Worm Propagation Model Research Articles

ON DISCRETE-TIME MODELS OF NETWORK WORM PROPAGATION GENERATED BY QUADRATIC OPERATORS

In this paper we consider the discrete-time dynamical systems generated by network worm propagation models based on the theory of quadratic stochastic operators(QSO). This approach simultaneously solves two important problems: exploring of the QSO trajectory‘s behavior, we described the set of limit points, thereby completely solved the main problem of dynamical systems (i), we showed a new application of the theory QSOs in worm propagation modelling (ii). We demonstrated that proposed discrete-time biologically-inspired model represents also realistic picture of the worm propagation process and such analytical models can be used in decision of some problems of computer networks.

Dynamic analysis and optimal control of worm propagation model with saturated incidence rate

In order to prevent the propagation of computer worms effectively, based on the latent character of worms, the exposed compartments of computer and USB device are introduced respectively, and a series of computer worm propagation models with saturation incidence rate are proposed. The qualitative behavior of the proposed model is studied. Firstly, the threshold R0 of the model is derived by using the next-generation matrix method, which completely characterized the stability of disease free equilibrium and endemic equilibrium. If R0 < 1, the disease free equilibrium is asymptotically stable, implying that the worm dies out eventually and its attack remains under control; if R0 > 1, the asymptotic stability of endemic equilibrium under certain conditions is proved, which means that the worm is always persistent and uncontrollable under such conditions. Secondly, the theoretical results are verified by numerical study, in which the relative importance of each parameter in worm prevalence is evaluated by sensitivity analysis. Finally, so as to minimize the number of computer and USB device carrying computer worms in short span of time, the worm propagation model is extended to incorporate three control strategies. The Pontryagin’s maximum principle is used to characterize the controls’ optimal levels. According to the control effect diagram, the combined strategy is effective in minimizing the transmission dynamics of worm virus in computer and USB devices populations respectively.

Analysis of Delay-Aware Worm Propagation Model in Wireless IoT Systems With Ratio-Dependent Functional Response

This article presents a delayed susceptibility, exposure, infectivity, recovery, and vaccination (SEIRV) model with nonlinear incidence and ratio-dependent functional responses. Model limitations and local stability analyses were examined with strict consideration of delay awareness. In addition, the presence of Hopf bifurcations with delay as a bifurcation parameter was investigated along with feature distributions with appropriate constraints. Numerical simulations are presented to verify the proposed theoretical results. In particular, if the latency exceeds the threshold, worm propagation in the system may become out of control. We demonstrated that the propagation characteristics of worms can easily be predicted and eliminated if the delay values are below a suitable threshold. Finally, we conclude that worm propagation is controllable by shifting the presence of Hopf bifurcations.

Stability analysis and optimal control of worm propagation model with saturated incidence rate

Worms spreading through Web-based scanning and removable devices pose a serious threat to Internet security. This paper is devoted to solving the problems of computer worms. A nonlinear mathematical model of the problem is established, and the characteristics and mechanisms of worm propagation are analyzed by means of the stability theory of differential equations, optimal control and computer simulation. The results provide some new insights to computer security, which is to predict the tendency of worm propagation through the stability of endemic equilibrium, identify the epidemic control strategies by the stability of disease-free equilibrium, and evaluate the prevalence of worms based on the final scale of infected devices. The performance of our model is evaluated by numerical simulation, and the results indicate that our combined strategy can combat the worm propagation. The results may be helpful to inhibit the worm spread widely in the network.

Global stability for a SEIQR worm propagation model in mobile internet

Abstract Recently, propagation models of worms in the mobile environment are drawing extensive attention, particularly in the Wi-Fi scenario. Considering that worm-free equilibrium is exponential convergent means that the propagation time and control time of worms are much shorter than for other asymptotic convergence. Besides, the global asymptotic stability of the endemic equilibrium is more important than the local asymptotic stability, which reflects the more global qualitative behavior of the worm propagation. In this paper, we discuss the global dynamics of SEIQR worm propagation model in mobile internet proposed by Xiao et al. [X. Xiao, P. Fu, C. Dou, Q. Li, G. Hu, and S. Xia, “Design and analysis of SEIQR worm propagation model in mobile internet,” Commun. Nonlinear Sci. Numer. Simulat., vol. 43, pp. 341–350, 2017] to improve and complement the related results. Through a series of mathematical derivations, sufficient conditions are derived to ensure the global exponentially stability of worm-free equilibrium, and the exponential convergent rate can be unveiled. Then, by using the classical geometric approach, it is shown that the endemic equilibrium is globally asymptotically stable and the system is persistent when R 0 > 1. Moreover, numerical simulations are given to demonstrate our theoretical results.

