Optimal Control Analysis of Computer Virus Transmission

Computer virus has become a global problem and affecting many industries both developed and the developing countries.In this study, a deterministic computer virus model is formulated incorporating removal devices. The basic properties of the model is studied and the reproduction number is calculated. The steady states are studied and found to be stable. We analyze different properties with parameter change by carrying out the sensitivity analysis of the model. Time optimal control is included and Pontryagin’s Maximum Principle is used to characterize the all necessary condition for controlling the spread of computer virus. The most effective strategy for controlling computer virus is the combination of all the three controls. Graphical illustrations are presented to show the effects.

[1]  Jitendra Singh,et al.  Cyber-Attacks in Cloud Computing: A Case Study , 2014 .

[2]  A. bstract,et al.  STOCHASTIC FEATURES OF COMPUTER VIRUSES: TOWARDS THEORETICAL ANALYSIS AND SIMULATION , 2005 .

[3]  Mohammad A. Safi,et al.  Global Stability Analysis of SEIR Model with Holling Type II Incidence Function , 2012, Comput. Math. Methods Medicine.

[4]  Bimal Kumar Mishra,et al.  Fuzzy epidemic model for the transmission of worms in computer network , 2010 .

[5]  Bimal Kumar Mishra,et al.  Dynamic model of worms with vertical transmission in computer network , 2011, Appl. Math. Comput..

[6]  Bimal Kumar Mishra,et al.  Dynamic Model on the Transmission of Malicious Codes in Network , 2013 .

[7]  Oluwole Daniel Makinde,et al.  Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives , 2013 .

[8]  J. López Gondar,et al.  A mathematical model for virus infection in a system of interacting computers , 2003 .

[9]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[10]  Jingsha He,et al.  An Evolutionary Multi-objective Approach for Modelling Network Security , 2017, Int. J. Netw. Secur..

[11]  Salisu M. Garba,et al.  Backward bifurcations in dengue transmission dynamics. , 2008, Mathematical biosciences.

[12]  Navnit Jha,et al.  SEIQRS model for the transmission of malicious objects in computer network , 2010 .

[13]  Bimal Kumar Mishra,et al.  Mathematical models on computer viruses , 2007, Appl. Math. Comput..

[14]  J. Janssen,et al.  Deterministic and Stochastic Optimal Control , 2013 .

[15]  Wei-Xin Jin.  Applying Epidemiology in Computer Virus Prevention : Prospects and Limitations , 2010 .

[16]  Tao Dong,et al.  Modeling Computer Virus and Its Dynamics , 2013 .

[17]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  M. Javidi,et al.  Stability analysis of a novel VEISV propagation model of computer worm attacks , 2014 .

[20]  Samir Kumar Pandey,et al.  Epidemic Model on the Computer Viruses in the Network , 2015 .

[21]  Carlos Castillo-Chavez,et al.  Tuberculosis models with fast and slow dynamics: the role of close and casual contacts. , 2002, Mathematical biosciences.

[22]  Dong Li,et al.  An Epidemic Model of Mobile Phone Virus , 2006, 2006 First International Symposium on Pervasive Computing and Applications.

[24]  Mikhail Styugin.  Establishing Systems Secure from Research with Implementation in Encryption Algorithms , 2018, Int. J. Netw. Secur..

[25]  John T. Workman,et al.  Optimal Control Applied to Biological Models , 2007 .

[26]  Folashade B. Agusto,et al.  Optimal chemoprophylaxis and treatment control strategies of a tuberculosis transmission model , 2009 .

[27]  Kevin A. Kwiat,et al.  Modeling the spread of active worms , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[28]  Hong Zhang,et al.  A Lyapunov functional for a SIRI model with nonlinear incidence of infection and relapse , 2013, Appl. Math. Comput..

[29]  Lu-Xing Yang,et al.  Towards the Epidemiological Modeling of Computer Viruses , 2012 .

[30]  Xiaofan Yang,et al.  Modeling and analysis of the spread of computer virus , 2012 .

[31]  Guillermo Abramson,et al.  Mathematical modeling of the spread of infectious diseases , 2008 .

[32]  Mostafa Rachik,et al.  Optimal control and infectiology: Application to an HIV/AIDS model , 2006, Appl. Math. Comput..

[33]  Tadashi Dohi,et al.  Estimating Computer Virus Propagation Based on Markovian Arrival Processes , 2010, 2010 IEEE 16th Pacific Rim International Symposium on Dependable Computing.

[34]  J. Hyman,et al.  Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model , 2008, Bulletin of mathematical biology.

[35]  Mohammad Hadi Farahi,et al.  Optimal Control Strategy for a Fully Determined HIV Model , 2010 .

[36]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[37]  José Roberto Castilho Piqueira,et al.  Dynamic models for computer viruses , 2008, Comput. Secur..