A DYNAMICAL ANALYSIS OF THE VIRUS REPLICATION EPIDEMIC MODEL

I. KUSBEYZI AYBAR

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Abstract

In this article, the stability and the computational algebraic properties of a virus replication epidemic model is investigated. The model is represented by a three dimensional dynamical system with six parameters. The conditions for the existence of Hopf bifurcation in the system are given. Then, the model with the Beddington- DeAngelis functional response instead of the original nonlinear response function has been studied in order to understand the eect of the Beddington-DeAngelis functional response on the qualitative properties of the system. The stability of the systems at the singular points is investigated and the conditions for the systems to have the analytic rst integrals and Hopf bifurcation are given. Finally, the results are illustrated by giving numerical examples.

Keywords

epidemic model, stability, analytic rst integral, algebraic invariant, Hopf bifurcation.