SVEIRS epidemic model with delays and partial immunization for internet worms

Original Research


A delayed SVEIRS model for the transmission of worms in internet with partial immunization is proposed. The impact of the possible combination of the two delays on the model is investigated. By analyzing the corresponding characteristic equations and regarding the possible combination of the two delays as the bifurcation parameter, local stability of the endemic equilibrium and existence of local Hopf bifurcation at the viral equilibrium are addressed, respectively. Further, explicit formulas that determine direction and stability of the Hopf bifurcation are derived with the help of the normal form theory and the center manifold theorem. Finally, some numerical simulations are carried out to verify the obtained theoretical findings.


Delays Hopf bifurcation SVEIRS model Periodic solutions 



The authors are grateful to the editor and the anonymous referees for their valuable comments and suggestions on the paper.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2017

Authors and Affiliations

  1. 1.School of Management Science and EngineeringAnhui University of Finance and EconomicsBengbuChina

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