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.

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 Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Karim Khan ◽  
Rahat Zarin ◽  
Amir Khan ◽  
Abdullahi Yusuf ◽  
Mohammed Al-Shomrani ◽  
...  
Keyword(s):  
Global Stability ◽  
Equilibrium Point ◽  
Lyapunov Theory ◽  
Endemic Equilibrium ◽  
Qualitative Behavior ◽  
Geometrical Approach ◽  
Local And Global Stability ◽  
Free Case ◽  
Compound Matrix ◽  
Disease Free

AbstractIn this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number $R_{0}$ R 0 of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition $R_{0}<1$ R 0 < 1 . Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and $R_{0}>1$ R 0 > 1 . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

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.

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.

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.

scholarly journals An SIRS Epidemic Model Incorporating Media Coverage with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Huitao Zhao ◽  
Yiping Lin ◽  
Yunxian Dai
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Periodic Orbits ◽  
Epidemic Model ◽  
Media Coverage ◽  
Critical Value ◽  
Endemic Equilibrium ◽  
Sirs Epidemic Model ◽  
The Stability ◽  
Disease Free

An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction numberR0<1. However, whenR0>1, the stability of the endemic equilibrium will be affected by the time delay; there will be a family of periodic orbits bifurcating from the endemic equilibrium when the time delay increases through a critical value. Finally, some examples for numerical simulations are also included.

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 epidemic model for HIV–TB co-infection with infection-age

2014 ◽  
Vol 07 (04) ◽  
pp. 1450043 ◽  
Author(s):  
Xiao-Yan Wang ◽  
Yan-Ping Bai ◽  
Jun-Yuan Yang ◽  
Feng-Qin Zhang
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Semigroup Theory ◽  
Lyapunov Functionals ◽  
Local And Global Stability ◽  
Infection Age ◽  
Reproduction Numbers ◽  
Theoretical Results ◽  
Disease Free

A nonlinear mathematical HIV–TB model with infection-age is proposed in this paper. The basic reproduction numbers according to HIV and TB are respectively determined whether one of the diseases dies out or persists. The local and global stability of the disease-free and dominated equilibria are discussed by employing integral semigroup theory and Lyapunov functionals. The persistence of the system is also obtained by the persistence theories of the systems. The simulation illustrates the theoretical results.

scholarly journals Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 1045-1063
Author(s):  
Bojana Jovanovic ◽  
Jasmina Ðordjevic ◽  
Jelena Manojlovic ◽  
Nenad Suvak
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic Model ◽  
Basic Reproduction Number ◽  
Stochastic Models ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Stochastic Version ◽  
Analysis Of Stability ◽  
Parameter Values ◽  
Disease Free

Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARS-CoV-2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the disease-free equilibrium are derived and, in addition, conditions for existence of bifurcation state related to endemic equilibrium are established. For stochastic model, conditions for extinction and persistence in mean of the disease are derived. Complete sensitivity analysis of thresholds between the extinction and mean-persistence are performed for both the deterministic and the stochastic version of the model. Influence of variation in parameter values is illustrated for epidemics in Wuhan in early 2020.

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