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The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…

Dynamical Systems · Mathematics 2021-04-27 William G. Faris

The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations $S(t)$ and $R(t)$ of susceptible and recovered…

Populations and Evolution · Quantitative Biology 2020-11-11 Angel Ballesteros , Alfonso Blasco , Ivan Gutierrez-Sagredo

Exact solution of the Susceptible-Infectious-Recovered (SIR) epidemic model is derived, and various properties of solution are obtained directly from the exact solution. It is shown that there exists an exact solution of an initial value…

Populations and Evolution · Quantitative Biology 2022-10-04 Norio Yoshida

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

We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming…

Statistical Mechanics · Physics 2015-05-30 H. Thomas Williams , Irina Mazilu , Dan Mazilu

Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an…

Populations and Evolution · Quantitative Biology 2014-08-28 Max O. Souza

Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets (particularly the COVID-19), few of them present a formal dynamic characterization in terms of equilibrium sets and stability. Such…

Optimization and Control · Mathematics 2021-06-03 A. H. González , A. L. Anderson , A. Ferramosca , E. A. Hernandez-Vargas

In this paper, we introduce a novel numerical approach for approximating the SIR model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental…

Numerical Analysis · Mathematics 2023-08-17 Vo Anh Khoa , Pham Minh Quan , Ja'Niyah Allen , Kbenesh W. Blayneh

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…

Adaptation and Self-Organizing Systems · Physics 2015-05-13 Eric Forgoston , Lora Billings , Ira B. Schwartz

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several…

Dynamical Systems · Mathematics 2019-05-14 Samia Ghersheen , Vladimir Kozlov , Vladimir G. Tkachev , Uno Wennergren

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

The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost…

Dynamical Systems · Mathematics 2021-07-26 N. H. Du , N. N. Nhu

An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48). The solution is created by analytically continuing the divergent…

Populations and Evolution · Quantitative Biology 2021-01-05 Nathaniel S. Barlow , Steven J. Weinstein

We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…

Dynamical Systems · Mathematics 2023-06-05 Jean-Baptiste Burie , Arnaud Ducrot , Quentin Griette

The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…

Optimization and Control · Mathematics 2020-11-06 Vivek S. Borkar , D. Manjunath

The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the…

Probability · Mathematics 2018-10-01 Jianhai Bao , Jinghai Shao

Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection is important in this case. We formulated a SIR model that describes the coinfection of…

Dynamical Systems · Mathematics 2019-05-14 Samia Ghersheen , Vladimir Kozlov , Vladimir G. Tkachev , Uno Wennergren

We revisit the classic Susceptible-Infected-Recovered (SIR) epidemic model and one of its nonlocal variations recently developed in \cite{Guan}. We introduce several new approaches to derive exact analytical solutions in the classical…

Analysis of PDEs · Mathematics 2021-06-24 Li , Guan , Dong Li , Ke Wang , Kun Zhao

In this paper we study a susceptible infectious recovered (SIR) model with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of differential equations for…

Social and Information Networks · Computer Science 2022-12-20 Duan-Shin Lee , Ting-Zhe Liu , Ruhui Zhang , Cheng-Shang Chang

We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the autonomous scenario, covering aspects such as local and…

Dynamical Systems · Mathematics 2024-04-22 Javier López-de-la-Cruz , Alexandre N. Oliveira-Sousa