Ascaridia galli challenge model for worm propagation in young chickens with or without immunosuppression

With the continued growth of free-range egg production, the importance of the chicken roundworm Ascaridia galli is increasing. Investigations into this parasite would be facilitated by the availability of characterised strains and clear guidelines on optimal methods of multiplication and maintenance. Currently, there is lack of well-defined in vivo models for maintaining A. galli and the potential of using host immunosuppression to boost parasite development and worm egg output has not been investigated. To determine the most efficient way of propagating A. galli in young chickens an experiment with a 2 × 3 × 4 × 2 factorial design involving age of chicken at infection (day-old or 14 days old), immunosuppression (dexamethasone (DEX), cyclophosphamide (CY) or sham), infective egg dose (0, 100, 300 or 900 embryonated eggs/bird) and time of worm recovery after infection (8 or 10 weeks post-infection) was conducted. The experiment used a total of 384 layer cockerel chicks. Infection was delivered orally in 3 split doses over one week and immunosuppressants were administered by intramuscular injection concurrently with the infections. Body weight, excreta egg counts, intestinal worm count and worm establishment rate were assessed. The only sign of ascaridiosis noted was mild diarrhoea at the time of slaughter in some birds with a significant- positive association with worm count. Infection caused a significant dose dependent reduction in body weight in non-immunosuppressed birds but this effect was ameliorated by immunosuppression. Age at infection had no significant effect on the studied variables although both worm and egg counts were numerically higher in the day-old infected groups. Egg dose significantly influenced the prevalence of infection, worm establishment rate, worm egg production and mean worm count. The 300 and 900 egg doses resulted in significantly higher worm count and egg production than the 100 egg dose. A significant negative correlation was observed between egg dose and worm establishment rate indicating an inverse relationship. Immunosuppression with DEX, but not CY resulted in significantly higher mean worm burden than in control chickens with excreta egg counts also considerably higher in DEX treated birds. Our results suggest that trickle infection at day-old with infective doses of 300 eggs coupled with immunosuppression with DEX would provide the most efficient way to propagate A. galli worms in vivo, as using older birds or a higher egg dose did not provide any advantage.

Hopf bifurcation of a VEIQS worm propagation model in mobile networks with two delays

The spread of worm virus has brought great loss to our production and life. In this paper, a new Vulnerable-Exposed-Infectious-Quarantined-Secured (VEIQS) worm propagation model with a saturated incidence and two delays is proposed. The local stability of the worm-existence equilibrium and the occurrence of Hopf bifurcation at the critical values of the two delays are obtained by regarding different combinations of time delays as bifurcation parameters. It shows that the model is ideal stable when the time delay is below the critical value and a Hopf bifurcation occurs when the time delay is above the critical value. In particular, direction and stability of the Hopf bifurcation are determined by using the center manifold theorem. Finally, some numerical simulations are presented in order to verify the analytical results.

Evolution algebras and dynamical systems of a worm propagation model

ABSTRACT We consider an evolution algebra identifying the coefficients of SIS–SIR worm propagation models as the structure constants of the algebra. The basic properties of this algebra are studied. We prove that it is a commutative (and hence flexible), not associative and baric algebra. We describe the full set of idempotent elements and the full set of absolute nilpotent elements. We find all the fixed points of the dynamical systems. We also study several properties of the algebra connecting them to dynamical systems.

An epidemic model with multiple delays for the propagation of worms in wireless sensor networks

A delayed SEIRS worm propagation model with the inclusion of a finite communication radius and node density for wireless sensor networks is investigated in this paper. By using different combinations of the three delays as bifurcating parameter and analyzing distribution of roots of the corresponding characteristic equation, sufficient conditions are derived for local stability of the endemic equilibrium and the existence of a Hopf bifurcation at the endemic equilibrium are addressed. By constructing a suitable Lyapunov function, sufficient conditions for global stability of the endemic equilibrium are determined. Finally, numerical simulations for a set of parameter values are performed to illustrate the analytical findings.

