scholarly journals The Method for Risk Evaluation in Assembly Process based on the Discrete-Time SIRS Epidemic Model and Information Entropy

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1029 ◽  
Author(s):  
Mengyao Wu ◽  
Wei Dai ◽  
Zhiyuan Lu ◽  
Yu Zhao ◽  
Meiqing Wang
Keyword(s):  
Discrete Time ◽  
Information Entropy ◽  
Epidemic Model ◽  
Risk Evaluation ◽  
Disease Model ◽  
Propagation Mechanism ◽  
Assembly Process ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Optimal Assembly

In the past decade years, much attention has been attached on assembly process reliability in manufacturing system, because the quality and cost of product are highly determined by assembly process. However, existing research on reliability in assembly are mainly focused on study of size deviation propagation. In this paper, the method for risk evaluation in assembly process based on the discrete-time SIRS epidemic model and information entropy was proposed. Firstly, aiming at the issue of assembly process optimization, innovative solutions are proposed from the perspectives of reliability and cost by decomposing the assembly into general path and rework path. Secondly, the propagation mechanism of defects in optimal assembly approach were studied through combining the infectious disease model and information entropy. According to the bifurcation phenomenon in the SIRS model, the entropy increment of assembly process Δ H b a s e when defect emergence occurs is calculated. Thirdly, the information entropy increment of optimal assembly approach Δ H is used to evaluate the assembly risk by comparing with the Δ H b a s e . Finally, a case study of assembly risk evaluation for the oil pump was presented to verify the advantage of this method.

scholarly journals When will the Covid-19 epidemic fade out?

2020 ◽  
Author(s):  
Ilaria Renna
Keyword(s):  
Infectious Diseases ◽  
Discrete Time ◽  
Epidemic Model ◽  
Small World ◽  
Small World Network ◽  
Sirs Model ◽  
Gaussian Fit

AbstractA discrete-time deterministic epidemic model is proposed with the aim of reproducing the behaviour observed in the incidence of real infectious diseases. For this purpose, we analyse a SIRS model under the framework of a small world network formulation. Using this model, we make predictions about the peak of the Covid-19 epidemic in Italy. A Gaussian fit is also performed, to make a similar prediction.

Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 155-156 ◽  
pp. 23-26
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Liang Cui ◽  
Cai Juan Li
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Disease Free

In this paper, we study the global dynamics of an SIRS epidemic model with nonlinear inci- dence rate. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asy- mptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the an- alytical results.

scholarly journals Dynamics of a Stochastic SIRS Epidemic Model with Regime Switching and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Unique Positive Solution ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Incident Rate ◽  
Stochastic Sirs Epidemic Model

The purpose of this work is to investigate the dynamic behaviors of the SIRS epidemic model with nonlinear incident rate under regime switching. We establish the existence of a unique positive solution of our system. Furthermore, we obtain the conditions for the extinction of diseases, and we show the existence of the stationary distribution for our stochastic SIRS model under regime switching. Numerical simulations are employed to illustrate our theoretical analysis.

scholarly journals The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Feng Feng ◽  
Zong Wang
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Numerical Method ◽  
Epidemic Model ◽  
Numerical Technique ◽  
Environmental Perturbations ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Balanced Implicit Method ◽  
Stochastic Sirs Epidemic Model

Sudden environmental perturbations may affect the positivity of the solution of the susceptible-infected-recovered-susceptible (SIRS) model. Most of the SIRS epidemic models have no analytical solution. Thus, in order to find the appropriate solution, the numerical technique becomes more essential for us to solve the dynamic behavior of epidemics. In this paper, we are concerned with the positivity of the numerical solution of a stochastic SIRS epidemic model. A new numerical method that is the balanced implicit method (BIM) is set, which preserves the positivity under given conditions. The BIM method can maintain positive numerical solution. An illustrative numerical instance is presented for the numerical BIM of the stochastic SIRS model.

