Global stability for a delayed multi-group SIRS epidemic model with cure rate and incomplete recovery rate

2015 ◽  
Vol 08 (04) ◽  
pp. 1550048 ◽  
Author(s):  
Yoshiaki Muroya ◽  
Toshikazu Kuniya
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Recovery Rate ◽  
Lyapunov Functional ◽  
Global Analysis ◽  
Endemic Equilibrium ◽  
Group Model ◽  
Cure Rate ◽  
Sirs Epidemic Model ◽  
Number Formula

In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a "delayed" multi-group SIRS epidemic model with cure rate and incomplete recovery rate which does not depend on the delays and is an extension of the "light drug model" studied in the recent paper [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl. 410 (2014) 719–732] to a multi-group model. Applying a Lyapunov functional on total population of each compartment, we offer new techniques for the delayed system, how to prove the permanence, the existence of the endemic equilibrium and the global stability of disease-free equilibrium for the reproduction number [Formula: see text] and endemic equilibrium for [Formula: see text].

scholarly journals Global Analysis of SIRS Epidemic Model With General Incidence Function and Incomplete Recovery Rates Stochastical Model

2020 ◽  
Vol 12 (6) ◽  
pp. 100
Author(s):  
Dramane Ouedraogo ◽  
Ali Traore ◽  
Aboudramane Guiro
Keyword(s):  
Stochastic Model ◽  
Global Stability ◽  
Stochastic Models ◽  
Epidemic Model ◽  
Global Analysis ◽  
Endemic Equilibrium ◽  
Epidemic Models ◽  
Local And Global Stability ◽  
Sirs Epidemic Model ◽  
Disease Free

In this paper, deterministic and stochastic models are developped for a class of SIRS epidemic models. Firstly, The conditions for the existence, local and global stability of the disease-free equilibrium and endemic equilibrium are obtained. Secondly, we built the stochastic model. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and stochastic model.

scholarly journals Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model

2011 ◽  
Vol 16 (1) ◽  
pp. 59-76 ◽  
Author(s):  
A. Lahrouz ◽  
L. Omari ◽  
D. Kiouach
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Epidemic Model ◽  
Global Analysis ◽  
Stochastic Version ◽  
Noise Perturbation ◽  
Sirs Epidemic Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Endemic Equilibrium State

We present in this paper an SIRS epidemic model with saturated incidence rate and disease-inflicted mortality. The Global stability of the endemic equilibrium state is proved by constructing a Lyapunov function. For the stochastic version, the global existence and positivity of the solution is showed, and the global stability in probability and pth moment of the system is proved under suitable conditions on the intensity of the white noise perturbation.

STABILITY ANALYSIS OF A DELAYED SIRS EPIDEMIC MODEL WITH VACCINATION AND NONLINEAR INCIDENCE

2012 ◽  
Vol 05 (06) ◽  
pp. 1250050 ◽  
Author(s):  
XIAOHONG TIAN
Keyword(s):  
Epidemic Model ◽  
Local Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Threshold Value ◽  
Iteration Scheme ◽  
Endemic Equilibrium ◽  
Globally Asymptotically Stable ◽  
Sirs Epidemic Model ◽  
Disease Free

In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of disease-free equilibrium of the model is established. By constructing Lyapunov functional, sufficient conditions are established for the local stability of an endemic equilibrium of the model. Further, a threshold value is obtained. By using comparison arguments, it is proved when the threshold value is less than unity, the disease-free equilibrium is globally asymptotically stable. When the threshold value is greater than unity, by using an iteration scheme and by constructing appropriate Lyapunov functional, respectively, sufficient conditions are derived for the global stability of the endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.

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.

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

2006 ◽  
Vol 26 (2) ◽  
pp. 291-306 ◽  
Author(s):  
Jin Zhen ◽  
Zhien Ma ◽  
Maoan Han
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Sirs Epidemic Model

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 of multi-group SEIRS epidemic models with vaccination

2018 ◽  
Vol 11 (01) ◽  
pp. 1850006
Author(s):  
Dejun Fan ◽  
Pengmiao Hao ◽  
Dongyan Sun ◽  
Junjie Wei
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Lyapunov Functionals ◽  
Group Model ◽  
Single Group ◽  
Connected Network ◽  
Reproduction Numbers ◽  
Seirs Epidemic Model ◽  
Strongly Connected ◽  
Strongly Connected Network

In this paper, a susceptible–exposed–infective–recovered–susceptible (SEIRS) epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.

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