Virus Propagation Model Research Articles

Dynamics analysis of a new fractional-order SVEIR-KS model for computer virus propagation: Stability and Hopf bifurcation

This work investigates the stability and Hopf bifurcation of a fractional-order model of the computer virus known as Susceptible–Vaccinated–Exposed–Infected–Recovered–Kill Signals (SVEIR-KS) that has two delays. Utilizing the linearization technique, Laplace transform, Routh–Hurwitz criteria, and Hopf bifurcation theorem of fractional-order differential systems, the sufficient criteria for the system’s stability and Hopf bifurcation are determined. The study demonstrates that the stability and occurrence of the Hopf bifurcation of the fractional-order computer virus model are profoundly affected by fractional order q and time delays. In order to confirm the validity of the theoretical results, various simulations and examples with appropriate parameters are provided. The results show a negative correlation between the delay critical value and the fractional order q. Additionally we also dig into the effect in which kill signals prevent computer viruses from spreading over a network.

Analytical solutions of virus propagation model in blockchain networks

The main goal of this paper is to find analytical solutions of a system of nonlinear ordinary differential equations arising in the virus propagation in blockchain networks. The presented method reduces the problem to an Abel differential equation of the first kind and solve it directly.

Dynamics and Control Strategies for SLBRS Model of Computer Viruses Based on Complex Networks

Dynamics and Control Strategies for SLBRS Model of Computer Viruses Based on Complex Networks

Analysis and numerical simulation of computer virus propagation model based on limited resources

Computer viruses present a substantial threat to our daily lives. Traditional models for the propagation of computer viruses primarily concentrate on network structures. In this paper, we take into account the constrained availability of resources in the context of computer virus prevention and control. We introduce a computer virus propagation model based on resource limitations. By examining the stability of both toxic and non-toxic equilibria within the model, we employ Matlab and Python for numerical analysis to simulate various computer virus propagation scenarios. Additionally, we present corresponding defense mechanisms for combatting these viruses.

Hybrid control of Turing instability and bifurcation for spatial-temporal propagation of computer virus

ABSTRACT In this era of information technology, information leakage and file corruption due to computer virus intrusion have been serious issues. How to detect and prevent the spread of the computer virus is the major challenge we are facing now. To target this problem, a class of virus propagation models with hybrid control scheme are formulated to investigate the dynamic evolution and prevention from a spatial-temporal perspective in this paper. Diffusion-induced Turing instability is detected in response to the computer virus propagation. The introduction of hybrid control scheme can effective suppress Turing instability and turn the propagation system back to a stable state. And then, the time delay is selected as the bifurcation parameter. If the time delay exceeds the bifurcation threshold, the propagation will be destabilised and a Hopf bifurcation will occur. The hybrid control tactic can not only regulate the occurrence of Hopf bifurcation well, but also optimise the properties of bifurcating period solutions. In the end, the correctness and validity of the theoretical results are verified via numerical simulations.

Numerical performances based artificial neural networks to deal with the computer viruses spread on the complex networks

This paper shows the outcomes of computer virus propagation (CVP) model, represented with susceptible, exposed, infected, quarantine and recovered computers (SEIRQ), classes based mathematical model using the stochastic procedures. The systematic study of the CVP based SEIRQ model represents that the equilibrium state of virus-free is stable globally with reproduction not more than one, while the viral symmetry is attractive globally. The numerical performances of the CVP based SEIRQ model are presented by using the stochastic computational framework based on the artificial neural networks (ANNs) together with the Levenberg-Marquardt backpropagation (LBMB) called as ANNs-LBMB. The learning procedures via ANNs-LBMB for solving the CVP based SEIRQ model are implemented to indorse the statics using the testing, authorization, and training. Thirteen numbers of neurons and the data selection for training 72%, testing 12% and validation 16% are selected to solve the model. For the numerical outcomes of the CVP based SEIRQ model using the ANNs-LBMB, a dataset is considered through the Adams approach. The accuracy and reliability performances of the scheme are presented by using the values of the absolute error (AE) along with the observations of state transitions (STs), regression, mean square error (MSE) and error histograms (EHs).

