Modeling of Computer Virus Propagation with Fuzzy Parameters

Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.To understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this work.It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity,which depends on the quantity of virus.Considering this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy numbers.Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models.The essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy senses.Moreover,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and analyzed.In the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic system.It can be considered a reliable tool to predict such types of solutions.

Hopf Bifurcation of Nonresident Computer Virus Model with Age Structure and Two Delays Effects

This paper constructed and studied a nonresident computer virus model with age structure and two delays effects. The non-negativity and boundedness of the solution of the model have been discussed, and then gave the basic regeneration number, and obtained the conditions for the existence and the stability of the virus-free equilibrium and the computer virus equilibrium. Theoretical analysis shows the conditions under which the model undergoes Hopf bifurcation in three different cases. The numerical examples are provided to demonstrate the theoretical results.

ON GLOBAL STABILITY OF A NONRESIDENT COMPUTER VIRUS MODEL

In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.

STABILITY ANALYSIS OF A COMPUTER VIRUS PROPAGATION MODEL WITH ANTIDOTE IN VULNERABLE SYSTEM

We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold Ro. If Ro 〈 1, the virusfree equilibrium is globally asymptotically stable, and if R0 〉 1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.

A Stochastic Numerical Analysis for Computer Virus Model with Vertical Transmission Over the Internet

We are presenting the numerical analysis for stochastic SLBR model of computer virus over the internet in this manuscript.We are going to present the results of stochastic and deterministic computer virus model.Outcomes of the threshold number C∗hold in stochastic computer virus model.If C∗<1 then in such a condition virus controlled in the computer population while C∗>1 shows virus spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,bounded-ness and positivity as well-defined by Mickens.On this basis,we can suggest a collection of plans for eradicating viruses spreading across the internet effectively.

Hopf Bifurcation of a Nonresident Computer Virus Model with Delay

In this paper, a delayed nonresident computer virus model with graded infection rate is considered in which the following assumption is imposed: latent computers have lower infection ability than infectious computers. With the aid of the bifurcation theory, sufficient conditions for stability of the infected equilibrium of the model and existence of the Hopf bifurcation are established. In particular, explicit formulae which determine direction and stability of the Hopf bifurcation are derived by means of the normal form theory and the center manifold reduction for functional differential equations. Finally, a numerical example is given in order to show the feasibility of the obtained theoretical findings.

Spatio-Temporal Dynamics and Structure Preserving Algorithm for Computer Virus Model

The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered(SLBR)epidemic model.It describes the computer virus dynamics with vertical transmission via the internet.In these types of dynamics models,the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design.By taking into account this key property,the positivity preserving algorithm is designed to solve the underlying SLBR system.Since,the state variables associated with the phenomenon,represent the computer nodes,so they must take in absolute.Moreover,the continuous system(SLBR)acquires two steady states i.e.,the virus-free state and the virus existence state.The stability of the numerical design,at the equilibrium points,portrays an exceptional aspect about the propagation of the virus.The designed discretization algorithm sustains the stability of both the steady states.The computer simulations also endorse that the proposed discretization algorithm retains all the traits of the continuous SLBR model with spatial content.The stability and consistency of the proposed algorithm are verified,mathematically.All the facts are also ascertained by numerical simulations.

Numerical Simulations for Stochastic Computer Virus Propagation Model

We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript.We are comparing the solutions of stochastic and deterministic computer virus models.Outcomes of a threshold number R0 hold in stochastic computer virus model.If R_(0)<1 then in such a condition virus controlled in the computer population while R_(0)>1 shows virus rapidly spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical properties.On this basis,we can suggest a collection of strategies for removing virus’s propagation in the computer population.

Numerical Study of Computer Virus Reaction Diffusion Epidemic Model

Reaction–diffusion systems are mathematical models which link to several physical phenomena.The most common is the change in space and time of the meditation of one or more materials.Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases.We investigated the transmission dynamics of the computer virus in which connected to each other through network globally.The current study devoted to the structure-preserving analysis of the computer propagation model.This manuscript is devoted to finding the numerical investigation of the reaction–diffusion computer virus epidemic model with the help of a reliable technique.The designed technique is finite difference scheme which sustains the important physical behavior of continuous model like the positivity of the dependent variables,the stability of the equilibria.The theoretical analysis of the proposed method like the positivity of the approximation,stability,and consistency is discussed in detail.A numerical example of simulations yields the authentication of the theoretical results of the designed technique.

