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Analysis of a SEIR-KS Mathematical Model For Computer Virus Propagation in a Periodic Environment

Author

Listed:
  • Aníbal Coronel

    (Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, 3780000 Chillán, Chile)

  • Fernando Huancas

    (Departamento de Matemática, Facultad de Ciencias Naturales, Matemática y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras 3360, 8330378 Ñuñoa-Santiago, Chile)

  • Ian Hess

    (Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, 3780000 Chillán, Chile)

  • Esperanza Lozada

    (Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, 3780000 Chillán, Chile)

  • Francisco Novoa-Muñoz

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, 4051381 Concepción, Chile)

Abstract

In this work we develop a study of positive periodic solutions for a mathematical model of the dynamics of computer virus propagation. We propose a generalized compartment model of SEIR-KS type, since we consider that the population is partitioned in five classes: susceptible ( S ); exposed ( E ); infected ( I ); recovered ( R ); and kill signals ( K ), and assume that the rates of virus propagation are time dependent functions. Then, we introduce a sufficient condition for the existence of positive periodic solutions of the generalized SEIR-KS model. The proof of the main results are based on a priori estimates of the SEIR-KS system solutions and the application of coincidence degree theory. Moreover, we present an example of a generalized system satisfying the sufficient condition.

Suggested Citation

  • Aníbal Coronel & Fernando Huancas & Ian Hess & Esperanza Lozada & Francisco Novoa-Muñoz, 2020. "Analysis of a SEIR-KS Mathematical Model For Computer Virus Propagation in a Periodic Environment," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:761-:d:356438
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    References listed on IDEAS

    as
    1. Zhang, Yuhuai & Zhu, Jianjun, 2019. "Dynamic behavior of an I2S2R rumor propagation model on weighted contract networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    2. Eric Ávila-Vales & Erika Rivero-Esquivel & Gerardo Emilio García-Almeida, 2017. "Global Dynamics of a Periodic SEIRS Model with General Incidence Rate," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-14, November.
    3. Zhu, Linhe & Liu, Mengxue & Li, Yimin, 2019. "The dynamics analysis of a rumor propagation model in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 118-137.
    Full references (including those not matched with items on IDEAS)

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