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Related papers: Oscillations in SIRS model with distributed delays

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We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…

Populations and Evolution · Quantitative Biology 2024-03-13 Hidetsugu Sakaguchi , Keito Yamasaki

We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…

Analysis of PDEs · Mathematics 2024-02-02 Romain Ducasse , Maxime Laborde

The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in…

Populations and Evolution · Quantitative Biology 2022-08-17 Mohamed Ben Alaya , Walid Ben Aribi , Slimane Ben Miled

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

The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection…

Populations and Evolution · Quantitative Biology 2020-10-07 E. Sadurní , G. Luna-Acosta

The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a…

Physics and Society · Physics 2023-09-26 Jiaying Zhou , Yong Ye , Alex Arenas , Sergio Gómez , Yi Zhao

We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…

Pattern Formation and Solitons · Physics 2018-02-14 Lawrence M. Chen , Matt Holzer , Anne Shapiro

We study the spread of disease in an SIS model. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold…

Dynamical Systems · Mathematics 2014-04-21 Mustapha Ait Rami , Vahid S. Bokharaie , Oliver Mason , Fabian R. Wirth

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…

Applications · Statistics 2025-05-07 Omar Melikechi , Alexander L. Young , Tao Tang , Trevor Bowman , David Dunson , James Johndrow

Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these…

Tissues and Organs · Quantitative Biology 2021-01-20 Malik A Dawi , Jose J Munoz

We introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In…

Populations and Evolution · Quantitative Biology 2022-03-03 Michael Bestehorn , Thomas M. Michelitsch , Bernard A. Collet , Alejandro P. Riascos , Andrzej F. Nowakowski

SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure…

Populations and Evolution · Quantitative Biology 2022-01-19 Richmond Opoku-Sarkodie , Ferenc A. Bartha , Mónika Polner , Gergely Röst

We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…

Classical Analysis and ODEs · Mathematics 2019-01-01 Martin Bohner , Sabrina Streipert , Delfim F. M. Torres

The SIRS model with constant vaccination and immunity waning rates is well known to show a transition from a disease-free to an endemic equilibrium as the basic reproduction number $r_0$ is raised above threshold. It is shown that this…

Populations and Evolution · Quantitative Biology 2024-10-28 Florian Nill

Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system…

Dynamical Systems · Mathematics 2021-01-26 Driss Kiouach , Yassine Sabbar

This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…

Systems and Control · Electrical Eng. & Systems 2021-03-01 Ciyuan Zhang , Humphrey Leung , Brooks Butler , Philip. E. Paré

Many infectious diseases are comprised of multiple strains with examples including Influenza, tuberculosis, and Dengue virus. The time evolution of such systems is linked to a complex landscape shaped by interactions between competing…

Populations and Evolution · Quantitative Biology 2023-11-21 Nir Gavish , Musa Rabiu

The infection dynamics of a population under stationary isolation conditions is modeled. It is underlined that the stationary character of the isolation measures can be expected to imply that an effective SIR model with constant parameters…

Populations and Evolution · Quantitative Biology 2021-10-19 Alejandro Cabo Montes de Oca , Nana Geraldine Cabo Bizet

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…

Chaotic Dynamics · Physics 2012-09-21 K. B. Blyuss , Y. N. Kyrychko

We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…

Dynamical Systems · Mathematics 2024-04-10 Panagiotis Kaklamanos , Andrea Pugliese , Mattia Sensi , Sara Sottile