Existence and Uniqueness of Endemic States for the Age-structured MSEIR Epidemic Model

2002 ◽  
Vol 18 (3) ◽  
pp. 441-454 ◽  
Author(s):  
Xue-zhi Li ◽  
Geni Gupur ◽  
Guang-tian Zhu
Keyword(s):  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Age Structured

Hopf Bifurcation of an Age-Structured Epidemic Model with Quarantine and Temporary Immunity Effects

2021 ◽  
Vol 31 (12) ◽  
pp. 2150183
Author(s):  
Lili Liu ◽  
Jian Zhang ◽  
Ran Zhang ◽  
Hongquan Sun
Keyword(s):  
Hopf Bifurcation ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Reproduction Number ◽  
Exponential Polynomial ◽  
Uniqueness Of Solutions ◽  
Fourth Degree ◽  
Age Structured ◽  
The Stability ◽  
Distribution Of Roots

In this paper, we investigate an epidemic model with quarantine and recovery-age effects. Reformulating the model as an abstract nondensely defined Cauchy problem, we discuss the existence and uniqueness of solutions to the model and study the stability of the steady state based on the basic reproduction number. After analyzing the distribution of roots to a fourth degree exponential polynomial characteristic equation, we also derive the conditions of Hopf bifurcation. Numerical simulations are performed to illustrate the results.

Existence and uniqueness of endemic states for the age-structured S–I–R epidemic model

1998 ◽  
Vol 150 (2) ◽  
pp. 177-190 ◽  
Author(s):  
Youngjoon Cha ◽  
Mimmo Iannelli ◽  
Fabio A. Milner
Keyword(s):  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Age Structured

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

scholarly journals Lockdown measures and their impact on single- and two-age-structured epidemic model for the COVID-19 outbreak in Mexico

2021 ◽  
pp. 108590
Author(s):  
J. Cuevas-Maraver ◽  
P.G. Kevrekidis ◽  
Q.Y. Chen ◽  
G.A. Kevrekidis ◽  
Víctor Villalobos-Daniel ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Age Structured

scholarly journals Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 147 ◽  
Author(s):  
Toshikazu Kuniya
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Transmission Function ◽  
Endemic Equilibrium ◽  
Dimensional System ◽  
Relevant Parameter ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Age Structured

In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the reduction of the model into a four-dimensional system of ordinary differential equations (ODEs). We show that the unique endemic equilibrium of the reduced system exists if the basic reproduction number for the original system is greater than unity. Furthermore, we perform the stability analysis of the endemic equilibrium and obtain a fourth-order characteristic equation. By using the Routh–Hurwitz criterion, we numerically show that the endemic equilibrium is asymptotically stable in some epidemiologically relevant parameter settings.

scholarly journals Kestabilan Model Epidemi SEIR Dengan Laju Insidensi

2015 ◽  
Vol 10 (2) ◽  
pp. 74
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Equation System ◽  
Differential Equation System ◽  
Equilibrium Existence

In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with incidence rate. From the model it will be found investigated the existence and uniqueness solution  of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue. 

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