world-wide pandemic. The novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely contagious and the original outbreak from Asia has now spread to all continents. This…

Physics and Society · Physics 2020-06-26 Priyanka , Vicky Verma
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