AM  Vol.6 No.11 , October 2015
Global Stability of SEIQRS Computer Virus Propagation Model with Non-Linear Incidence Function
Author(s) Qaisar Badshah
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.

Cite this paper
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.

[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.