Study of the stability of a SEIRS model for computer worm propagation

A. Martin del Rey, J.D. Hernández Guillén; Luis Hernández Encinas
Physica A - Nonlinear Analysis, 479, 411-421

Nowadays, malware is the most important threat to information security. In this sense, several mathematical models to simulate malware spreading have appeared. They are compartmental models where the population of devices is classified into different compartments: susceptible, exposed, infectious, recovered, etc. The main goal of this work is to propose an improved SEIRS (Susceptible–Exposed–Infectious–Recovered–Susceptible) mathematical model to simulate computer worm propagation. It is a continuous model whose dynamic is ruled by means of a system of ordinary differential equations. It considers more realistic parameters related to the propagation; in fact, a modified incidence rate has been used. Moreover, the equilibrium points are computed and their local and global stability analyses are studied. From the explicit expression of the basic reproductive number, efficient control measures are also obtained.


We would like to thank the anonymous referees for their valuable suggestions and comments.

J.D. Hernández Guillén thanks Ministerio de Educación, Cultura y Deporte (Spain) for her departmental collaboration grant.

This work has been supported by Ministerio de Economía y Competitividad (Spain) and the European Union through FEDER funds under grants TIN2014-55325-C2-1-R, TIN2014-55325-C2-2-R and MTM2015-69138-REDT.