Sensitivity and Generalized Sensitivity Studies of the SIR and SEIR Models of Computer Virus
SIR and SEIR Model of Dynamics of Computer Virus
Keywords:
Computer virus, self-replication, reproductive ratio, infectivity, sensitivity, generalized sensitivityAbstract
In this article, the sensitivity and generalized sensitivity analyses of the SIR and SEIR models of the dynamics of computer virus is presented. From the sensitivity studies of the SIR model, it follows that both the parameters in the model affect the model output in the beginning. The sensitivity of the SEIR model shows that the susceptible computers in the network are affected majorly by the rate at which external computers are connected to the network and the recovery rate of the susceptible computer due to the anti-virus ability of the network. From the generalized sensitivity of the SIR model, it follows that both the infected rate and the recovery rate are sensitive in the beginning and are highly correlated. The generalized sensitivities of the SEIR model show that the recovery rate of the infected computers that are cured is insensitive with respect to the measurements from all compartments.
References
Piqueira, J.R., A.A. De Vasconcelos, C.E. Gabriel, & V.O. Araujo. Dynamic models for computer viruses. Computers and Security 27(7): 355-359 (2008).
Kraus, J. Selbstreproduktion bei Programmen. Diplom thesis, University of Dortmund, Dortmund (1980).
Peng, M., X. He. J. Huang, & T. Dong. Modeling computer virus and its dynamics. Mathematical Problems in Engineering (84): Art. ID 842614, 5 pp. (2013).
Piqueira, J.R.C., & V.O. Araujo. A modified epidemiological model for computer viruses. Applied Mathematics and Computation 213(2): 355-360 (2009).
Kermack, W. O., & A. G. McKendrick. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 115(772): 700-721 (1927).
Kermack, W. O., & A. G. McKendrick. Contributions to the mathematical theory of epidemics. II. The problem of endemicity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 138(834): 55-83 (1932).
Kermack, W.O., & A.G. McKendrick. Contributions to the mathematical theory of epidemics. III. Further studies of the problem of endemicity. Proceedings of the Royal Society of London. Series A. Containing Papers of a Mathematical and Physical Character 141(843): 94-122 (1933).
Dimitriu, G. & V.L. Boiculese. Sensitivity study for a SEIT epidemic model. In: E-Health and Bioengineering Conference (EHB), IEEE, Iasi, Romania, pp.1-4. 1-4 (2015)
Kappel, F. & M. Munir. Generalized sensitivity functions for multiple output systems. Journal of Inverse and Ill-Posed Problems (2016). doi:10.1515/jiip-2016-0024.
Munir, M. Generalized Sensitivity Functions in Physiological Modeling. PhD thesis, University of Graz, Graz, Austria (2010).