scholarly journals A Computer Virus Propagation Model Using Delay Differential Equations with Probabilistic Contagion and Immunity

2014 ◽  
Vol 6 (5) ◽  
pp. 111-128 ◽  
Author(s):  
M. S. S . Khan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Computer Virus ◽  
Propagation Model ◽  
Virus Propagation ◽  
Delay Differential ◽  
Computer Virus Propagation Model

scholarly journals Stochastic Modeling of Plant Virus Propagation with Biological Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 456
Author(s):  
Benito Chen-Charpentier
Keyword(s):  
Differential Equations ◽  
Plant Virus ◽  
Propagation Model ◽  
Gillespie Algorithm ◽  
Virus Diseases ◽  
Virus Propagation ◽  
Healthy Environment ◽  
Fundamental Part ◽  
Negative Effect ◽  
Delay Differential

Plants are vital for man and many species. They are sources of food, medicine, fiber for clothes and materials for shelter. They are a fundamental part of a healthy environment. However, plants are subject to virus diseases. In plants most of the virus propagation is done by a vector. The traditional way of controlling the insects is to use insecticides that have a negative effect on the environment. A more environmentally friendly way to control the insects is to use predators that will prey on the vector, such as birds or bats. In this paper we modify a plant-virus propagation model with delays. The model is written using delay differential equations. However, it can also be expressed in terms of biochemical reactions, which is more realistic for small populations. Since there are always variations in the populations, errors in the measured values and uncertainties, we use two methods to introduce randomness: stochastic differential equations and the Gillespie algorithm. We present numerical simulations. The Gillespie method produces good results for plant-virus population models.

scholarly journals Global Behavior of a Computer Virus Propagation Model on Multilayer Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chunming Zhang
Keyword(s):  
Theoretical Analysis ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Behavior ◽  
Sufficient Condition ◽  
Multilayer Networks ◽  
Virus Propagation ◽  
Simulation Results ◽  
Computer Virus Propagation Model ◽  
Vital Factor

This paper presents a new linear computer viruses propagation model on multilayer networks to explore the mechanism of computer virus propagation. Theoretical analysis demonstrates that the maximum eigenvalue of the sum of all the subnetworks is a vital factor in determining the viral prevalence. And then, a new sufficient condition for the global stability of virus-free equilibrium has been obtained. The persistence of computer virus propagation system has also been proved. Eventually, some numerical simulation results verify the main conclusions of the theoretical analysis.

scholarly journals Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Threshold Value ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Virus Propagation ◽  
Globally Asymptotically Stable ◽  
Existence And Stability ◽  
Computer Virus Propagation Model

A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold valueR0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable ifR0<1, whereas the virus equilibrium is globally asymptotically stable ifR0>1. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.

scholarly journals Global Bifurcation of a Novel Computer Virus Propagation Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jianguo Ren ◽  
Yonghong Xu ◽  
Jiming Liu
Keyword(s):  
Global Bifurcation ◽  
Computer Virus ◽  
Propagation Model ◽  
Virus Spread ◽  
Virus Propagation ◽  
Virus Prevalence ◽  
Parameter Values ◽  
First Time ◽  
Computer Virus Propagation Model ◽  
Theoretical Results

In a recent paper by J. Ren et al. (2012), a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.

A novel computer virus propagation model and its dynamics

2012 ◽  
Vol 89 (17) ◽  
pp. 2307-2314 ◽  
Author(s):  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Luosheng Wen ◽  
Jiming Liu
Keyword(s):  
Computer Virus ◽  
Propagation Model ◽  
Virus Propagation ◽  
Computer Virus Propagation Model
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