Computer Virus

Computer viruses are small software programs that are designed to spread from one computerto another and to interfere with computer operation.A virus might delete data on your computer,use your e-mail program to spread itself to othercomputers,or even erase everything on your hard disk.Viruses are most easily spread by attach-ments in e-mail messages or instant messaging messages.That is why it is essential that you

Computer Virus

If you work with acomputer, it is certain that youcan not avoid dealing with atleast one computer virus. Buthow much do you know aboutit? Well,actually,a computervirus is not a biological one ascauses illnesses to people.It is akind of computer programcompiled by human beings.It isharmful data made of

Dynamic detection for computer virus based on immune system

Inspired by biological immune system, a new dynamic detection model for computer virus based on immune system is proposed. The quantitative description of the model is given. The problem of dynamic description for self and nonself in a computer virus immune system is solved, which reduces the size of self set. The new concept of dynamic tolerance, as well as the new mechanisms of gene evolution and gene coding for immature detectors is presented, improving the generating efficiency of mature detectors, reducing the false-negative and false-positive rates. Therefore, the difficult problem, in which the detector training cost is exponentially related to the size of self-set in a traditional computer immune system, is thus overcome. The theory analysis and experimental results show that the proposed model has better time efficiency and detecting ability than the classic model ARTIS.

Dynamic model of computer viruses under the effect of removable media and external computers

This paper investigates the propagation of computer viruses and establishes a novel propagation model. In contrast to the existing models,this model can directly indicate the impact of removable media and external computers on the propagation of computer virus. The stability results of equilibrium point are derived by Hurwitz criterion and Bendixson Dulac criterion. The effectiveness of the proposed results is shown by numerical simulation. In order to show the superiority of the proposed model,some comparisons with the existing models are presented. The acceptable threshold and the reasonable strategies for suppressing the propagation of computer virus are also suggested,respectively.

Computational Analysis for Computer Network Model with Fuzziness

A susceptible,exposed,infectious,quarantined and recovered(SEIQR)model with fuzzy parameters is studied in this work.Fuzziness in the model arises due to the different degrees of susceptibility,exposure,infectivity,quarantine and recovery among the computers under consideration due to the different sizes,models,spare parts,the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus,etc.Each individual PC has a different degree of infectivity and resis-tance against infection.In this scenario,the fuzzy model has richer dynamics than its classical counterpart in epidemiology.The reproduction number of the developed model is studied and the equilibrium analysis is performed.Two different techniques are employed to solve the model numerically.Numerical simulations are performed and the obtained results are compared.Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.

Malicious code passive propagation model and vaccine distribution model of P2P networks

To fight against malicious codes of P2P networks, it is necessary to study the malicious code propagation model of P2P networks in depth. The epidemic of malicious code threatening P2P systems can be divided into the active and passive propagation models and a new passive propagation model of malicious code is proposed, which differentiates peers into 4 kinds of state and fits better for actual P2P networks. From the propagation model of malicious code, it is easy to find that quickly making peers get their patched and upgraded anti-virus system is the key way of immunization and damage control. To distribute patches and immune modules efficiently, a new exponential tree plus （ET＋） and vaccine distribution algorithm based on ET＋ are also proposed. The performance analysis and test results show that the vaccine distribution algorithm based on ET＋ is robust, efficient and much more suitable for P2P networks.

Infection Functions for Virus Propagation in Computer Networks:An Empirical Study

There has been an increasing amount of interest in modeling virus propagation in recent years. However, the group-based infection mechanism of computer viruses is not well understood and the selection of infection function in virus propagation modeling has not been well studied. This paper describes a point-to-group （P2G） infection mode to describe virus propagation in networks with information sharing groups. Simulations compare the constant infection and I-type infection functions with the new E-type infection function in the small-world-network environment. The simulation results show that the E-type infection function shows superior performances to that of the traditional I-type infection function in modeling the P2G virus infection mechanism and the I-type infection function shows better performance in modeling the random infection mechanism.