Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs
Joint Authors
Omari, Lahcen
El Ansari, Youness
El Myr, Ali
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-10-18
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations.
This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software.
The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations.
First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state.
Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system.
The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero).
The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough.
Numerical simulations are carried out to illustrate the theoretical results.
American Psychological Association (APA)
El Ansari, Youness& El Myr, Ali& Omari, Lahcen. 2017. Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1151321
Modern Language Association (MLA)
El Ansari, Youness…[et al.]. Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-13.
https://search.emarefa.net/detail/BIM-1151321
American Medical Association (AMA)
El Ansari, Youness& El Myr, Ali& Omari, Lahcen. Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1151321
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151321