scholarly journals Two Quarantine Models on the Attack of Malicious Objects in Computer Network

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Bimal Kumar Mishra ◽  
Aditya Kumar Singh
Keyword(s):  
Numerical Methods ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Incidence Rate ◽  
Computer Network ◽  
Endemic Equilibrium ◽  
Mass Action ◽  
System Of Differential Equations ◽  
Simple Mass ◽  
Threshold Equilibrium

SEIQR (Susceptible, Exposed, Infectious, Quarantined, and Recovered) models for the transmission of malicious objects with simple mass action incidence and standard incidence rate in computer network are formulated. Threshold, equilibrium, and their stability are discussed for the simple mass action incidence and standard incidence rate. Global stability and asymptotic stability of endemic equilibrium for simple mass action incidence have been shown. With the help of Poincare Bendixson Property, asymptotic stability of endemic equilibrium for standard incidence rate has been shown. Numerical methods have been used to solve and simulate the system of differential equations. The effect of quarantine on recovered nodes is analyzed. We have also analyzed the behavior of the susceptible, exposed, infected, quarantine, and recovered nodes in the computer network.

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

Modelling and Experimental Studies of Sorption in the Near Field of a Cementitious Repository

1989 ◽  
Vol 176 ◽  
Author(s):  
P.L. Brown ◽  
A. Haworth ◽  
R. McCrohon ◽  
S.M. Sharland ◽  
C.J. Tweed
Keyword(s):  
Near Field ◽  
Experimental Studies ◽  
Mass Action ◽  
Chemical Equilibria ◽  
Transport Code ◽  
Mass Action Model ◽  
Action Model ◽  
Modelling Studies ◽  
Simple Mass

ABSTRACTA joint experimental and modelling programme is reported, which aims to improve our understanding of sorption processes of radionuclides onto repository materials. Diffusion/sorption experiments of sorption onto cement are described, although results are limited at this stage. The modelling studies use the coupled chemical equilibria and transport code CHEQMATE to simulate some of these experiments. The chemical part of the model is based on a simple mass-action model of sorption. More detailed comparisons will continue when the experiments are terminated, and the samples are sectioned.

scholarly journals New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

2018 ◽  
Vol 1 (3) ◽  
pp. 30 ◽  
Author(s):  
Hussein ALKasasbeh ◽  
Irina Perfilieva ◽  
Muhammad Ahmad ◽  
Zainor Yahya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Approximation Methods ◽  
System Of Differential Equations ◽  
Fuzzy Transform ◽  
Fuzzy Partition ◽  
Fuzzy Approximation ◽  
One Step ◽  
Basic Functions

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

scholarly journals Global stability analysis for a model with carriers and non-linear incidence rate

2020 ◽  
Vol 14 (1) ◽  
pp. 409-420
Author(s):  
Miller Cerón Gómez ◽  
Eduardo Ibarguen Mondragon ◽  
Patricia Lopez Molano
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Incidence Rate ◽  
Global Stability Analysis ◽  
Non Linear

scholarly journals Analysis of HIV Transmission of Commercial Sex Wokers and Their Clients with Condom Use Treatment

2019 ◽  
Vol 125 ◽  
pp. 05003 ◽  
Author(s):  
Sutimin ◽  
Siti Khabibah ◽  
Dita Anies Munawwaroh ◽  
R. Heri Soelistyo U
Keyword(s):  
Condom Use ◽  
Global Stability ◽  
Sex Workers ◽  
Hiv Transmission ◽  
Equilibrium States ◽  
Endemic Equilibrium ◽  
Reproduction Ratio ◽  
Aids Epidemic ◽  
The Impact ◽  
Hiv Aids

A model of the HIV/AIDS epidemic among sex workers and their clients is discussed to study the effects of condom use in the prevention of HIV transmission. The model is addressed to determine the existence of equilibrium states, and then analyze the global stability of disease free and endemic equilibrium states. The global stability of equilibria depends on the vales of the basic reproduction ratio derived from the next generation matrix of the model. The endemic equilibrium state is globally stable when the ratio exceeds unity. The simulation results are presented to discuss the effect of condom use treatment in preventing the spread of HIV/AIDS among sex workers and their clients. The results show that the effectiveness level in using condoms in sexual intercourse corresponds to the decreasing level of the spread of HIV/AIDS. We use Maple and Matlab software to simulate the impact of condom use.

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