Dynamics of fractional plant virus propagation model with influence of seasonality and intraspecific competition

All biological forms of life rely on plants for many of their basic needs. Nonetheless, viruses can often infect plants. The ecosystem that depends on it could be destroyed as a result. An insect vector may be responsible for the virus's spread from plant to plant. A fractional order epidemic model is developed since it gives the more realistic solutions as the epidemics always persists in some or the other region and never becomes zero. The dynamics of the plant virus propagation model with effect from seasonality (PVP‐S) and intraspecific competition among predators are investigated in terms of existence of solutions, boundedness, and uniqueness. Analysis of plant virus propagation with effect from seasonality and intraspecific competition among predators in terms of fractional order is the novelty of this model. Here, we observe that the infection almost becomes zero in case of integral value, whereas it always persists as the fractional order is introduced, which is more realistic in nature. The occurrence of transcritical bifurcation for the model has been investigated. The proposed nonlinear model is numerically studied by the Adams–Bashforth–Moulton method. This study reveals the effectiveness of the numerical technique as well as the effect of the fractional order derivative on PVP‐S dynamics.

A new study for global dynamics and numerical simulation of a discrete-time computer virus propagation model

Truong Ha Hai, Pham Hoai Thu, Hoang Manh Tuan Abstract— This work is devoted to conducting a new study for global dynamics and numerical simulation of a discrete-time computer virus propagation model, which was constructed in our recent work. By utilizing well-known results on asymptotic stability of discrete-time dynamical systems, we establish the global asymptotic stability of a unique viral equilibrium point, whereas only its local asymptotic stability was previously analyzed. After that, we investigate convergence and provide an error bound for the discrete-time model. Next, the step doubling strategy is applied to control errors. The result is that the accuracy of approximations generated by the discrete-time model is enhanced. The obtained results not only improve the ones constructed in the benchmark work, but also can be useful to study reliable numerical methods for mathematical models of malware. Finally, we present two numerical experiments that support and illustrate the theoretical findings of this study.

Network virus propagation and security situation awareness based on Hidden Markov Model

The security situation of the network is determined by the observation state and hidden state of a complex virus system. To analyze the relationship between the two states and evaluate the trends in the security situation of the system, we construct a new model for security situation awareness based on Hidden Markov Model (HMM). Firstly, the paper examines the impact of virus propagation on network security and proposes a new SIR (Susceptible–Infected–Recovered) virus propagation model on scale-free networks. Secondly, we construct a Hidden Markov Model for network security, and this model designs and utilizes the Forward Algorithm and Viterbi Algorithm to assess the security status of epidemic networks. Finally, we ascertain the effectiveness of the model and algorithms through model examples and simulation experiments. The results show that the proposed algorithm is highly efficient in analyzing the security of virus systems and has great application value in predicting the security trends of networks.

Stability and Hopf bifurcation analysis for fractional-order SVEIR computer virus propagation model with nonlinear incident rate and two delays

This paper is concerned with the stability and Hopf bifurcation for a fractional-order Susceptible-Vaccinated-Exposed-Infectious-Recovered (SVEIR) computer virus propagation model with a nonlinear incident rate. By employing the linearization technique and Routh-Hurwitz method, the sufficient criterion is established for the locally asymptotic stability of endemic equilibrium point. The Hopf bifurcation is also studied for the SVEIR computer virus model by taking time delay as the bifurcation parameter. The research results show that the stability and Hopf bifurcation of proposed model are significantly affected by both time delay and the order of the fractional derivative. Examples with proper parameters and several simulations are given to illustrate the validity of the theoretical results.

