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 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 Modeling Computer Virus and Its Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Mei Peng ◽  
Xing He ◽  
Junjian Huang ◽  
Tao Dong
Keyword(s):  
Basic Reproduction Number ◽  
Stable Equilibrium ◽  
Reproduction Number ◽  
Computer Virus ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Numerical Examples ◽  
Virus Model ◽  
Virus Spreading ◽  
The Basic Reproduction Number

Based on that the computer will be infected by infected computer and exposed computer, and some of the computers which are in suscepitible status and exposed status can get immunity by antivirus ability, a novel coumputer virus model is established. The dynamic behaviors of this model are investigated. First, the basic reproduction numberR0, which is a threshold of the computer virus spreading in internet, is determined. Second, this model has a virus-free equilibriumP0, which means that the infected part of the computer disappears, and the virus dies out, andP0is a globally asymptotically stable equilibrium ifR0<1. Third, ifR0>1then this model has only one viral equilibriumP*, which means that the computer persists at a constant endemic level, andP*is also globally asymptotically stable. Finally, some numerical examples are given to demonstrate the analytical results.

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 Modelling and Analysis of Propagation Behavior of Computer Viruses with Nonlinear Countermeasure Probability and Infected Removable Storage Media

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xulong Zhang ◽  
Yong Li
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Computer Virus ◽  
Dynamical Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Computer Viruses ◽  
Viral Spread ◽  
Propagation Behavior ◽  
Storage Media

The dissemination of countermeasures is diffusely recognized as one of the most valid strategies of containing computer virus diffusion. In order to better understand the impacts of countermeasure and removable storage media on viral spread, this paper addresses a dynamical model, which incorporates nonlinear countermeasure probability and infected removable storage media. Theoretical analysis reveals that the unique (viral) equilibrium of the model is globally asymptotically stable. This main result is also illustrated by some numerical experiments. Additionally, the numerical experiments of different countermeasure probabilities are conducted.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Global dynamics for a live-virus-blood model with distributed time delay

2017 ◽  
Vol 10 (05) ◽  
pp. 1750067 ◽  
Author(s):  
Ding-Yu Zou ◽  
Shi-Fei Wang ◽  
Xue-Zhi Li
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Live Virus ◽  
Number Formula ◽  
Distributed Time Delay ◽  
The Basic Reproduction Number

In this paper, the global properties of a mathematical modeling of hepatitis C virus (HCV) with distributed time delays is studied. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states. It is shown that if the basic reproduction number [Formula: see text] is less than unity, then the uninfected steady state is globally asymptotically stable. If the basic reproduction number [Formula: see text] is larger than unity, then the infected steady state is globally asymptotically stable.

scholarly journals On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Stanislas Ouaro ◽  
Ali Traoré
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Mass Action ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Vector Borne Disease ◽  
Special Cases ◽  
Vector Borne ◽  
The Basic Reproduction Number

We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.

scholarly journals Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yu Ji ◽  
Muxuan Zheng
Keyword(s):  
Viral Infection ◽  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Reproduction Numbers ◽  
The Basic Reproduction Number ◽  
General Standard

The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction numberR0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, ifR0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host.

Dynamics of a delayed epidemic model with varying immunity period and nonlinear transmission

2015 ◽  
Vol 08 (02) ◽  
pp. 1550027 ◽  
Author(s):  
Aadil Lahrouz
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Incidence Rates ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
The Basic Reproduction Number

An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.

An age-structured epidemic model with waning immunity and general nonlinear incidence rate

2018 ◽  
Vol 11 (05) ◽  
pp. 1850069 ◽  
Author(s):  
Xia Wang ◽  
Ying Zhang ◽  
Xinyu Song
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Waning Immunity ◽  
Age Structured ◽  
The Basic Reproduction Number

In this paper, a susceptible-vaccinated-exposed-infectious-recovered epidemic model with waning immunity and continuous age structures in vaccinated, exposed and infectious classes has been formulated. By using the Fluctuation lemma and the approach of Lyapunov functionals, we establish a threshold dynamics completely determined by the basic reproduction number. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, and otherwise the endemic steady state is globally asymptotically stable.

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