Global Stability of SEIQRS Computer Virus Propagation Model with Non-Linear Incidence Function

DOI: 10.4236/am.2015.611170   PDF   HTML   XML   2,154 Downloads   2,628 Views   Citations


In this paper, we present an SEIQRS epidemic model with non-linear incidence function. The proposed model exhibits two equilibrium points, the virus free equilibrium and viral equilibrium. The model stability is connected with the basic reproduction number R0. If R0 < 1 then the virus free equilibrium point is stable locally and globally. In the opposite case R0 > 1, then the model is locally and globally stable at viral equilibrium point. Numerical methods are used for supporting the analytical work.

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Badshah, Q. (2015) Global Stability of SEIQRS Computer Virus Propagation Model with Non-Linear Incidence Function. Applied Mathematics, 6, 1926-1938. doi: 10.4236/am.2015.611170.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Newman, M.E.J., Forrest, S.H. and Newman, J.B. (2002) Email Networks and the Spread of Computerviruses. Physical Review, 66, 035101-035104.
[2] Wang, F., Yang, F., Zhang, Y. and Ma, J. (2014) Stability Analysis of a SEIQRS Model with Graded Infection Rates for Internet Worms. Journal of Computers, 9, 2420-2427.
[3] Wang, F.W., Zhang, Y.K., Wang, C.G., Ma, J.F. and Moon, S.J. (2010) Stability Analysis of a SEIQV Epidemic Model for Rapid Spreading Worms. Computers & Security, 29, 410-418.
[4] Liu, J. (2014) Hopf Bifurcation in a Delayed SEIQRS Model for the Transmission of Malicious Objects in Computer Network. Journal of Applied Mathematics, 2014.
[5] Mishra, B.K. and Jha, N. (2010) SEIQRS Model for the Transmission of Malicious Objects in Computer Network. Applied Mathematical Modeling, 34, 710-715.
[6] Li, T. and Xue, Y. (2013) Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent. Applied Mathematics, 4, 109-117.
[7] Mishra, B.K. and Ansari, G.M. (2012) Differential Epidemic Model of Virus and Worms in Computer Network. International Journal of Network Security, 14, 149-155.
[8] Kumar, M., Mishra, B.K. and Panda, T.C. (2015) Effect of Quarantine and Vaccination on Infectious Nodes in Computer Network. International Journal of Computer Networks and Applications, 2.
[9] Ge, S.T., et al. (2013) Stability Analysis of SEIQR Model in Computer Networks. 25th Chinese Control and Decision Conference.
[10] Mishra, B.K. and Simgh, A.K. (2012) SIjRSE-Epidemic Model with Multiple Groups of Infection in Computer Network. International Journal of Nonlinear Science, 13, 357-362.
[11] Lahrouz, A., Omari, L., Kiouach, D. and Belmati, A. (2012) Complete Global Stability for an SIRS Epidemic Model with Generalized Non-Linear Incidence and Vaccination. Applied Mathematics and Computation, 218, 6519-6525.
[12] Driessche, V.D. and Watmough, J. (2002) Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180, 29-48.
[13] Stein, Z.A. and LaSalle, J.P. (1979) The Stability of Dynamical Systems. SIAM Journal on Applied Mathematics, 21, 418-420.
[14] Li, M.Y. and Muldowney, J.S. (1996) A Geometric Approach to Global-Stability Problems. SIAM Journal on Mathematical Analysis, 27, 1070-1083.
[15] Li, M.Y. and Muldowney, J.S. (1995) On R.A. Smith’s Autonomous Convergence Theorem. Journal of Mathematics, 25, 365-378.
[16] Freedman, H.I., Ruan, S. and Tang, M. (1994) Uniform Persistence and Flows near a Closed Positively Invariant Set. Journal of Differential Equations, 6, 583-600.
[17] Martin, R.H. (1974) Logarithmic Norms and Projections Applied to Linear Differential Systems. Journal of Mathematical Analysis and Applications, 45, 432-454.
[18] Liu, X. and Yang, L. (2012) Stability Analysis of an SEIQV Epidemic Model with Saturated Incidence Rate. Nonlinear Analysis: Real World Applications, 13, 2671-2679.

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