THRESHOLD AND STABILITY RESULTS FOR AN SIRS EPIDEMIC MODEL WITH A GENERAL PERIODIC VACCINATION STRATEGY

2005 ◽  
Vol 13 (02) ◽  
pp. 131-150 ◽  
Author(s):  
I. A. MONEIM ◽  
D. GREENHALGH
Keyword(s):  
Epidemic Model ◽  
Vaccination Strategy ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Globally Asymptotically Stable ◽  
Epidemic Dynamics ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Periodic Disease

An SIRS epidemic model with general periodic vaccination strategy is analyzed. This periodic vaccination strategy is discussed first for an SIRS model with seasonal variation in the contact rate of period T = 1 year. We start with the case where the vaccination strategy and the contact rate have the same period and then discuss the case where the period of the vaccination strategy is LT, where L is an integer. We investigate whether a periodic vaccination strategy may force the epidemic dynamics to have periodic behavior. We prove that our SIRS model has a unique periodic disease free solution (DFS) whose period is the same as that of the vaccination strategy, which is globally asymptotically stable when the basic reproductive number R0 is less than or equal to one in value. When R0 > 1, we prove that there exists a non-trivial periodic solution of period the same as that of the vaccination strategy. Some persistence results are also discussed. Threshold conditions for these periodic vaccination strategies to ensure that R0 ≤ 1 are derived.

A SIMPLE DISCRETE-TIME ANALOGUE PRESERVING THE GLOBAL STABILITY OF A CONTINUOUS SIRS EPIDEMIC MODEL

2013 ◽  
Vol 06 (02) ◽  
pp. 1350001 ◽  
Author(s):  
YOICHI ENATSU ◽  
YOSHIAKI MUROYA
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Epidemic Model ◽  
Discrete Model ◽  
Continuous Model ◽  
The Other ◽  
Infected Population ◽  
Sirs Epidemic Model ◽  
Backward Euler ◽  
Euler Discretization

In this paper, we consider the backward Euler discretization derived from a continuous SIRS epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.

Dynamics analysis and optimal control strategy for a SIRS epidemic model with two discrete time delays

2020 ◽  
Vol 95 (3) ◽  
pp. 035213
Author(s):  
Linhe Zhu ◽  
Xuewei Wang ◽  
Huihui Zhang ◽  
Shuling Shen ◽  
Yimin Li ◽  
...  
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Epidemic Model ◽  
Time Delays ◽  
Dynamics Analysis ◽  
Optimal Control Strategy ◽  
Sirs Epidemic Model

Dynamics of a stochastic periodic SIRS model with time delay

2020 ◽  
pp. 2050072
Author(s):  
Xiangyun Shi ◽  
Yimeng Cao
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Ultimate Boundedness ◽  
Sirs Epidemic Model ◽  
Dynamical Behaviors ◽  
Sirs Model ◽  
Global Positive Solution ◽  
Stochastically Ultimate Boundedness

Dynamical behaviors of a stochastic periodic SIRS epidemic model with time delay are investigated. By constructing suitable Lyapunov functions and applying Itô’s formula, the existence of the global positive solution and the property of stochastically ultimate boundedness of model (1.1) are proved. Moreover, the extinction and the persistence of the disease are established. The results are verified by numerical simulations.

Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 479-481 ◽  
pp. 1495-1498 ◽  
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Hong Kai Sun
Keyword(s):  
Hopf Bifurcation ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Asymptotical Stable ◽  
Disease Free

An SIRS epidemic model with nonlinear incidence rate is studied. It is assumed that susceptible and infectious individuals have constant immigration rates. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the analytical results.

A KICKED EPIDEMIC SIRS MODEL

2012 ◽  
Vol 22 (10) ◽  
pp. 1250251
Author(s):  
F. PALADINI ◽  
I. RENNA ◽  
L. RENNA
Keyword(s):  
Infectious Diseases ◽  
Numerical Simulations ◽  
Population Size ◽  
Discrete Time ◽  
Epidemic Model ◽  
Seasonal Variability ◽  
Sirs Model ◽  
Variable Population ◽  
Variable Population Size

A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behavior observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose, we introduce, in a naïve discrete-time SIRS model, seasonal variability (i) in the loss of immunity and (ii) in the infection probability, modeled by sequences of kicks. Effects of a variable population size (assumed as logistic) are also analyzed. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.

Sign in / Sign up

Export Citation Format

Share Document