Computer Virus Spreading Model Research Articles

Optimal Control of Computer Virus Spreading Model with Partial Immunization

Optimal Control of Computer Virus Spreading Model with Partial Immunization

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 parameters and being 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.

A Virus Propagation Model and Optimal Control Strategy in the Point-to-Group Network to Information Security Investment

Epidemiological dynamics is a vital method in studying the spread of computer network viruses. In this paper, an optimal control measure is proposed based on the SEIR virus propagation model in point-to-group information networks. First, considering the need for antivirus measures in reality, an optimal control problem is introduced, and then a controlled computer virus spread model in point-to-group information networks is established. Second, the optimal control measure is formulated by making a tradeoff between control cost and network loss caused by virus intrusion. Third, optimal control strategies are theoretically investigated by Pontryagin’s maximum principle and the Hamiltonian function. Finally, through numerical simulations, effective measures for controlling virus spread in point-to-group information networks are proposed.

Hopf bifurcation analysis of SEIR-KS computer virus spreading model with two-delay

Computer virus has caused terrible damage. Establishing appropriate mathematical model is beneficial for comprehending the propagation regular pattern of computer virus. So, in this paper, we build a new Susceptible-Exposed-Infected-Kill signals-Recovered (SEIR-KS) computer virus model with two delays. At first, we obtain the basic regeneration number. Afterwards, we regard time delays as parameters and investigate the local stability and Hopf bifurcation of the endemic equilibrium by discussing the distribution of the eigenvalues of the corresponding characteristic equation. Then, we research direction and stability of Hopf bifurcation. In addition, we take some numerical simulations by Matlab to validate the correctness of theoretical results. At last, we analyze the basic reproductive rate and put forward some scientific advices.

Dynamics of a nonlinear SIQRS computer virus spreading model with two delays

<abstract> In this paper, a Susceptible-Infected-Quarantined-Susceptible (SIQRS) computer virus propagation model with nonlinear infection rate and two-delay is formulated. The local stability of virus-free equilibrium without delay is examined. Furthermore, we also expound and prove that time-delay plays a crucial role in sufficient conditions for the local stability of the virus-existence equilibrium and the occurrence of Hopf bifurcation at the critical value. Especially, direction and stability of the Hopf bifurcation are demonstrated. Finally, some numerical simulations are presented in order to verify the theoretical results. </abstract>

Existence Results for a Computer Virus Spreading Model with Atangana-Baleanu Derivative

A computer virus is actually a kind of computer program that changes the operation of the computer and tries to hide itself in other files without the user's consent or knowledge. In this paper we deal with a computer virus spreading model benefiting from Atangana-Baleanu derivative in Caputo sense with non- local and non- singular kernels. The solution properties of our fractional model are established benefiting from Arzelo-Ascoli theorem.

Dynamics of Epidemic Computer Virus Spreading Model with Delays

The vulnerability that exists in the computer network by the infection of virus as soon as the resources are exposed requires the study of the nature of propagation of virus into the network. In this work we have formulated a novel epidemic Susceptible-Infected-Recovered model that deals with the infected nodes in the network in terms of the development of immunity attained after recovery. Positivity and boundedness of the proposed model is examined. Local stability analysis of the proposed model without delay is also analyzed by Routh–Hurwitz criteria apart from the delay sensitivity analysis. The time series analysis regarding the nature of the susceptible, infected and recovered nodes in the network has been performed using real control parameters $$\beta$$ (infection rate of the computers), $$\gamma$$ (recovered rate of the infected computers). We also analyzed that time delay may play significant role on the stability of the proposed model since whenever delay exceeds the critical value the system loses its stability and a Hopf bifurcation occurs. The numerical simulation results justify that the proposed model is validated against the analytical studies of virus propagation thus verifying the theoretical results.

Hopf bifurcation of a computer virus spreading model in the network with limited anti-virus ability

A delayed computer virus spreading model in the network with limited anti-virus ability is proposed in the present paper. Local stability and the existence of a Hopf bifurcation are proved by taking the time delay as the bifurcation parameter and analyzing the distribution of the roots of the corresponding characteristic equation. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, a numerical example is presented to demonstrate our obtained results.

Propagation Effect of a Virus Outbreak on a Network with Limited Anti-Virus Ability.

