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

Aníbal Coronel, Fernando Huancas, Ian Hess, Esperanza Lozada and Francisco Novoa-Muñoz
Additional contact information
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

Mathematics, 2020, vol. 8, issue 5, 1-20

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.

Keywords: periodic solutions; positive solutions; SEIR-KS model; computer virus model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/5/761/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/5/761/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:5:p:761-:d:356438

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().