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Related papers: SIR model with vaccination: bifurcation analysis

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This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the…

Dynamical Systems · Mathematics 2018-07-17 Jayanta Kumar Ghosh , Uttam Ghosh , M. H. A. Biswas , Susmita Sarkar

This study investigates bifurcation dynamics in an SIRS epidemic model with cubic saturated incidence, extending the quadratic saturation framework established by Lu, Huang, Ruan, and Yu (Journal of Differential Equations, 267, 2019). We…

Dynamical Systems · Mathematics 2025-09-26 Henan Wang , Xu Chen , Wenxuan Li , Suli Liu , Huilai Li

To understand the impact of vaccination, we consider a SIVR (susceptible-infected-vaccinated-recovered) model which combines impulsive vaccination into the classical SIR model. The final size is firstly defined and estimated, and then the…

Populations and Evolution · Quantitative Biology 2024-10-29 Phyu Phyu Win , Zhigui Lin , Mengyun Zhang

We study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population…

Dynamical Systems · Mathematics 2023-05-23 Stefania Ottaviano , Mattia Sensi , Sara Sottile

In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over…

Populations and Evolution · Quantitative Biology 2025-01-30 Joseph Páez Chávez , Aytül Gökçe , Thomas Götz , Burcu Gürbüz

This study focuses on the modeling, mathematical analysis, developing theories, and numerical simulation of Influenza virus transmission. We have proved the existence, uniqueness, positivity, and boundedness of the solutions. Also,…

Populations and Evolution · Quantitative Biology 2024-03-19 Kazi Mehedi Mohammad , Asma Akter Akhi , Md. Kamrujjaman

We revisit here a landmark five parameter SIR-type model of [DvdD93, Sec. 4], which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also…

Populations and Evolution · Quantitative Biology 2022-01-11 Florin Avram , Rim Adenane , Gianluca Bianchin , Andrei Halanay

An age-dependent SIR model is considered with the aim to develop a state-feedback vaccination law in order to eradicate a disease. A dynamical analysis of the system is performed using the principle of linearized stability and shows that,…

Optimization and Control · Mathematics 2022-05-18 Candy Sonveaux , Joseph J. Winkin

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

The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination in influencing the spreading of the disease is of particular interest. There has also been a lot of debate on the role of…

Dynamical Systems · Mathematics 2023-07-25 Aytül Gökçe , Burcu Gürbüz , Alan D. Rendall

A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…

Populations and Evolution · Quantitative Biology 2025-12-25 Oleg B. Shiryaev

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

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 develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (willing or unwilling), with the goal of discovering how disease spread is influenced by changing opinions…

Dynamical Systems · Mathematics 2024-08-16 Yi Jiang , Kristin M. Kurianski , Jane HyoJin Lee , Yanping Ma , Daniel Cicala , Glenn Ledder

In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where…

Probability · Mathematics 2024-10-10 Christian Borgs , Karissa Huang , Christian Ikeokwu

We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…

Populations and Evolution · Quantitative Biology 2024-10-29 Frank Ball , Abid Ali Lashari , David Sirl , Pieter Trapman

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total…

Dynamical Systems · Mathematics 2011-03-28 M. De la Sen , A. Ibeas , S. Alonso-Quesada

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that…

Quantitative Methods · Quantitative Biology 2015-06-22 Edwin C. Yuan , David L. Alderson , Sean Stromberg , Jean M. Carlson

We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…

Classical Analysis and ODEs · Mathematics 2021-07-09 Andres David Báez-Sánchez , Nara Bobko

We construct an SIR-type model for COVID-19, incorporating as a parameter the susceptible individuals' cautiousness level. We determine the model's basic reproduction number, study the stability of the equilibria analytically, and perform a…

Dynamical Systems · Mathematics 2022-04-06 Benny Yong , Livia Owen , Jonathan Hoseana