Stability Analysis of Stochastic SEIA Worm Propagation Models with Anti-virus Software

Stability Analysis of Stochastic SEIA Worm Propagation Models with Anti-virus Software

Novel non‐linear dynamics P2P network worm propagation and immune model

This study proposes a novel non-linear dynamic worm propagation model in order to describe the dynamics model of conditional triggered worm's propagation in the network, then proposes an immune dynamics model. First, the authors build impact factor according to actual condition; second, the conditions trigger type worm propagation model is established and the corresponding immune model is constructed; third, the epidemic is deduced non-toxic balance and do not sufficient conditions for the flood of worm is proved based on the theory of worm propagation model, and then the conditions of the worm will not overflow sufficient is proved through simulation experiments; finally, according to the simulation analysis and the characteristics of worm propagation, a series of control strategies are proposed, as well as the changing trend of worms in the network with immune ability. A series of simulation results show that the proposed models are reasonable and effective, it can more accurately reflect the worm propagation process in the real peer-to-peer (P2P) network, which can also accurately predict the worm propagation trend in P2P network.

Impulsive Switching Epidemic Model with Benign Worm Defense and Quarantine Strategy

The issue on how to effectively control Internet malicious worms has been drawn significant attention owing to enormous threats to the Internet. Due to the rapid spreading of malicious worms, it is necessary to explore the integrated measures to automatically mitigate the propagation on the Internet. In this paper, a novel worm propagation model is established, which combines both impulsive quarantine and benign worm implementation. Then, sufficient conditions for the global stability of worm-free periodic solution and the permanence of the benign worm are obtained. Finally, the effects of quarantine strategy are assessed and some feasible strategies that can constrain the propagation of malicious worm are provided by numerical simulation.

Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model

Mobile devices are considerably pervasive in society, but also increase their vulnerability to worm attacks from mobile networks. In this paper, we propose a new Vulnerable-Exposed-Infectious-Quarantined-Secured worm propagation model with saturated incidence and strategies of both vaccination and quarantine. We obtain that the basic reproduction number R0 is a sharp threshold parameter such that the worm-free equilibrium is asymptotically stable for R0 ≤ 1, implying that the worm dies out eventually and its attack remains under control; the worm-existence equilibrium is asymptotically stable when R0 > 1, namely, the worm is always persistent and spreading within a population. This paper provides some novel insights to cyber security by that (a) the stability of worm-free equilibrium establishes the control strategies to reduce the intensity of worm attacks, and the optimal control strategy is proposed by using Pontryagins Minimum Principle; (b) the stability of worm-existence equilibrium predicts the tendency of worm propagation in a long run and assesses the level of the worm popularity by the final scale of infected devices. Numerical simulations are implemented to illustrate the feasibility of the theoretical results and the effectiveness of the control strategies.

Modelling and Detection of Worm Propagation for Web Vehicular Ad Hoc Network (WVANET)

Web Vehicular Ad Hoc Network becomes the major research platform these days. This web vehicular ad hoc network is fundamentally different from the earlier vehicular ad hoc network communication models as it makes use of web technology to disseminate the messages among the nodes. When web technology is integrated in vehicular ad hoc network, the communication performance is greatly increased. However, the new web vehicular ad hoc network communication model should be prevented from various security threats. The major security threat to web vehicular ad hoc network is worm propagation. As web VANET operates through web technology, it is possible to the nodes to get infected with the worms. Once a node is infected with worm, it can spread out to the other nodes in the network that are vulnerable. This worm can propagate to all the vulnerable nodes and infect them within a fraction of time. The entire communication architecture can be collapsed due to this worm propagation and even these worms can broadcast false messages in the network to create accidents or to divert the nodes in such a way it will lead to collision. All the nodes should not be vulnerable to prevent itself from worm infection. This paper provides the worm propagation model for web vehicular ad hoc network. Further it provides detection measures of worm to enhance the security concern of web vehicular ad hoc network.

