scholarly journals An SLBRS Model with Vertical Transmission of Computer Virus over the Internet

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Maobin Yang ◽  
Zhufan Zhang ◽  
Qiang Li ◽  
Gang Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Behavior ◽  
Vertical Transmission ◽  
Computer Virus ◽  
The Internet ◽  
Asymptotically Stable ◽  
Qualitative Properties ◽  
Globally Asymptotically Stable ◽  
New Model ◽  
System Parameters

By incorporating an additional recovery compartment in the SLBS model, a new model, known as the SLBRS model, is proposed in this paper. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a thresholdℛ0. Specially, virus-free equilibrium is globally asymptotically stable ifℛ0≤1, whereas the viral equilibrium is globally asymptotically stable ifℛ0>1. Next, the sensitivity analysis ofℛ0to four system parameters is also analyzed. On this basis, a collection of strategies are advised for eradicating viruses spreading across the Internet effectively.

scholarly journals Propagation Behavior of Virus Codes in the Situation That Infected Computers Are Connected to the Internet with Positive Probability

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lu-Xing Yang ◽  
Xiaofan Yang
Keyword(s):  
Theoretical Analysis ◽  
Threshold Value ◽  
Computer Virus ◽  
The Internet ◽  
Asymptotically Stable ◽  
Positive Probability ◽  
Globally Asymptotically Stable ◽  
New Model ◽  
Propagation Behavior ◽  
Viral Equilibrium

All the known models describing the propagation of virus codes were based on the assumption that a computer is uninfected at the time it is being connected to the Internet. In reality, however, it is much likely that infected computers are connected to the Internet. This paper is intended to investigate the propagation behavior of virus programs provided infected computers are connected to the Internet with positive probability. For that purpose, a new model characterizing the spread of computer virus is proposed. Theoretical analysis of this model indicates that (1) there is a unique (viral) equilibrium, and (2) this equilibrium is globally asymptotically stable. Further study shows that, by taking active measures, the percentage of infected computers can be made below an acceptable threshold value.

scholarly journals Global Stability of an Epidemic Model of Computer Virus

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaofan Yang ◽  
Bei Liu ◽  
Chenquan Gan
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Computer Virus ◽  
Propagation Model ◽  
Parameter Analysis ◽  
The Internet ◽  
Asymptotically Stable ◽  
Unique Equilibrium ◽  
Globally Asymptotically Stable ◽  
Computer Viruses

With the rapid popularization of the Internet, computers can enter or leave the Internet increasingly frequently. In fact, no antivirus software can detect and remove all sorts of computer viruses. This implies that viruses would persist on the Internet. To better understand the spread of computer viruses in these situations, a new propagation model is established and analyzed. The unique equilibrium of the model is globally asymptotically stable, in accordance with the reality. A parameter analysis of the equilibrium is also conducted.

scholarly journals Propagation of Computer Virus under Human Intervention: A Dynamical Model

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Chenquan Gan ◽  
Xiaofan Yang ◽  
Wanping Liu ◽  
Qingyi Zhu ◽  
Xulong Zhang
Keyword(s):  
Reproduction Number ◽  
Computer Virus ◽  
Parameter Analysis ◽  
Dynamical Model ◽  
The Internet ◽  
Asymptotically Stable ◽  
Human Intervention ◽  
Globally Asymptotically Stable ◽  
Propagation Behavior ◽  
The Basic Reproduction Number

This paper examines the propagation behavior of computer virus under human intervention. A dynamical model describing the spread of computer virus, under which a susceptible computer can become recovered directly and an infected computer can become susceptible directly, is proposed. Through a qualitative analysis of this model, it is found that the virus-free equilibrium is globally asymptotically stable when the basic reproduction numberR0≤1, whereas the viral equilibrium is globally asymptotically stable ifR0>1. Based on these results and a parameter analysis, some appropriate measures for eradicating the spread of computer virus across the Internet are recommended.

scholarly journals A New Model for Capturing the Spread of Computer Viruses on Complex-Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chunming Zhang ◽  
Tianliang Feng ◽  
Yun Zhao ◽  
Guifeng Jiang
Keyword(s):  
Computer Virus ◽  
Propagation Model ◽  
Asymptotically Stable ◽  
Virus Propagation ◽  
Systematic Analysis ◽  
Globally Asymptotically Stable ◽  
Computer Viruses ◽  
New Model ◽  
Globally Attractive ◽  
Computer Virus Propagation Model

Based on complex network, this paper proposes a novel computer virus propagation model which is motivated by the traditional SEIRQ model. A systematic analysis of this new model shows that the virus-free equilibrium is globally asymptotically stable when its basic reproduction is less than one, and the viral equilibrium is globally attractive when the basic reproduction is greater than one. Some numerical simulations are finally given to illustrate the main results, implying that these results are applicable to depict the dynamics of virus propagation.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Threshold Value ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Virus Propagation ◽  
Globally Asymptotically Stable ◽  
Existence And Stability ◽  
Computer Virus Propagation Model

