Global stability of an SEI model for plant diseases

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Yuming Chen ◽  
Junyuan Yang
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Total Population ◽  
Endemic Equilibrium ◽  
Plant Diseases ◽  
Globally Stable ◽  
Sei Model

AbstractWe propose an SEI epidemic model for plant diseases, which incorporates disease latency, disease-caused removal, and constant recruitment in both susceptible and exposed classes. Because of the recruitment and disease-caused removal, the total population is varying. It is shown that the model only has an endemic equilibrium and the equilibrium is globally stable.

scholarly journals Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion

2018 ◽  
Vol 31 (1) ◽  
pp. 26-56 ◽  
Author(s):  
HUICONG LI ◽  
RUI PENG ◽  
TIAN XIANG
Keyword(s):  
Infectious Disease ◽  
Total Population ◽  
Initial Boundary ◽  
Endemic Equilibrium ◽  
Diffusion Term ◽  
Frequency Dependent ◽  
Susceptible Population ◽  
Cross Diffusion ◽  
Special Cases ◽  
Globally Stable

This paper is concerned with two frequency-dependent susceptible–infected–susceptible epidemic reaction–diffusion models in heterogeneous environment, with a cross-diffusion term modelling the effect that susceptible individuals tend to move away from higher concentration of infected individuals. It is first shown that the corresponding Neumann initial-boundary value problem in an n-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly in-time bounded regardless of the strength of the cross-diffusion and the spatial dimension n. It is further shown that, even in the presence of cross-diffusion, the models still admit threshold-type dynamics in terms of the basic reproduction number $\mathcal {R}_0$ – i.e. the unique disease-free equilibrium is globally stable if $\mathcal {R}_0\lt1$, while if $\mathcal {R}_0\gt1$, the disease is uniformly persistent and there is an endemic equilibrium (EE), which is globally stable in some special cases with weak chemotactic sensitivity. Our results on the asymptotic profiles of EE illustrate that restricting the motility of susceptible population may eliminate the infectious disease entirely for the first model with constant total population but fails for the second model with varying total population. In particular, this implies that such cross-diffusion does not contribute to the elimination of the infectious disease modelled by the second one.

Global stability of an SEIR epidemic model with vaccination

2016 ◽  
Vol 09 (06) ◽  
pp. 1650082 ◽  
Author(s):  
Lili Wang ◽  
Rui Xu
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Globally Asymptotically Stable ◽  
Compound Matrices ◽  
Comparison Arguments ◽  
The Basic Reproduction Number

In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

2016 ◽  
Vol 09 (05) ◽  
pp. 1650068 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Yasir Khan ◽  
Sehra Khan ◽  
Saeed Islam
Keyword(s):  
Global Stability ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free ◽  
The Basic Reproduction Number

This study considers SEIVR epidemic model with generalized nonlinear saturated incidence rate in the host population horizontally to estimate local and global equilibriums. By using the Routh–Hurwitz criteria, it is shown that if the basic reproduction number [Formula: see text], the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if [Formula: see text]. The geometric approach is used to present the global stability of the endemic equilibrium. For [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

Global Stability of an Age Structured SEIRS Epidemic Model with Screening

2015 ◽  
Vol 713-715 ◽  
pp. 1725-1728
Author(s):  
Zhong Hua Zhang ◽  
Yao Hong Suo
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Contact Rate ◽  
Seirs Epidemic Model ◽  
Screen Function ◽  
Age Structured

We formulate an age structured SEIRS model with general screen function and contact rate. A condition is obtained, and under which the endemic equilibrium is locally stable. By constructing suitable Lyapunov function, the global stability of the endemic equilibrium is discussed.

scholarly journals Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations

1993 ◽  
Vol 34 (3) ◽  
pp. 282-295 ◽  
Author(s):  
Xiaodong Lin ◽  
Joseph W.-H. So
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Epidemic Models ◽  
Uniform Persistence ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Rates ◽  
Effective Contact

AbstractWe consider the epidemic model with subpopulations introduced in Hethcote [5]. It is shown that if the endemic equilibrium exists, then the system is uniformly persistent. Moreover, the endemic equilibrium is globally asymptotically stable under the assumption of small effective contact rates between different subpopulations.

Global asymptotic stability for a SEI reaction–diffusion model of infectious diseases with immigration

2018 ◽  
Vol 11 (03) ◽  
pp. 1850044
Author(s):  
Salem Abdelmalek ◽  
Samir Bendoukha
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Global Asymptotic Stability ◽  
Epidemic Model ◽  
Lyapunov Functional ◽  
Reaction Diffusion ◽  
Stability Of Solutions ◽  
Reaction Diffusion Model ◽  
Globally Stable

This paper studies the local and global stability of solutions for a spatially spread SEI epidemic model with immigration of individuals using a Lyapunov functional. It is shown that in the presence of diffusion, the unique steady state remains globally stable. Numerical results obtained through Matlab simulations are presented to confirm the findings of this study.

scholarly journals ANALISIS TITIK EKUILIBRIUM ENDEMIK MODEL EPIDEMI SEIV DENGAN LAJU PENULARAN NONLINEAR

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Nurul Hikmah
Keyword(s):  
Equilibrium Point ◽  
Key Words ◽  
Incidence Rate ◽  
Nonlinear Model ◽  
Epidemic Model ◽  
Behavioral Change ◽  
Global Analysis ◽  
Endemic Equilibrium ◽  
Nonlinear Incidence Rate ◽  
Globally Stable

Abstrak. Pada paper ini diberikan model epidemi SEIV dengan laju penularan nonlinear. Model ini menjelaskan tentang efek psikologi dari perubahan perilaku individu yang rentan ketika jumlah individu yang terinfeksi mengalami peningkatan. Dalam paper ini akan dilakukan analisis global dari model epidemi SEIV dan menyelidiki kestabilan global titik ekuilibrium endemik , selanjutnya diperoleh bahwa titik ekuilibrium endemik model epidemi SEIV stabil global. Kata Kunci : SEIV, titik ekuilibrium, kestabilan Abstract. In this paper, we consider a SEIV epidemic model with nonlinear incidence rate. This model describes the psychological effect of the behavioral change of susceptible individuals when the number of infectious individuals increases. By carrying out a global analysis of the model and studying the globally stability of the endemic equilibrium in this paper, we show that the endemic equilibrium of a SEIV epidemic model is globally stable. Key words: SEIV, equilibrium point, stability

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