Analysing and modelling worm propagation speed in the smart grid communication infrastructure

In an advanced metering infrastructure (AMI), smart meters may communicate in an ad-hoc fashion to perform functionalities like remote metering and demand response. However, the AMI is susceptible to cyber-physical threats caused by malware such as worms. In this work, we derive a probabilistic model for worm propagation in the AMI. The accuracy of the model is validated using three worm propagation scenarios. This model can be used to estimate the time required to infect N meters in the AMI based on the worm propagation technique deployed by the attacker. In addition, we use the derived model to investigate the sensitivity of worm propagation to different parameters such as transmission range, worm size, number and location of target meters. We also demonstrate how an attacker can improve the propagation speed of the worm by modifying the worm's target list. The latter is done by comparing the three introduced propagation scenarios. Improving the worm's propagation speed can amplify the possible physical consequence of the attack.

Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.

An Epidemic Model of Computer Worms with Time Delay and Variable Infection Rate

With rapid development of Internet, network security issues become increasingly serious. Temporary patches have been put on the infectious hosts, which may lose efficacy on occasions. This leads to a time delay when vaccinated hosts change to susceptible hosts. On the other hand, the worm infection is usually a nonlinear process. Considering the actual situation, a variable infection rate is introduced to describe the spread process of worms. According to above aspects, we propose a time-delayed worm propagation model with variable infection rate. Then the existence condition and the stability of the positive equilibrium are derived. Due to the existence of time delay, the worm propagation system may be unstable and out of control. Moreover, the threshold τ0 of Hopf bifurcation is obtained. The worm propagation system is stable if time delay is less than τ0. When time delay is over τ0, the system will be unstable. In addition, numerical experiments have been performed, which can match the conclusions we deduce. The numerical experiments also show that there exists a threshold in the parameter a, which implies that we should choose appropriate infection rate β(t) to constrain worm prevalence. Finally, simulation experiments are carried out to prove the validity of our conclusions.

Dynamics of a delayed worm propagation model with quarantine

A delayed SEIQRS-V model with quarantine describing the dynamics of worm propagation is considered in the present paper. Local stability of the endemic equilibrium is addressed and the existence of a Hopf bifurcation at the endemic equilibrium is established by analyzing the corresponding characteristic equation. By means of the normal form theory and the center manifold theorem, properties of the Hopf bifurcation at the endemic equilibrium are investigated. Finally, numerical simulations are also given to support our theoretical conclusions.

Study of the stability of a SEIRS model for computer worm propagation

Nowadays, malware is the most important threat to information security. In this sense, several mathematical models to simulate malware spreading have appeared. They are compartmental models where the population of devices is classified into different compartments: susceptible, exposed, infectious, recovered, etc. The main goal of this work is to propose an improved SEIRS (Susceptible–Exposed–Infectious–Recovered–Susceptible) mathematical model to simulate computer worm propagation. It is a continuous model whose dynamic is ruled by means of a system of ordinary differential equations. It considers more realistic parameters related to the propagation; in fact, a modified incidence rate has been used. Moreover, the equilibrium points are computed and their local and global stability analyses are studied. From the explicit expression of the basic reproductive number, efficient control measures are also obtained.

Propagation Modeling and Defending of a Mobile Sensor Worm in Wireless Sensor and Actuator Networks.

WSANs (Wireless Sensor and Actuator Networks) are derived from traditional wireless sensor networks by introducing mobile actuator elements. Previous studies indicated that mobile actuators can improve network performance in terms of data collection, energy supplementation, etc. However, according to our experimental simulations, the actuator’s mobility also causes the sensor worm to spread faster if an attacker launches worm attacks on an actuator and compromises it successfully. Traditional worm propagation models and defense strategies did not consider the diffusion with a mobile worm carrier. To address this new problem, we first propose a microscopic mathematical model to describe the propagation dynamics of the sensor worm. Then, a two-step local defending strategy (LDS) with a mobile patcher (a mobile element which can distribute patches) is designed to recover the network. In LDS, all recovering operations are only taken in a restricted region to minimize the cost. Extensive experimental results demonstrate that our model estimations are rather accurate and consistent with the actual spreading scenario of the mobile sensor worm. Moreover, on average, the LDS outperforms other algorithms by approximately 50% in terms of the cost.