Distributed immune time-delay SEIR-S model for new power system information network virus propagation

The new power system information network has the security problem of computer virus attack, and the study of its transmission mechanism is helpful to discover the law and influence of virus transmission. In this paper, the research method of epidemic theory is introduced, and a new Susceptible-Exposed-Infectious-Recovered-Susceptible(SEIR-S) virus model is proposed. The immune time-delay parameter is introduced to simulate the evolution and mutation of the virus so that nodes immune to the virus can still be re-infected after a certain time interval. At the same time, the immune time of different nodes is different, and the distributed immune time delay is used to enhance the authenticity of the simulated virus transmission; and considering the influence of the scale-free characteristics of the information network, this paper establishes a continuous Markov chain based on time. The transmission process of the virus, and then deduce the theoretical analysis results of the virus infection rate threshold. Based on theoretical analysis, the propagation process of the SEIR-S virus model with distributed immune time delay was simulated by using the Monte Carlo method, and the accuracy of the threshold formula of virus infection rate was verified. The influence rule of the hysteresis parameter, that is, increasing the average immune time of nodes to viruses can reduce the infection density of the network in a steady, and at the same time, making the immune time of network nodes obey a normal distribution can effectively reduce the oscillation effect of viruses on the network.

Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses

Abstract— The aim of this work is to construct high-order numerical schemes that preserve the dynamical properties of a mathematical model describing the spread of computer viruses on the Internet. For this purpose, we first apply Mickens’ methodology to formulate a dynamically consistent nonstandard finite difference (NSFD) scheme for the model under consid­eration. After that, the constructed NSFD scheme is combined with Richardson’s extrapolation method to generate higher-accuracy numerical approximations. The result is that we obtain extrapolated numerical schemes that not only preserve the dynamical proper­ties of the computer virus propagation model but also provide higher-accuracy numerical approximations. In addition, a set of numerical examples is conducted to illustrate and support the theoretical findings and to show the advantages of the proposed numerical schemes.

An industrial virus propagation model based on SCADA system

Supervisory control and data acquisition (SCADA) systems are widely used in the national infrastructure. As more and more SCADA systems have been connected to the Internet, SCADA systems are facing great network security threats, especially attacks from industrial viruses. This paper aims to propose a novel mathematical model of industrial viruses propagation over SCADA systems. Then, the existence and stability of the equilibrium point of this model are studied. To better control the spread of this virus with limited resources, an optimal control system is established for the model. Then, the existence of optimal control is proved, and the corresponding optimal control system is derived. Numerical simulation results show that our proposed control method can effectively control the spread of industrial viruses.

Dynamically consistent nonstandard numerical schemes for solving some computer virus and malware propagation models

This work is devoted to constructing reliable numerical schemes for some computer virus and malware propagation models. We apply the Mickens' methodology to formulate nonstandard finite difference (NSFD) schemes for some epidemiological models describing the spread of computer viruses and malware. Positivity, boundedness and global asymptotic stability (GAS) of the proposed NSFD schemes are studied rigorously. It should be emphasized that the GAS of the NSFD models are established based on an extension of the classical Lyapunov's direct method. As an important consequence, we conclude that the constructed NSFD schemes are dynamically consistent with respect to the positivity, boundedness and GAS of the continuous models. Finally, a set of numerical examples is conducted to support the theoretical findings and to demonstrate advantages of the NSFD schemes over some well-known standard ones. The numerical examples show that the used standard numerical schemes fail to preserve the qualitative dynamical properties of the continuous models for all finite step sizes; consequently, they can generate numerical approximations that are completely different from the exact solutions. Conversely, the NSFD schemes can provide reliable numerical solutions regardless of chosen step sizes.

Computer virus propagation models: A mathematical review

The physical world has come together by the connection of devices on an extra ordinary level through internet of things. This forms a very complex and dynamic network system and number of heterogeneous device are connected with each other. Physical objects connected in a network, interchange data with other connected devices via communication networks. The data interchange is very helpful in a number of domains in day-to-day life of human beings. Security of connection and data is one of the major challenges for this connection and communication. A computer virus is a potential threat resulting into the damage of connected devices into a network and the data. Epidemic models, similar with biological virus spread models, are widely studied to investigate the behaviour of computer viruses. The primary objective of the article is to categorize a number of computer virus propagation model, so that their comparative studies becomes easier. This article contains a qualitative review and categorization of computer virus propagation models into three categories, namely, compartment model, network model and stochastic model. The study is helpful to further investigate the virus propagation mechanism and to control them optimally.

