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SVEIRS epidemic model with delays and partial immunization for internet worms

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030, China

    Zizhen Zhang & Yougang Wang

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  1. Zizhen Zhang
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  2. Yougang Wang
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Correspondence to Zizhen Zhang.

Additional information

This research was supported by Natural Science Foundation of Anhui Province (Nos. 1608085QF145, 1608085QF151, 1708085MA17) and Natural Science Foundation of the Higher Education Institutions of Anhui Province (No. KJ2015A144).

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Zhang, Z., Wang, Y. SVEIRS epidemic model with delays and partial immunization for internet worms. J. Appl. Math. Comput. 57, 333–358 (2018). https://doi.org/10.1007/s12190-017-1109-0

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  • DOI: https://doi.org/10.1007/s12190-017-1109-0

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