This paper describes a new computer virus spreading model which takes into account the possibility of a virus outbreak on a network with limited anti-virus ability. Then, the model is investigated for the existence of equilibria and their stabilities are proved and illustrated. Moreover, it is found that these two factors are not only relative to the threshold value determining whether the virus becomes extinct or not, but that they are also relative to the virus epidemic levels. Theoretical and experimental results indicate that, in some ways, it would be practically possible to eradicate the virus or suppress its prevalence below a suitable level. Consequently, some suggestions are proposed that may help eradicate or suppress virus propagation over a real computer network.

The effect of network topology on the spread of computer viruses: a modelling study

ABSTRACTThis paper is intended to investigate the effect of network topology on the spread of computer viruses in the presence of removable storage media. For that purpose, a novel network-based computer virus spreading model is proposed. Both theoretically and experimentally, it is shown that, under proper conditions, viruses on a scale-free network would tend to extinction. Experimental results show that either smaller maximum node degree or larger power-law exponent is conducive to the containment of virus spreading. To our knowledge, this is the first time the effect of network topology on virus spreading is investigated in this context.

Influence of node mobility on virus spreading behaviors in multi-hop network

Multi-hop network has received growing attention recently with the widely use of wireless network communication technology. At the same time, the security of multi-hop network is facing more serve challenges. Unfortunately, classic techniques for computer virus spreading model cannot be applied to multi-hop network because of ignoring dynamic topology of network. In this paper, classic susceptible-infected (SI) model, susceptible-infected-susceptible (SIS) model and susceptible-infected-removed (SIR) model are applied to multi-hop network based on random way-point (RWP) model, and contact duration of virus is introduced. Virus spreading behaviors are examined through contact duration of virus, communication radius of node, distribution density of node, and the number of initial infected nodes. Simulation results show that node mobility has significant effect on virus spreading behaviors. In particular, a special node speed that can lead network to appear the fastest-spreading virus phenomenon is found. The special speed is approximately equal to the ratio of communication radius of node to contact duration of virus. Distribution density of node and the number of initial infected nodes almost do not affect the special speed.

A computer virus spreading model based on resource limitations and interaction costs

Computer viruses are major threats to Internet security and privacy, therefore many researchers are addressing questions linked to virus propagation properties, spreading models, epidemic dynamics, tipping points, and control strategies. We believe that two important factors – resource limitations and costs – are being overlooked in this area due to an overemphasis on power-law connectivity distributions of scale-free networks affecting computer virus epidemic dynamics and tipping points. The study show (a) a significant epidemic tipping point does exists when resource limitations and costs are considered, with the tipping point exhibiting a lower bound; (b) when interaction costs increase or usable resources decrease, epidemic tipping points in scale-free networks grow linearly while density curves decrease linearly; (c) regardless of whether Internet user resources obey delta, uniform, or normal distributions, they retain the same epidemic dynamics and tipping points as long as the average value of those resources remains unchanged across different scale-free networks; (d) it is possible to control the spread of a computer virus in a scale-free network if resources are restricted and if costs associated with infection events are significantly increased through the use of a throttling strategy.

Optimal control of computer virus under a delayed model

This paper addresses the issue of how to suppress the spread of computer virus by means of the optimal control method. First, a controlled delayed computer virus spread model is established. Second, an optimal control problem is formulated by making a tradeoff between the control cost and the control effect. Third, the optimal control strategies are theoretically investigated. Finally, it is experimentally shown that the spread of infected nodes can be suppressed effectively by adopting an optimal control strategy.

Optimal control in a novel computer virus spread model

In this paper, we propose a computer virus spread model with optimal control, which is intended to keep both infected nodes and systemic cost levels low. Then the existence and uniqueness results of the optimality system are both proved. Numerical results show that the spread of computer virus can be controlled effectively with proper control strategy.

An Impulse Model for Computer Viruses

Computer virus spread model concerning impulsive control strategy is proposed and analyzed. We prove that there exists a globally attractive infection-free periodic solution when the vaccination rate is larger thanθ0. Moreover, we show that the system is uniformly persistent if the vaccination rate is less thanθ1. Some numerical simulations are finally given to illustrate the main results.

A Stochastic Dynamic Model of Computer Viruses

A stochastic computer virus spread model is proposed and its dynamic behavior is fully investigated. Specifically, we prove the existence and uniqueness of positive solutions, and the stability of the virus-free equilibrium and viral equilibrium by constructing Lyapunov functions and applying Ito's formula. Some numerical simulations are finally given to illustrate our main results.