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Related papers: Kinetic SIR equations and particle limits

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We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the…

Analysis of PDEs · Mathematics 2022-08-02 Romain Ducasse , Samuel Nordmann

For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of…

Populations and Evolution · Quantitative Biology 2020-11-18 Michael te Vrugt , Jens Bickmann , Raphael Wittkowski

Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…

Populations and Evolution · Quantitative Biology 2025-10-30 Daniel Perkins , Davis Hunter , Drake Brown , Trevor Garrity , Wyatt Pochman

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

This paper examines a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and constant total population. The infection mechanism in the model is described by a nonlinear term of the form…

Analysis of PDEs · Mathematics 2024-12-20 Rui Peng , Rachidi B Salako , Yixiang Wu

We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the…

Physics and Society · Physics 2025-04-17 Gadi Fibich , Guy Rothmann

In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…

Probability · Mathematics 2025-11-18 Armand Kanga , Etienne Pardoux

We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe…

Physics and Society · Physics 2022-12-08 S. P. Lukyanets , I. S. Gandzha , O. V. Kliushnichenko

The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's…

Physics and Society · Physics 2021-06-09 Petter Holme

We consider Susceptible-Infected-Recovered (SIR) models on dense dynamic random graphs, in which the joint dynamics of vertices and edges are co-evolutionary, i.e., they influence each other bidirectionally. In particular, edges appear and…

Probability · Mathematics 2026-02-17 Simone Baldassarri , Peter Braunsteins , Frank den Hollander , Michel Mandjes

We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be…

Dynamical Systems · Mathematics 2021-07-20 Yuanyuan Feng , Gautam Iyer , Lei Li

Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR)…

Populations and Evolution · Quantitative Biology 2019-11-28 Sang Woo Park , Benjamin M. Bolker

A theoretical framework for the description of Susceptible-Infected-Removed (SIR) spreading processes with synergistic transmission of infection on a lattice is developed. The model incorporates explicitly the effects of a time-dependent…

Populations and Evolution · Quantitative Biology 2013-12-25 Sergei Taraskin , Francisco J. Pérez-Reche

We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…

Probability · Mathematics 2024-04-08 Frank Ball , David Sirl , Pieter Trapman

This paper deals with systems of spherical particles immersed in a viscous fluid. Two aspects are studied, namely the controllability of such systems, with particular attention to the case of one active particle and either one or two…

Analysis of PDEs · Mathematics 2024-10-23 Marta Zoppello , Henry Shum , Marco Morandotti

We examine two basic assumptions of kinetic theory-- binary collisions and molecular chaos-- using numerical simulations of sheared granular materials. We investigate a wide range of densities and restitution coefficients and demonstrate…

Soft Condensed Matter · Physics 2015-06-25 Gregg Lois , Anael Lemaitre , Jean M. Carlson

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However the relation between the tumbling rate and the internal state of bacteria is poorly understood. The…

Analysis of PDEs · Mathematics 2021-08-27 Benoit Perthame , Weiran Sun , Min Tang , Shugo Yasuda

Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model…

Populations and Evolution · Quantitative Biology 2022-01-04 R. Jayatilaka , R. Patel , M. Brar , Y. Tang , N. M. Jisrawi , F. Chishtie , J. Drozd , S. R. Valluri

We study the impact of model parameter uncertainty on optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider testing for isolation as…

Systems and Control · Electrical Eng. & Systems 2022-09-07 Baike She , Shreyas Sundaram , Philip E. Paré

Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact…

Dynamical Systems · Mathematics 2016-10-31 Ágnes Bodó , Gyula Y. Katona , Péter L. Simon