Research on the application of big data visualization technology in urban road congestion

ABSTRACT In order to improve the effect of urban road congestion analysis, this paper aims to study the mechanism of traffic congestion diffusion under the condition that users have real-time traffic information, and analyze the urban road congestion situation combined with big data visualization technology. According to the characteristics of traffic flow propagation, this paper conducts multi-granularity abstraction and multi-scale modeling of node-intersection-link-network for the complex and dynamic traffic congestion process, and establishes an improved SIS virus propagation model for traffic congestion propagation. In addition, this paper uses the method of state transition probability to construct an interactive dynamic model of traffic congestion propagation and early warning information propagation in a multi-layer network. The experimental research results show that the big data visualization technology introduced in this paper can play an important role in urban road congestion.

Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

Plant disease incidence rate and impacts can be influenced by viral interactions amongst plant hosts. However, very few mathematical models aim to understand the viral dynamics within plants. In this study, we will analyze the dynamics of two models of virus transmission in plants to incorporate either a time lag or an exposed plant density into the system governed by ODEs. Plant virus propagation model by vector (PVPMV) divided the population into four classes: susceptible plants [S(t)], infectious plants [I(t)], susceptible vectors [X(t)], and infectious vectors [Y(t)]. The approximate solutions for classes S(t), I(t), X(t), and Y(t) are determined by the implementation of exhaustive scenarios with variation in the infection ratio of a susceptible plant by an infected vector, infection ratio of vectors by infected plants, plants' natural fatality rate, plants' increased fatality rate owing to illness, vectors' natural fatality rate, vector replenishment rate, and plants' proliferation rate, numerically by exploiting the knacks of the Adams method (ADM) and backward differentiation formula (BDF). Numerical results and graphical interpretations are portrayed for the analysis of the dynamical behavior of disease by means of variation in physical parameters utilized in the plant virus models.

Layered vaccine allocation for spatio-temporal vaccination of COVID-19

Optimal allocation of vaccine doses is a major challenge faced by the health authorities especially in the case of an ever-growing pandemic expansion and a limited supply availability. Based on a spatio-temporal compartmental virus propagation model applied to the case of SARS-CoV-2 virus, we investigate a layered vaccine allocation strategy for the subpopulations of a given country or a geographical region based on the prevalence of susceptible individuals as a prioritization metric. Our findings show that a relaxed layered allocation prioritization, where a maximum of regions benefit from vaccine doses is more effective in controlling the epidemic than a strict prioritization, focused only on the few most prioritized regions. These results are consistent among different vaccine rollout speeds for various limiting values of the priority list.

An Epidemic Patch-Enabled Delayed Model for Virus Propagation: Towards Evaluating Bifurcation and White Noise

The massive disruptions caused by malware, such as a virus in computer networks and other aspects of information and communication technology, have generated attention, making it a hot research topic. While antivirus and firewalls can be effective, there is also a need to understand the spread patterns of viral infection using epidemic models to curb its incidences. Many previous research attempts have produced analytical models for computer viruses under various infectiousness situations. As a result, we suggested the SLBS model, which considers infection latency and transient immunity in patched nodes. Under certain conditions, the local stability of all equilibrium points is investigated. By setting the delay parameter, we established the occurrence of a Hopf bifurcation (HB) as it crossed a crucial point by several analyses. We also used the centre manifold theorem and normal form theory to examine the attributes of the HB. While the former was used to study the time delay and direction of Hopf bifurcation, the latter was used to investigate external noise and its intensities. Finally, numerical simulations two dimensional and three-dimensional graphs were used to depict the perturbations of the model, thus bolstering the essentiality of the study.

Hopf bifurcation and optimal control of a delayed SLBPS virus-patch model

This paper formulates a Susceptible–Latent–Breaking out–Patched–Susceptible (SLBPS) virus propagation model with delay of temporary immunity. The influence of time delay on stability of the model is examined by analyzing the distribution of eigenvalues of the characteristic equation. Furthermore, we also demonstrate the direction and stability of the Hopf bifurcation. Lastly, optimal control strategies in terms of the rate at which susceptible, latent, break out nodes acquiring patches to improve performance of the model are presented. For the sake of the correctness of the theoretical analysis, some numerical simulations are also presented.