A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold valueR0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable ifR0<1, whereas the virus equilibrium is globally asymptotically stable ifR0>1. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.

scholarly journals Global Dynamics and Sensitivity Analysis of a Vector-Host-Reservoir Model

2016 ◽  
Vol 21 (2) ◽  
pp. 120
Author(s):  
Ibrahim M. ELmojtaba ◽  
Santanu Biswas ◽  
Joydev Chattopadhyay
Keyword(s):  
Sensitivity Analysis ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Animal Reservoir ◽  
Globally Asymptotically Stable ◽  
Numerical Result ◽  
Perform Sensitivity Analysis ◽  
Host Reservoir

The role of animal reservoir in the disease dynamics is not yet properly studied. In the present investigation a mathematical model of a vector-host-reservoir is proposed and analyzed to observe the global dynamics of the disease. We observe that the disease free equilibrium is globally asymptotically stable if the basic reproduction number ( ) is less than unity whereas unique positive equilibrium is globally asymptotically stable if and transcritical bifurcation occurs at . Our numerical result suggests that the biting rate plays an important role for the propagation of the disease and the recovery rate has not such important contribution towards eradication of the disease. We also perform sensitivity analysis of the model parameters and the results suggest that the death rate of reservoir may be used as a control parameter to eradicate the disease. 

scholarly journals Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

2022 ◽  
Author(s):  
Yves Tinda Mangongo ◽  
Joseph-Désiré Kyemba Bukweli ◽  
Justin Dupar Busili Kampempe ◽  
Rostin Matendo Mabela ◽  
Justin Manango Wazute Munganga
Keyword(s):  
Sensitivity Analysis ◽  
Recovery Rate ◽  
Global Sensitivity Analysis ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Sensitivity ◽  
Partial Rank Correlation

Abstract In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.

scholarly journals Modeling the Parasitic Filariasis Spread by Mosquito in Periodic Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Cheng ◽  
Xiaoyun Wang ◽  
Qiuhui Pan ◽  
Mingfeng He
Keyword(s):  
Sensitivity Analysis ◽  
Periodic Solution ◽  
Numerical Simulations ◽  
Parasitic Infection ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Periodic Environment ◽  
Disease Free

In this paper a mosquito-borne parasitic infection model in periodic environment is considered. Threshold parameterR0is given by linear next infection operator, which determined the dynamic behaviors of system. We obtain that whenR0<1, the disease-free periodic solution is globally asymptotically stable and whenR0>1by Poincaré map we obtain that disease is uniformly persistent. Numerical simulations support the results and sensitivity analysis shows effects of parameters onR0, which provided references to seek optimal measures to control the transmission of lymphatic filariasis.

BIFURCATION ANALYSIS ON AN HIV-1 MODEL WITH CONSTANT INJECTION OF RECOMBINANT

2012 ◽  
Vol 22 (03) ◽  
pp. 1250062 ◽  
Author(s):  
PEI YU ◽  
XINGFU ZOU
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Solution ◽  
Injection Rate ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
New Model ◽  
Hiv Virus ◽  
Hiv 1

This paper is a continuation of our previous work on an HIV-1 therapy model of fighting a virus with another virus [Jiang et al., 2009]. The work in [Jiang et al., 2009] investigated cascading bifurcations between equilibrium solutions, as well as Hopf bifurcation from a double-infected equilibrium solution. In this paper, we propose a modification of the model in [Revilla & Garcia-Ramos, 2003; Jiang et al., 2009] by adding a constant η to the recombinant virus equation, which accounts for the treatment of constant injection of recombinants. We study the dynamics of the new model and find that η plays an important role in the therapy. Unlike the previous model without injection of recombinant, which has three equilibrium solutions, this new model can only allow two biologically meaningful equilibrium solutions. It is shown that there is [Formula: see text] depending on η, such that the HIV free equilibrium solution [Formula: see text] is globally asymptotically stable when the basic reproduction ratio, [Formula: see text]; [Formula: see text] becomes unstable when [Formula: see text]. In the latter case, there occurs the double-infection equilibrium solution, [Formula: see text], which is stable when [Formula: see text] for some [Formula: see text] larger than [Formula: see text], and loses its stability when [Formula: see text] passes the critical value [Formula: see text] and bifurcates into a family of limit cycles through Hopf bifurcation. Our results show that appropriate injection rate can help eliminate the HIV virus in the sense that the HIV free equilibrium can be made globally asymptotically stable by choosing η > 0 sufficiently large. This is in contrast to the conclusion for the case with η = 0 in which, the recombinants do not help eliminate the HIV virus but only help reduce the HIV load in the long term sense.

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