The impact of nonlinear infection rate on the spread of computer virus

Yang, Lu‐Xing; Xiao, Yang

doi:10.1007/s11071-015-2140-z

Cited by 39 publications

(14 citation statements)

References 41 publications

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“…Many of these earlier mathematical models were achieved using a compartmental approach (such as SIRS, SIRA, SEIQR, etc.) [9,10,11,12,13,14,15,16,17,18,19,20,4,21,22,23] . Many of these models were able to describe migration of the viruses and treatment effects; however, they did not consider the inclusion of isolation period of those objects penetrated by malware [5].…”

Section: Introductionmentioning

confidence: 99%

An Epidemic Model of Malware Virus with Quarantine

Lanz

Rogers

Alford

2019

JAMCS

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In March of 2018, about 500,000 desktop computers were infected with cryptocurrency mining malware in less than 24 hours. In addition to attacking desktop computers, malware also attacks laptops, tablets, mobile phones. That is, any device connected via the Internet, or a network is at risk of being attacked. In recent years, mobile phones have become extremely popular that places them as a big target of malware infections. In this study, the effectiveness of treatment for infected mobile devices is examined using compartmental modeling. Many studies have considered malware infections which also include treatment effectiveness. However, in this study we examine the treatment effectiveness of mobile devices based on the type of malware infections accrued (hostile or malicious malware). This model considers six classes of mobile devices based on their epidemiological status: susceptible, exposed, infected by hostile malware, infected by malicious malware, quarantined, and recovered. The malware reproduction number, RM , was identified to discover the threshold values for the dynamics of malware infections to become both prevalent or Lanz et al.; JAMCS, 33(4): 1-10, 2019; Article no.JAMCS.49867 absent among mobile devices. Numerical simulations of the model give insights of various strategies that can be implemented to control malware epidemic in a mobile network.

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Section: Introductionmentioning

confidence: 99%

An Epidemic Model of Malware Virus with Quarantine

Lanz

Rogers

Alford

2019

JAMCS

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“…For example, virus incubation and virus immunity propagation models have been established and analyzed. The virus infection rate has been investigated in Yang and Yang for the effect on the spread of virus, and virus countermeasures or control models have been formulated to study the virus dynamics under the effect of protection mechanism in other studies . Those models provide a reasonable academic understanding of what their spreading conditions are and why a few malware types can diffuse better than others.…”

Section: Introductionmentioning

confidence: 99%

A compartmental model for global spread dynamics of malware under mutation

Ren

Xie

et al. 2019

Math Methods in App Sciences

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Malware mutation is pervasive among networks. Modeling and understanding its propagation characteristics have been of great importance. In this study, a new compartmental model that extends the present model by incorporating mutated malware into the modeling process as a separate dynamic variable is proposed and theoretically analyzed to deepen the understanding of the spreading mechanisms of mutated malware. The model involves two equilibria, namely, malware‐free equilibrium and malware equilibrium, wherein both have proven to be locally and globally asymptotically stable through the Routh‐Hurwitz criterion and Lyapunov functional approach, respectively. An epidemic threshold is obtained that clearly forms the boundary among the comprehensive dynamics of the model between two distinct ramifications: one with mutation infection prevalence and the other without any mutation infection. Both are incarnated via the existence and stability of the equilibria admitted by the model. Further analyses show that the mutation is related not only to the epidemic threshold, but also to the malware prevalence level. The numerical simulations based on the analytic results demonstrate that the diffusion of mutated malware can fall away or can be maintained at a suitable level.

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“…The overwhelming majority of the computer virus models mentioned assume a bilinear infection rate. However, there are several reasons why bilinear infection rate requires modification [21]. Especially, the propagation of computer viruses can be dramatically affected by the topology of the underlying network, and this may lead to some specific nonlinear infection rates.…”

Section: Introductionmentioning

confidence: 99%

Delay-induced Hopf bifurcation of an SVEIR computer virus model with nonlinear incidence rate

2018

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We are concerned with the Hopf bifurcation of an SVEIR computer virus model with time delay and nonlinear incident rate. First of all, by analyzing the associated characteristic equation we obtain sufficient conditions for its local stability and the existence of a Hopf bifurcation. Directly afterward, by means of the normal form theory and the center manifold theorem we derive explicit formulas that determine the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions. Finally, we carry out numerical simulations to illustrate and verify the theoretical results.

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The impact of nonlinear infection rate on the spread of computer virus

Cited by 39 publications

References 41 publications

An Epidemic Model of Malware Virus with Quarantine

An Epidemic Model of Malware Virus with Quarantine

A compartmental model for global spread dynamics of malware under mutation

Delay-induced Hopf bifurcation of an SVEIR computer virus model with nonlinear incidence rate

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